RRB NTPC (Graduate) CBT-I Official Paper (Held On: 24 Mar, 2026 Shift 3) (Previous Year Paper)

The correct answer is Narmada and Tapi.

Key Points

• The general slope of the Peninsular Plateau is from west to east, which is why most major rivers like the Godavari, Krishna, Kaveri, and Mahanadi flow towards the Bay of Bengal.
• Narmada and Tapi are the two major Peninsular rivers that flow from east to west, making them the primary exceptions to the general drainage pattern. Hence, statement 4 is correct.
• The Godavari and Krishna rivers originate in the Western Ghats and flow eastwards into the Bay of Bengal following the natural gradient of the plateau. Hence, statement 1 is incorrect as an exception.
• The Kaveri and Krishna rivers also follow the west-to-east direction and form large deltas on the eastern coast of India. Hence, statement 2 is incorrect as an exception.
• The Mahanadi originates in the highlands of Chhattisgarh and the Kaveri in the Brahmagiri range; both flow eastwards. Hence, statement 3 is incorrect as an exception.
• The reason Narmada and Tapi flow westwards is that they flow through Rift Valleys formed by faulting between the Vindhya and Satpura ranges, which divert them towards the Arabian Sea.

Additional Information

• The Narmada River:
• It rises in the Amarkantak hills in Madhya Pradesh at an elevation of about 1,057 meters.
• It flows for a total length of 1,312 km before joining the Arabian Sea in the Gulf of Khambhat.
• It creates a notable marble gorge near Jabalpur and the Dhuandhar Falls.
• The Sardar Sarovar Dam is built on this river in the state of Gujarat.
• The Tapi River:
• It originates in the Satpura ranges, in the Betul district of Madhya Pradesh.
• It flows nearly parallel to the Narmada but is much shorter in length, measuring approximately 724 km.
• Its basin covers parts of Madhya Pradesh, Gujarat, and Maharashtra.
• East Flowing Rivers (The General Trend):
• Godavari: It is the largest Peninsular river system, often referred to as the Dakshin Ganga. It has a length of 1,465 km and its catchment area is the largest in India after the Ganga.
• Krishna: Rising from a spring near Mahabaleshwar, it flows for 1,400 km. Major tributaries include the Tungabhadra, Koyana, and Musie.
• Mahanadi: It flows through Odisha to reach the Bay of Bengal with a length of about 860 km. The Hirakud Dam is a major project on this river.
• Kaveri: It rises in the Brahmagiri range of the Western Ghats and reaches the Bay of Bengal in Puducherry. Its length is 800 km.

Important Points

• Rift Valley Formation: The Narmada and Tapi do not form deltas because of the high gradient and the hard rocky terrain they flow through; instead, they form Estuaries.
• Luni River: Another exception in the Peninsular region is the Luni river in Rajasthan, which is the largest river in the Thar Desert and ends in the Rann of Kutch, making it an endorheic (inland drainage) river.
• Mahi River: This is a unique river in India that crosses the Tropic of Cancer (23.5° N) twice during its course.
• Water Divide: The Western Ghats act as the main water divide for the Peninsular rivers, separating the drainage flowing into the Arabian Sea from that flowing into the Bay of Bengal.

The correct answer is A-1, B-2, C-3, D-4.

Key Points

• Circle of Justice: This was a 13^th-century political theory described by chroniclers like Fakhr-i-Mudabbir. It explains that a king cannot survive without soldiers, and soldiers require salaries, which are derived from the revenue collected from peasants; however, peasants can only pay revenue when they are prosperous and happy, which happens when the king promotes justice and honest governance. Hence, the pairing A-1 is correct.
• Iqta: In the administrative system of the Delhi Sultanate, the territories were divided into several small and big tracts of land called Iqtas. These lands were granted to military commanders and governors, known as Iqtadars or Muqtis, who were responsible for revenue collection and maintaining military law and order in their respective regions. Hence, the pairing B-2 is correct.
• Razia Sultan: She was the daughter of Sultan Iltutmish and ascended the throne of Delhi in 1236. She was the first female sovereign of the Delhi Sultanate but faced severe opposition from the Turkish nobles and the Chahalgani (The Forty) due to the prevailing social prejudices against female leadership. Hence, the pairing C-3 is correct.
• Minhaj-us-Siraj: He was a famous 13^th-century chronicler who wrote the Tabaqat-i Nasiri. While he recognized that Razia Sultan was more able and qualified than all her brothers, he was critical of her rule because he believed that the social order created by God placed women as subordinate to men. Hence, the pairing D-4 is correct.

Additional Information

• The Iqtadari System: This system was formalized by Sultan Iltutmish (reigned 1211–1236). The Muqtis or Iqtadars were expected to lead military campaigns and maintain a required number of soldiers. In return, they collected land revenue as their salary and used a portion of it to pay their soldiers. To ensure control, the office of Muqti was not made hereditary, and they were frequently transferred between regions to prevent them from becoming too powerful or independent from the Sultan.
• Razia Sultan’s Reign: Razia Sultan ruled for a short period from 1236 to 1240. She famously discarded the purdah and appeared in the durbar (court) wearing male attire, which further antagonized the conservative nobility. Her appointment of an Abyssinian slave, Jamal-ud-Din Yaqut, to the high position of Amir-i-Akhur (Master of the Stables) led to a revolt by the Turkish officers, ultimately leading to her overthrow and death near Kaithal in 1240.
• Minhaj-us-Siraj and his Chronicles: Minhaj-us-Siraj wrote in Persian, the official language of the Delhi Sultanate. His work, Tabaqat-i Nasiri, is a primary source of information for the Slave Dynasty (Mamluk Dynasty). His writings reflect the gender-biased views of the contemporary Ulama and nobility, where the authority of a woman ruler was seen as a violation of the "ideal" social order.
• Social and Political Interdependence: The Circle of Justice emphasized that the stability of the Sultanate relied on the economic well-being of the peasantry. This highlights that land revenue was the backbone of the medieval Indian economy, and administrative reforms were often centered around maximizing this revenue while maintaining enough justice to prevent peasant uprisings or migrations.

Important Points

• The Delhi Sultanate: It consisted of five dynasties—the Mamluk (1206–1290), Khalji (1290–1320), Tughlaq (1320–1414), Sayyid (1414–1451), and Lodi (1451–1526). Most of these administrative terms, like Iqta and Circle of Justice, were central to the Mamluk and Khalji administrations.
• Audit and Control: Under Sultans like Alauddin Khalji, accountants were appointed to check the revenue collected by the Muqtis. This was a measure to ensure that the Iqtadars did not collect more than the prescribed tax and maintained the required number of troops as mandated by the state.
• Gender in Medieval Politics: The opposition to Razia Sultan was not just about her individual abilities but about the structural patriarchy of the 13^th-century political landscape. Even a capable daughter like Razia was considered less suitable than an incapable son in the eyes of the theologians and nobles.

The correct answer is Shaping the future: Driving economic transformation for equitable, inclusive and sustainable development.

Key Points

• The 16^th session of the United Nations Conference on Trade and Development (UNCTAD16) is scheduled to be held in Geneva, Switzerland, in October 2025. This session marks a critical juncture for global trade discussions, focusing on the needs of developing nations in a rapidly changing global economy.
• The official theme for the UNCTAD16 conference is "Shaping the future: Driving economic transformation for equitable, inclusive and sustainable development." This theme emphasizes the necessity of structural changes in economies to ensure that growth benefits everyone and protects the environment. Hence, the option containing this theme is correct.
• The conference aims to address the growing digital divide, the impact of climate change on trade, and the debt distress faced by many Global South countries. It seeks to provide a platform for consensus-building among 195 member states.
• The session will evaluate the progress made since UNCTAD15, which was held in Barbados in 2021, and will set the organization's work program for the next four years.
• Key focus areas include technology transfer, investment facilitation, and the diversification of exports for Least Developed Countries (LDCs) to build resilience against global shocks.

Additional Information

• About UNCTAD:
• UNCTAD was established in 1964 as a permanent intergovernmental body. It is the principal organ of the United Nations General Assembly dealing with trade, investment, and development issues.
• Its permanent secretariat is located in Geneva, and it currently has 195 member states. The organization's primary goal is to maximize the trade, investment, and development opportunities of developing countries and assist them in integrating into the world economy on an equitable basis.
• The current Secretary-General of UNCTAD is Rebeca Grynspan of Costa Rica, who took office in September 2021, becoming the first woman to lead the organization.
• Major Publications and Reports:
• UNCTAD publishes several flagship reports that serve as benchmarks for global policy, including the World Investment Report, the Trade and Development Report, and the Least Developed Countries Report.
• The World Investment Report focuses on Foreign Direct Investment (FDI) trends and policies, while the Digital Economy Report tracks the global expansion of e-commerce and digital trade.
• Evolution of Themes:
• UNCTAD15 (2021): Held in Bridgetown, Barbados, with the theme "From inequality and vulnerability to prosperity for all." It focused on recovering from the COVID-19 pandemic.
• UNCTAD14 (2016): Held in Nairobi, Kenya, with the theme "From decision to action," emphasizing the implementation of the 2030 Agenda for Sustainable Development.

Important Points

• Economic Transformation: This refers to the process of shifting resources from low-productivity activities (like subsistence agriculture) to high-productivity sectors (like manufacturing and high-tech services). UNCTAD16 highlights this as the key to long-term prosperity.
• Equitable and Inclusive Development: This ensures that the benefits of international trade are not concentrated in a few nations or among the wealthy, but reach marginalized communities and small-scale enterprises.
• Sustainable Development: Aligning trade policies with the Paris Agreement and the Sustainable Development Goals (SDGs) is a priority, specifically addressing carbon leakage and green financing.
• Intergovernmental Machinery: UNCTAD operates through the Trade and Development Board and various commissions that meet between the quadrennial conferences to monitor policy implementation and provide technical assistance to member states.

Shortcut Trick

⇒ CP per article = 620/12

⇒ SP per article = 93

⇒ Profit per article = 93 − 620/12 = 93 − 51.67 ≈ 41.33

⇒ % Profit = (41.33 / 51.67) × 100 = 80%

∴ Answer = 0.8

Alternate Method

Given:

Number of dozens = 33

CP per dozen = 620

SP per article = 93

Formula:

Profit % = (Profit / CP) × 100

Calculation:

⇒ Total articles = 33 × 12 = 396

⇒ Total CP = 33 × 620 = 20460

⇒ Total SP = 396 × 93 = 36828

⇒ Profit = 36828 − 20460 = 16368

⇒ Profit % = (16368 / 20460) × 100 = 80%

Final Answer: 0.8

Additional Information

1. Dozen: 1 dozen = 12 units

2. Profit: SP − CP

3. Profit %: (Profit/CP) × 100

4. Shortcut: Compare per unit instead of total

Shortcut Trick

⇒ Speeds = 1³, 2³, 3³, ... , 10³

⇒ Total distance = sum of cubes = (n(n+1)/2)²

⇒ = (10×11/2)² = 55² = 3025

⇒ Time = 10 hours

⇒ Avg speed = 3025/10 = 302.5

∴ Answer = 302.5 km/h

Alternate Method

Given:

Speed in i^th hour = i³ km/h

Total time = 10 hours

Formula:

Average speed = Total distance / Total time

Sum of cubes = [n(n+1)/2]²

Calculation:

⇒ Total distance = 1³ + 2³ + ... + 10³

⇒ = [10×11/2]² = 55² = 3025 km

⇒ Average speed = 3025 / 10 = 302.5 km/h

Final Answer: 302.5 km/h

Additional Information

1. Sum of Cubes: 1³ + 2³ + ... + n³ = [n(n+1)/2]²

2. Average Speed: Total distance / total time

3. Pattern: Cubes grow rapidly → higher total

4. Time-based Speed: Distance each hour = speed × 1 hr

The correct answer is India.

Key Points

• In the latest Asia Power Index, India has achieved a significant milestone by securing the 3^rd rank among 27 nations and territories.
• For the first time since the index's inception, India has surpassed Japan, which now occupies the 4^th position in terms of comprehensive power in the Asia-Pacific region.
• The United States continues to hold the 1^st rank with a score of 81.7, while China remains in the 2^nd rank with a score of 72.7.
• India's overall score reached 39.1, reflecting a steady upward trajectory in its regional influence and resource capabilities.
• The ranking highlights India's post-pandemic economic recovery and its growing diplomatic influence, which has seen a notable increase in recent years.

Additional Information

• About the Asia Power Index:
• The Asia Power Index is an annual data-driven assessment launched in 2018 by the Lowy Institute, an independent think tank based in Sydney, Australia.
• It measures the power of countries across eight thematic measures: Economic Capability, Military Capability, Resilience, Future Resources, Economic Relationships, Defense Networks, Diplomatic Influence, and Cultural Influence.
• India's Strategic Strengths:
• India performs exceptionally well in the Future Resources category, where it ranks 2^nd, trailing only behind the United States. This is due to its massive demographic dividend and projected economic growth.
• In terms of Diplomatic Influence, India has moved up to the 4^th position, reflecting its active engagement in global forums and regional leadership roles.
• The country is classified as a "Major Power", a status reserved for nations with scores above 10 in the index.
• Japan's Position:
• Japan slipped to the 4^th rank with a score of 38.9. While it remains a significant "Smart Power" that excels in Economic Relationships and Defense Networks, it faces challenges due to an aging population and economic stagnation.

Important Points

• Regional Dynamics: The index covers countries as far west as Pakistan, as far north as Russia, and as far into the Pacific as Australia, New Zealand, and the United States.
• India as an "Underachiever": Despite its 3^rd rank, the report notes that India is still an "underachiever" relative to its available resources, meaning its actual influence in the region is less than what its population and geography would suggest.
• Key Rankings for 2024/2025:
• Rank 1: United States (81.7)
• Rank 2: China (72.7)
• Rank 3: India (39.1)
• Rank 4: Japan (38.9)
• Rank 5: Australia (31.9)
• Strategic Implications: India’s rise is significantly bolstered by its membership in the Quadrilateral Security Dialogue (Quad) and its expanding military capability, where it currently ranks 4^th globally within the index's scope.

The correct answer is P-Quest Group.

Key Points

• The Quantum Diamond Microscope (QDM) was developed by the P-Quest Group, which stands for Precision Quantum Engineering, Science and Technology. This research group is based at the Indian Institute of Technology (IIT) Bombay.
• The development of this advanced imaging tool was led by Associate Professor Kasturi Saha from the Department of Electrical Engineering at IIT Bombay. The team unveiled this technology to enhance India's capabilities in quantum sensing and metrology.
• The Quantum Diamond Microscope is a high-sensitivity magnetic field imaging device that utilizes Nitrogen-Vacancy (NV) centers in synthetic diamonds as quantum sensors. This allows for the mapping of magnetic fields with micrometer-scale spatial resolution.
• The project is a significant milestone under the National Quantum Mission (NQM), which was approved by the Government of India in 2023 with a total outlay of over Rs. 6,000 crore to propel India into a leading role in quantum technology.
• The P-Quest Group at IIT Bombay focuses on using quantum states of light and matter for applications in communication, sensing, and computing. Their work on the microscope was supported by the Department of Science and Technology (DST) and the Ministry of Electronics and Information Technology (MeitY).

Additional Information

• Technological Features:
• The microscope operates by using a green laser to excite the NV centers in the diamond. As these centers return to their ground state, they emit red fluorescence, the intensity of which changes in response to local magnetic fields.
• It provides non-destructive testing capabilities, meaning it can inspect semiconductor chips and electronic circuits for defects without causing any physical damage to the components.
• The device can operate at room temperature, which is a major advantage over other quantum sensors that require cryogenic cooling (extremely low temperatures).
• Applications and Uses:
• Semiconductor Industry: It is used for failure analysis in integrated circuits (ICs), helping engineers locate short circuits or current leakages in microchips.
• Biomedical Imaging: The Quantum Diamond Microscope can be used to image magnetic nanoparticles within biological cells, aiding in advanced medical diagnostics and drug delivery research.
• Geology and Material Science: It assists in studying the magnetic properties of minerals and new 2D materials like graphene.
• National Quantum Mission (NQM):
• Launched in April 2023, the NQM aims to develop intermediate-scale quantum computers with 50-1000 physical qubits within eight years.
• The mission is implemented by the Department of Science and Technology (DST) and targets four main domains: Quantum Computing, Quantum Communication, Quantum Sensing and Metrology, and Quantum Materials and Devices.

Important Points

• Nitrogen-Vacancy (NV) Center: This is a point defect in the diamond lattice where a nitrogen atom replaces a carbon atom, and an adjacent site is empty (a vacancy). It is a key building block for quantum sensors due to its electron spin properties.
• India's Strategic Position: With the development of the Quantum Diamond Microscope, India joins a select group of countries, including the USA, Germany, and Australia, that possess indigenous capabilities in quantum imaging.
• Location of Development: The research was conducted at the IIT Bombay campus in Powai, Mumbai. The institute is one of the premier Technical Universities in India, consistently ranked high in the NIRF and QS World University Rankings.
• Date and Year: The formal announcement and successful demonstration of the prototype were highlighted in late 2024 and early 2025, marking a new era for deep-tech startups in the Indian ecosystem.

Shortcut Trick

⇒ Net effect = (1 − 5/100) × (1 + 60/100)

⇒ = 0.95 × 1.6 = 1.52

⇒ Gain = 52%

∴ Answer = 0.52

Alternate Method

Given:

CP = 331

Loss = 5%

Gain = 60%

Formula:

SP = CP × (1 ± %/100)

Calculation:

⇒ First sale (5% loss):

SP₁ = 331 × 0.95 = 314.45

⇒ Second sale (60% gain):

SP₂ = 314.45 × 1.6 = 503.12

⇒ Net gain = 503.12 − 331 = 172.12

⇒ Gain % = (172.12 / 331) × 100 = 52%

Final Answer: 0.52

Additional Information

1. Successive Change: Multiply factors directly

2. Loss/Gain Factor: Loss → (1 − x/100), Gain → (1 + x/100)

3. Net Effect: Product of factors − 1

4. Shortcut: Avoid stepwise, use multiplication directly

The logic followed here is:

Given:

NEAR → 3519

GROW → 8645

So, R is coded as 5

Hence, the correct answer is "Option 4".

The logic followed here is:

Logic: Multiply by 2 → Multiply by 2 → Divide by 2

For, 8 → 16 → 26 → 13

⇒ 8 × 2 = 16

⇒ 16 + 10 = 26

⇒ 26 ÷ 2 = 13

Similarly, 5 → 10 → 20 → 10

⇒ 5 × 2 = 10

⇒ 10 × 2 = 20

⇒ 20 ÷ 2 = 10

Now, applying the same logic to options:

Option 1) 24 → 48 → 68 → 34

⇒ 24 × 2 = 48

⇒ 48 + 20 = 68 

Option 2) 12 → 24 → 34 → 17

⇒ 12 × 2 = 24

⇒ 24 + 10 = 34

⇒ 34 ÷ 2 = 17 

Option 3) 36 → 72 → 144 → 72

⇒ 36 × 2 = 72

⇒ 72 × 2 = 144

⇒ 144 ÷ 2 = 72 

Option 4) 34 → 68 → 78 → 156

⇒ 34 × 2 = 68

⇒ 68 + 10 = 78

⇒ 78 × 2 = 156 

Hence, the correct answer is Option 2.

The correct answer is Kakatiya dynasty.

Key Points

• The Thousand Pillar Temple, also known as the Rudreshwara Swamy Temple, is a historic Hindu temple located in Hanamkonda town near Warangal in the state of Telangana, India.
• It was constructed in the year 1163 AD during the reign of the Kakatiya dynasty. The construction was commissioned by the ruler King Rudra Deva. Hence, the statement regarding its association with the Kakatiya dynasty is correct.
• The temple is a classic example of Kakatiya architecture, which reached its zenith during the 12^th century. It is built in the Vesara style and is famous for its intricate carvings and perforated stone screens.
• It is a Trikutalaya, which means it consists of three shrines dedicated to three different deities: Lord Shiva, Lord Vishnu, and Lord Surya (the Sun God). Hence, the statement about it being a triple shrine is correct.
• The temple is supported by one thousand pillars, which are intricately carved but positioned in a way that they never obstruct the view of the deities from any point in the temple.
• A massive monolithic Nandi (the sacred bull of Shiva) carved out of a single black basalt stone is placed at the entrance, reflecting the artistic brilliance of the Kakatiya era.

Additional Information

• Kakatiya Dynasty (1083–1323 AD):
• This dynasty ruled the eastern Deccan region, comprising modern-day Telangana and Andhra Pradesh.
• Their capital was initially Hanamkonda and later shifted to Orugallu (modern Warangal).
• Notable rulers include Ganapati Deva, Rani Rudrama Devi, and Prataparudra. They were known for constructing massive irrigation tanks and grand temples like the Ramappa Temple (a UNESCO World Heritage Site).
• Rashtrakuta Dynasty (753–982 AD):
• They ruled large parts of the Indian subcontinent between the 8^th and 10^th centuries.
• Their most famous architectural achievement is the Kailasa Temple at Ellora (Maharashtra), which is a rock-cut monolithic structure.
• Hoysala Dynasty (1006–1346 AD):
• Based in modern-day Karnataka, the Hoysalas are famous for their unique star-shaped temple plans.
• Major examples of their work include the Hoysaleswara Temple at Halebidu and the Chennakesava Temple at Belur, built primarily in the 12^th and 13^th centuries.
• Chalukya Dynasty:
• The Badami Chalukyas (6^th-8^th century) and the Western Chalukyas of Kalyani (10^th-12^th century) were major powers in the Deccan.
• They were pioneers of the Vesara style of architecture, with significant sites located in Aihole, Badami, and Pattadakal.

Important Points

• Architectural Features: The Thousand Pillar Temple was built using sandstone for the main structure, while the decorative elements and the Nandi bull were made from black basalt. The pillars are highly polished, giving them a mirror-like finish.
• Historical Significance: The temple was desecrated during the invasion of the Deccan by the Delhi Sultanate (led by Alauddin Khilji and later Ghiyasuddin Tughlaq) in the 14^th century.
• Cultural Impact: The Kakatiyas promoted the Telugu language and Shaivism. The Thousand Pillar Temple remains a primary pilgrimage and tourist destination in South India, showcasing the medieval engineering marvels of the region.

Shortcut Trick

⇒ Ratio L:B = 3:2

⇒ Let L = 3x, B = 2x ⇒ Area = 6x² = 600

⇒ x² = 100 ⇒ x = 10

⇒ L = 30, B = 20 ⇒ Perimeter = 2(50) = 100

⇒ Cost = 100 × 200 = 20000

∴ Answer = ₹20000

Alternate Method

Given:

Breadth = (2/3) Length

Area = 600 m²

Cost = ₹200/m

Formula:

Area = L × B

Perimeter = 2(L + B)

Calculation:

⇒ Let Length = L ⇒ Breadth = (2/3)L

⇒ L × (2/3)L = 600

⇒ (2/3)L² = 600

⇒ L² = 900 ⇒ L = 30 m

⇒ B = (2/3)×30 = 20 m

⇒ Perimeter = 2(30 + 20) = 100 m

⇒ Cost = 100 × 200 = 20000

Final Answer: ₹20000

Additional Information

1. Ratio Method: Convert fraction into ratio form

2. Rectangle: Area = L × B

3. Perimeter: 2(L + B)

4. Fencing Cost: Perimeter × rate

Given: A, B, C, D, E and F live on six different floors of the same building. 

The lowermost floor in the building is numbered 1, the floor above it is numbered 2 and so on till the topmost floor, which is numbered 6.

Only two people live below C.

Only two people live between B and C.

A lives above E but below C.

F does not live above D.

Now, person immediately below B: D

Hence, the correct answer is Option 1.

Shortcut Trick

⇒ Use identity: (3x + 2y)² − (3x − 2y)² = 24xy

⇒ 100 − (3x − 2y)² = 24×(3/2) = 36

⇒ (3x − 2y)² = 64

⇒ 3x − 2y = 8 (positive)

∴ Answer = 8

Alternate Method

Given:

3x + 2y = 10

2xy = 3

Formula:

(a + b)² − (a − b)² = 4ab

Calculation:

⇒ (3x + 2y)² = 100

⇒ Using identity:

(3x + 2y)² − (3x − 2y)² = 4×(3x×2y)

⇒ 100 − (3x − 2y)² = 24xy

⇒ 24xy = 24×(3/2) = 36

⇒ 100 − (3x − 2y)² = 36

⇒ (3x − 2y)² = 64

⇒ 3x − 2y = ±8

⇒ Positive value = 8

Final Answer: 8

Additional Information

1. Identity: (a+b)² − (a−b)² = 4ab

2. Trick: Use square identity to avoid solving variables

3. Product Given: xy helps eliminate variables

4. Positive Value: Take only + root

Shortcut Trick

Solve ÷ and × first:

⇒ (−60) ÷ (−6) = 10, (−2) × 9 = −18

⇒ Expression = −9 − 10 − 18

⇒ = −37

∴ Answer = −37

Alternate Method

Given:

(−9) − (−60) ÷ (−6) + (−2) × 9

Concept Used:

BODMAS rule

Calculation:

⇒ (−9) − 10 + (−2) × 9

⇒ (−9) − 10 − 18

⇒ −19 − 18

⇒ −37

∴ The correct answer is −37.

Additional Information

Sign Rule: − ÷ − = +, − × + = −

BODMAS: Solve Division and Multiplication first

Common Mistake: Wrong sign handling leads to errors

Shortcut Tip: Simplify signs first, then calculate

The correct answer is Deendayal Antyodaya Yojana.

Key Points

• Deendayal Antyodaya Yojana - National Rural Livelihoods Mission (DAY-NRLM) is a flagship program launched by the Ministry of Rural Development in June 2011. It was originally launched as Aajeevika - National Rural Livelihoods Mission and later renamed in 2015. Hence, statement 2 is correct.
• The primary objective of the program is to alleviate rural poverty by creating efficient and effective institutional platforms for the rural poor, enabling them to increase household income through sustainable livelihood enhancements and improved access to financial services.
• It focuses on promoting self-employment and organization of the rural poor into Self Help Groups (SHGs). This helps in building the capacities of the poor and providing them with skills and financial resources to start their own micro-enterprises.
• The Mahatma Gandhi National Rural Employment Guarantee Act (MGNREGA) is designed to provide guaranteed wage employment for at least 100 days in a financial year to unskilled manual laborers; it is not primarily a self-employment scheme. Hence, statement 1 is incorrect.
• The National Rural Health Mission (NRHM) was launched in April 2005 to provide accessible, affordable, and quality healthcare to the rural population, particularly the vulnerable sections. It does not focus on self-employment. Hence, statement 3 is incorrect.
• The Pradhan Mantri Awas Yojana (PMAY), specifically the Gramin (Rural) component launched in 2016, aims to provide pucca houses with basic amenities to all houseless householders and those living in kutcha houses. It is a housing scheme, not a self-employment program. Hence, statement 4 is incorrect.

Additional Information

• Evolution of DAY-NRLM: The program succeeded the Swarnajayanti Gram Swarozgar Yojana (SGSY). It is supported by the World Bank and is one of the world's largest initiatives to improve the livelihoods of the poor. It covers 28 States and 8 Union Territories across India.
• MGNREGA Features: Enacted in September 2005, this Act provides a legal guarantee for work. If work is not provided within 15 days of application, the applicant is entitled to an unemployment allowance. At least one-third of the beneficiaries must be women.
• PMAY-Gramin Details: The scheme targets the construction of 2.95 crore houses. The cost-sharing ratio between the Central and State governments is 60:40 in plain areas and 90:10 for North Eastern and Hilly States.
• NRHM Objectives: It seeks to reduce the Infant Mortality Rate (IMR) and Maternal Mortality Rate (MMR). It introduced the Accredited Social Health Activist (ASHA), a trained female community health activist, to act as an interface between the community and the public health system.

Important Points

• Core Pillars of DAY-NRLM: The scheme relies on social mobilization, financial inclusion, and sustainable livelihoods. It encourages universal social mobilization by ensuring at least one woman member from each rural poor household is brought into the SHG network.
• Livelihood Diversification: Under DAY-NRLM, the poor are encouraged to pursue farm (agriculture, livestock, fisheries) and non-farm (handicrafts, services, retail) occupations to ensure year-round income.
• Interest Subvention: The scheme provides interest subvention to SHG members who avail of bank loans, reducing the cost of credit and encouraging entrepreneurship among rural women.
• Identification of Beneficiaries: Unlike many schemes that use the BPL (Below Poverty Line) list, DAY-NRLM uses the Socio-Economic and Caste Census (SECC) 2011 data and a process called Participatory Identification of Poor (PIP) to identify target households.

Shortcut Trick

Total = 45×295 + 31×311 + 48×233

⇒ = 13275 + 9641 + 11184 = 34100

Total members = 45 + 31 + 48 = 124

⇒ Average = 34100 ÷ 124 = 275

∴ Answer = 275

Alternate Method

Given:

Group A: 45 members, avg = 295

Group B: 31 members, avg = 311

Group C: 48 members, avg = 233

Concept Used:

Overall Average = Total Amount ÷ Total Members

Calculation:

⇒ Total of A = 45 × 295 = 13275

⇒ Total of B = 31 × 311 = 9641

⇒ Total of C = 48 × 233 = 11184

⇒ Total amount = 13275 + 9641 + 11184 = 34100

⇒ Total members = 45 + 31 + 48 = 124

⇒ Average = 34100 ÷ 124 = 275

∴ Overall average = 275

Additional Information

Weighted Average: Multiply each average with its frequency

Formula: Average = Total Sum ÷ Total Count

Shortcut: Add all group totals first, divide once

Tip: Avoid dividing separately for each group

The logic followed here is:

Given: (Left) O ? Q ! R + S – T $ U * V / A P < W = X : (Right)

Now, we need letters which are immediately preceded by a letter and also immediately followed by a symbol.

So, Needed pattern is: Letter - Letter - Symbol

(Left) O ? Q ! R + S – T $ U * V / A P < W = X : (Right)

Now, Total = 1

Hence, the correct answer is Option 3.

The correct answer is 3.2 percent.

Key Points

• The International Monetary Fund (IMF), in its World Economic Outlook (WEO) update released in January 2026, has projected that the global economic expansion for the year 2027 will be 3.2 percent.
• This forecast indicates a steady growth trajectory for the global economy, maintaining a similar pace as projected for 2025 and 2026, which also hovered around the 3.1 to 3.2 percent mark.
• The 3.2 percent growth rate for 2027 is driven by the resilient performance of Emerging Market and Developing Economies, which are expected to grow at a faster rate compared to Advanced Economies.
• The report suggests that the global economy has moved past the significant inflationary pressures of the early 2020s, with monetary policy normalization expected to be well underway by 2027.
• According to the IMF, the stability in growth is attributed to improved supply-side conditions and the continued integration of Artificial Intelligence (AI) into the labor markets of high-income nations.

Additional Information

• The International Monetary Fund (IMF):
• The IMF is a major international financial institution, headquartered in Washington, D.C., consisting of 190 member countries.
• It was conceived in July 1944 at the United Nations Bretton Woods Conference in the United States.
• The primary mission of the IMF is to ensure the stability of the international monetary system, including the system of exchange rates and international payments.
• World Economic Outlook (WEO):
• The WEO is a comprehensive report published by the IMF twice a year, typically in April and October, with smaller "updates" published in January and July.
• It provides detailed analysis and forecasts for global growth, inflation, and trade, serving as a key reference for policymakers and economists worldwide.
• The reports use Gross Domestic Product (GDP) based on Purchasing Power Parity (PPP) weights to aggregate global and regional growth figures.
• Economic Classifications:
• Advanced Economies: These include the United States, Euro Area, Japan, and the United Kingdom. These regions often see lower but more stable growth rates.
• Emerging Market and Developing Economies: This group includes major players like India and China. India has consistently been one of the fastest-growing major economies in these reports.
• Key Economic Indicators:
• Global Inflation: The IMF tracks headline and core inflation. By 2027, global headline inflation is projected to align closer to central bank targets.
• Fiscal Policy: The WEO often emphasizes the need for fiscal consolidation to manage the rising public debt levels across various nations.

Important Points

• Projected Trends: The January 2026 update highlights that while growth is steady at 3.2 percent, the medium-term growth prospects remain lower than the historical average of 3.8 percent seen between 2000 and 2019.
• Risks to Forecast: Potential risks to the 2027 expansion include geopolitical tensions, fluctuations in commodity prices (such as crude oil), and potential disruptions in global supply chains.
• Managing Director: As of the report period, the IMF is led by its Managing Director, a position held by Kristalina Georgieva (who started her term in 2019).
• Comparison with World Bank: Similar to the IMF, the World Bank also releases the Global Economic Prospects report, though their methodologies and specific GDP growth numerical values may vary slightly based on different base years and calculation methods.

The correct answer is Fourth Schedule.

Key Points

• The Fourth Schedule of the Constitution of India deals with the allocation of seats in the Rajya Sabha (the Council of States) to the various States and Union Territories. Hence, the first option is correct.
• The allocation of these seats is determined based on the population of each state. Consequently, the number of representatives varies from state to state; for example, Uttar Pradesh has the highest representation with 31 seats, while smaller states like Sikkim have only 1 seat.
• This schedule is linked with Article 4(1) and Article 80(2) of the Indian Constitution, which mandate the structure and composition of the upper house of Parliament.
• The Rajya Sabha currently has a total of 245 members, although the maximum strength is fixed at 250. Out of these, 233 members are representatives of the States and Union Territories, and 12 members are nominated by the President for their contributions to art, literature, science, and social services.
• Among the Union Territories, only Delhi (3 seats), Puducherry (1 seat), and Jammu & Kashmir (4 seats) have representation in the Rajya Sabha because their population sizes are large enough to warrant it.

Additional Information

• First Schedule:
• This schedule contains the names of the States and Union Territories along with their territorial jurisdiction and extent.
• It currently lists 28 States and 8 Union Territories following the Jammu and Kashmir Reorganisation Act, 2019 and the merger of Dadra and Nagar Haveli and Daman and Diu in 2020.
• Second Schedule:
• It lists the provisions relating to the emoluments, allowances, and privileges of high-ranking officials.
• This includes the President of India, Governors of States, Speaker and Deputy Speaker of the Lok Sabha, Chairman and Deputy Chairman of the Rajya Sabha, and Judges of the Supreme Court and High Courts.
• Sixth Schedule:
• It contains provisions for the administration of tribal areas in the four northeastern states of Assam, Meghalaya, Tripura, and Mizoram.
• It allows for the creation of Autonomous District Councils (ADCs) to safeguard the rights of tribal communities and manage land, forests, and local customs.
• Seventh Schedule:
• This schedule deals with the division of powers between the Union and the States through three lists: the Union List (currently 100 subjects), the State List (currently 61 subjects), and the Concurrent List (currently 52 subjects).

Important Points

• The Rajya Sabha is known as the Permanent House because it is not subject to dissolution.
• Members of the Rajya Sabha are elected for a term of 6 years, and one-third of the members retire every second year.
• The election process involves the elected members of the Legislative Assemblies of the States and Union Territories using the system of proportional representation by means of a single transferable vote.
• The Vice-President of India serves as the ex-officio Chairman of the Rajya Sabha.
• The Representation of the People Act, 1951 governs various aspects of the election and functioning of the members in accordance with the Constitution.

The correct answer is Kalashram.

Key Points

• Kalashram is the world-renowned institution founded by the Kathak maestro Pandit Birju Maharaj in New Delhi.
• The primary focus of this institution is to impart training in the field of Kathak dance, along with other associated disciplines like Yoga, Painting, Vocal Music, and the playing of musical instruments.
• Pandit Birju Maharaj established this institute to preserve and promote the Kalka-Bindadin Gharana of Lucknow, which is characterized by its graceful movements and intricate footwork.
• The institution reflects the philosophy of Birju Maharaj, which treats dance as a holistic art form integrated with spiritual and physical well-being.
• The training at Kalashram follows the traditional Guru-Shishya Parampara, ensuring the authentic transmission of Kathak techniques to future generations.

Additional Information

• Pandit Birju Maharaj (born Brijmohan Nath Mishra) was born on 4 February 1938 and passed away on 17 January 2022. He was a legendary figure in Indian classical dance.
• He belonged to the Lucknow "Kalka-Bindadin" Gharana, a lineage that has produced some of the greatest Kathak dancers in India.
• Birju Maharaj was a multi-talented artist; besides being a dancer, he was a singer, composer, and poet. He was proficient in playing the Tabla, Pakhawaj, and Dholak.
• In recognition of his immense contribution to the arts, he was awarded the Padma Vibhushan, India's second-highest civilian award, in 1986.
• He also served as the Head of Faculty and Director at the Kathak Kendra (National Institute of Kathak Dance) in New Delhi for many years before founding Kalashram.
• Kathak is one of the eight major forms of Indian classical dance. Its origin is attributed to the traveling storytellers of ancient Northern India, known as Kathakars.

Important Points

• Global Reach: Pandit Birju Maharaj took Kathak to the global stage, performing in numerous countries and establishing a worldwide following.
• Choreography in Cinema: He contributed significantly to Indian Cinema by choreographing iconic dance sequences in movies like Shatranj Ke Khilari (directed by Satyajit Ray), Devdas, Bajirao Mastani, and Vishwaroopam.
• Awards and Honors: Apart from the Padma Vibhushan, he received the Sangeet Natak Akademi Award in 1964, the Kalidas Samman, and a National Film Award for Best Choreography in 2012.
• Lineage: He was the son and disciple of Jagannath Maharaj, popularly known as Acchan Maharaj. His uncles were the famous Lachhu Maharaj and Shambhu Maharaj.
• Artistic Features: Kathak is distinguished by its Chakkars (vertical spins), Tatkar (footwork), and Abhinaya (expressional dance), all of which were mastered and taught by Birju Maharaj at Kalashram.

The correct answer is Real-time Predictive Analytics.

Key Points

• Real-time Predictive Analytics is the use of data, statistical algorithms, and machine learning techniques to identify the likelihood of future outcomes based on historical and current data. In e-commerce and finance, it is essential for processing big data at high speeds.
• In the context of financial trading, these systems analyze massive volumes of rapidly changing market data, including stock prices, currency fluctuations, and trading volumes, to execute trades in milliseconds.
• The primary function of this technology is to detect complex patterns and market trends that are invisible to human analysts, allowing institutional investors to make informed investment decisions and manage risk effectively.
• In e-commerce, Predictive Analytics is used for dynamic pricing, where prices of products change in real-time based on consumer demand, competitor pricing, and inventory levels.
• This technology relies on high-performance computing and cloud-based infrastructures to ensure that data processing happens with minimal latency, which is critical for high-frequency trading (HFT).

Additional Information

• Data Encryption and Security Software: This involves cryptographic protocols like AES-256 or SSL/TLS to protect financial transactions and user data from cyber threats. While critical for trust in e-commerce, its application is security, not market analysis.
• Inventory Management Systems: These are software applications used by retailers to track stock levels, orders, sales, and deliveries. They ensure supply chain efficiency but do not possess the analytical capabilities to inform investment decisions in trading.
• Word Processing and Desktop Publishing: These tools, such as Microsoft Word or Adobe InDesign, are used for creating documents, reports, and marketing brochures. They are administrative tools and have no function in real-time data analysis or automated trading.
• Global Adoption: Real-time analytics is widely used in countries like the USA, United Kingdom, and India to power fintech applications and stock exchange operations.

Important Points

• Algorithmic Trading: This refers to computer-programmed trading that follows a defined set of instructions. It currently accounts for over 70% of the trading volume in US equity markets.
• Sentiment Analysis: A subset of predictive analytics where Natural Language Processing (NLP) is used to scan news articles, social media, and financial reports to determine market sentiment (bullish or bearish).
• Big Data Characteristics: The data analyzed in financial trading is often characterized by the three Vs: Volume (large scale), Velocity (high speed), and Variety (different formats like numerical, text, and social media feeds).
• Historical Context: The move toward electronic trading and predictive modeling accelerated in the 2000s, drastically reducing the spreads and increasing the liquidity of global markets.

The logic followed here is:

For, SGYU → UJAX

Now, ASGG → CVIJ

Now, applying the same logic for GBMP:

So, GBMP → IEOS

Hence, the correct answer is Option 1.

The correct answer is Chemical weathering.

Key Points

• Chemical weathering is the fundamental process responsible for the development of karst landscapes. This type of weathering involves the chemical transformation of rock minerals into new compounds, often leading to the dissolution of the rock. Hence, the statement regarding chemical weathering being the primary cause is correct.
• The specific chemical process involved is carbonation. When rainwater passes through the atmosphere and soil, it absorbs carbon dioxide (CO2), forming a weak solution of carbonic acid.
• This acidic water reacts with soluble rocks, most notably limestone (which is composed of calcium carbonate), dolomite, and gypsum. The reaction converts insoluble calcium carbonate into soluble calcium bicarbonate, which is then carried away in solution.
• As the rock dissolves over thousands of years, it creates unique surface and sub-surface features such as sinkholes (also known as dolines), caves, caverns, and disappearing streams.
• The formation of karst requires specific conditions: the presence of highly jointed, dense, and thinly bedded soluble rocks near the surface, along with moderate to heavy rainfall to sustain the dissolution process.

Additional Information

• Mechanical Weathering: Also known as physical weathering, it refers to the physical disintegration of rocks into smaller fragments without any change in their chemical makeup. Common processes include frost wedging, abrasion, and pressure release. While it breaks down rocks, it does not produce the dissolution features seen in karst. Hence, the statement regarding mechanical weathering forming karst is incorrect.
• Biological Weathering: This is the breakdown of rocks caused by living organisms. For example, plant roots may grow into cracks and exert pressure, or lichens and bacteria may produce organic acids that slowly corrode minerals. It often acts in tandem with chemical weathering but is not the primary architect of karst. Hence, the statement regarding biological weathering as the primary cause is incorrect.
• Thermal Weathering: This occurs due to expansion and contraction of rock minerals resulting from temperature fluctuations. It is most prevalent in arid and desert regions where the diurnal temperature range is high. Hence, the statement regarding thermal weathering forming karst is incorrect.
• Geographic Distribution: Famous karst regions include the Karst Plateau in Slovenia (from which the name originates), the Yucatán Peninsula in Mexico, and the Ha Long Bay in Vietnam. In India, karst features are prominent in the Bastar district of Chhattisgarh (Kotumsar caves) and parts of the Himalayas.

Important Points

• Speleothems: These are mineral deposits formed in caves as a result of chemical precipitation. The most common are stalactites (hanging from the ceiling), stalagmites (rising from the floor), and pillars (formed when the two meet).
• Uvalas and Poljes: In advanced stages of karst topography, individual sinkholes may coalesce to form larger depressions called uvalas. Extremely large, flat-bottomed depressions are known as poljes, which can cover several square kilometers.
• Hydrogeology: Karst aquifers are vital sources of groundwater, providing water for millions of people worldwide. However, they are highly vulnerable to pollution because surface water can enter the underground system rapidly through sinkholes without significant filtration.
• Climate Influence: Chemical weathering is significantly more effective in hot and humid climates. The rate of rock dissolution increases with higher temperatures and greater water availability.

The logic followed here is based on the alphabetical positional difference between consecutive letters in each cluster:

Option 1: HKN

Option 2: QTW

Option 3: ILN

Option 4: JMP

Thus, ILN is different from the rest.

Hence, the odd one out is Option 3.

Given:

Sneha starts from Q → 5 km East

She turns left → 7 km North

She turns right → 3 km East

She turns right → 7 km South

She turns left → 2 km East

 

So, Sneha is 10 km East from starting point.

Hence, the correct answer is Option 1.

The correct answer is 5% of the sum insured.

Key Points

• The Pradhan Mantri Fasal Bima Yojana (PMFBY) was launched on 18^th February 2016 by Prime Minister Narendra Modi to provide financial support to farmers suffering crop loss/damage arising out of unforeseen events.
• Under this scheme, there is a uniform premium of only 2% to be paid by farmers for all Kharif crops. This is the standard rate for food crops and oilseeds during the monsoon season.
• For all Rabi crops, the premium to be paid by the farmers is 1.5%. This lower rate is applicable for the winter cropping season.
• In the case of annual commercial and annual horticultural crops, the premium to be paid by farmers is 5% of the sum insured. Hence, the statement regarding the 5% rate for commercial crops is correct.
• The balance premium (the difference between the actual premium rate and the rate paid by farmers) is paid by the Government (shared equally by the Central and State Governments) to provide the full insured amount to the farmers.

Additional Information

• Objectives of PMFBY:
• To provide insurance coverage and financial support to the farmers in the event of failure of any of the notified crops as a result of natural calamities, pests, and diseases.
• To stabilize the income of farmers to ensure their continuance in farming.
• To encourage farmers to adopt innovative and modern agricultural practices.
• To ensure the flow of credit to the agriculture sector.
• Scheme Administration:
• The scheme is administered by the Ministry of Agriculture and Farmers Welfare, Government of India.
• It replaced the National Agricultural Insurance Scheme (NAIS) and the Modified National Agricultural Insurance Scheme (MNAIS) to remove their inherent drawbacks.
• Coverage and Scope:
• The scheme covers Yield Losses (standing crops), Prevented Sowing/Planting, and Post-Harvest Losses (up to a maximum period of 14 days from harvesting).
• It also includes Localized Calamities such as hailstorms, landslides, and inundation affecting isolated farms in the notified area.
• Since Kharif 2020, the scheme has been made voluntary for all farmers, whereas earlier it was compulsory for loanee farmers.

Important Points

• Technology Integration: The scheme promotes the use of modern technology like Smartphones for capturing and uploading data of crop cutting to reduce the delay in claim payment to farmers. Remote Sensing and Drones are also utilized for estimation of crop losses.
• Premium Subsidy Sharing: The Central Government and State Governments share the premium subsidy on a 50:50 basis, except for the North-Eastern States, where the sharing ratio is 90:10 (since 2020) to encourage higher penetration in these regions.
• Exclusions: Risks like war, nuclear risks, malicious damage, and other preventable risks are generally excluded from the insurance coverage.
• Implementation Agency: PMFBY is implemented by the Agriculture Insurance Company of India (AIC) and several private insurance companies empanelled by the government based on competitive bidding.
• Numerical Data: Since its inception, the scheme has covered over 30 crore farmer applications and has paid out claims worth billions of rupees, significantly improving the social security net for the Indian farming community.

The correct answer is Bal Gangadhar Tilak.

Key Points

• Bal Gangadhar Tilak was the leader who famously declared "Swaraj is my birthright and I shall have it" in 1916. This slogan became a rallying cry for millions of Indians during the struggle for independence. Hence, the first option is correct.
• He was a prominent figure in the Extremist Phase (1905-1919) of the Indian National Movement. Unlike the Moderates, Tilak advocated for self-rule (Swaraj) rather than mere constitutional reforms.
• Tilak earned the title "Lokmanya", which translates to "accepted by the people as their leader". The British colonial authorities referred to him as the "Father of Indian Unrest", a term coined by Valentine Chirol.
• He utilized journalism as a tool for political education, publishing two newspapers: Kesari in Marathi and The Mahratta in English. Through these, he criticized the British Government and spread nationalist ideas.
• To bridge the gap between the masses and the political movement, he popularized the Ganpati Festival in 1893 and the Shivaji Festival in 1895 in Maharashtra.

Additional Information

• Bipin Chandra Pal: Known as the "Father of Revolutionary Thoughts in India", he was a key part of the Lal-Bal-Pal triumvirate. He played a major role in the Swadeshi Movement following the Partition of Bengal in 1905 and advocated for the boycott of British goods. Hence, the second option is incorrect.
• Lala Lajpat Rai: Popularly known as "Punjab Kesari" or the "Lion of Punjab", he was another pillar of the Extremist faction. He founded the Punjab National Bank and was a leading figure in the protest against the Simon Commission in 1928, where he suffered fatal injuries during a lathi charge. Hence, the fourth option is incorrect.
• Aurobindo Ghose: An intellectual leader of the Extremist Phase, he emphasized the concept of Passive Resistance. He later retired from active politics and moved to Pondicherry to focus on spirituality and yoga, writing famous works like "The Life Divine" and "Savitri". Hence, the third option is incorrect.
• Extremist Phase (1905-1919): This period marked a shift from the Moderates' policy of "Prayers, Petitions, and Protests" to more radical methods including Swadeshi, Boycott, and National Education. The Surat Split of 1907 saw the formal separation of the Moderates and Extremists within the Indian National Congress.

Important Points

• Home Rule Movement: In April 1916, Bal Gangadhar Tilak launched the Indian Home Rule League at Belgaum. He worked alongside Annie Besant to demand Self-Government for India within the British Empire.
• Lucknow Pact: Tilak played a crucial role in the 1916 Lucknow Session, where he was instrumental in the Lucknow Pact between the Indian National Congress and the Muslim League, as well as the reunion of Moderates and Extremists.
• Literary Works: While serving a six-year prison term in Mandalay (Burma) from 1908 to 1914, Tilak wrote "Gita Rahasya", an interpretation of the Bhagavad Gita focused on Karma Yoga (the path of action). He also authored "The Arctic Home in the Vedas", where he proposed a theory about the origin of the Aryans.

Shortcut Trick

Subtract (2)−(1): X − Z = −2

Subtract (3)−(2): X − 2Z = −2

⇒ Subtract both ⇒ Z = 0

⇒ Then X = −2

⇒ Put in (1): Y = 7

∴ Answer: X = −2, Y = 7, Z = 0

Alternate Method

Given:

X + 2Y + 4Z = 12

2X + 2Y + 3Z = 10

3X + 2Y + Z = 8

Concept Used:

Elimination method

Calculation:

⇒ (2X + 2Y + 3Z) − (X + 2Y + 4Z) = 10 − 12

⇒ X − Z = −2

⇒ (3X + 2Y + Z) − (2X + 2Y + 3Z) = 8 − 10

⇒ X − 2Z = −2

⇒ (X − Z) − (X − 2Z) = −2 − (−2)

⇒ Z = 0

⇒ X − Z = −2

⇒ X = −2

⇒ X + 2Y + 4Z = 12

⇒ −2 + 2Y + 0 = 12

⇒ 2Y = 14

⇒ Y = 7

∴ The correct answer is X = −2, Y = 7, Z = 0.

Additional Information

Elimination Trick: Subtract equations to cancel common terms

Efficiency: Always target same coefficients (here 2Y cancels)

Check: Substitute back to verify solution

Tip: Reduce system to 2 variables first, then solve

Shortcut Trick

N = 80 ⇒ N/2 = 40

Cumulative freq: 9, 28, 62 → Median class = 30–60

⇒ Use formula: Median = L + [(N/2 − cf)/f] × h

⇒ = 30 + [(40 − 28)/34] × 30

⇒ = 30 + (12/34)×30 ≈ 30 + 10.59

∴ Answer ≈ 40.59

Alternate Method

Given:

Total frequency (N) = 80

Concept Used:

Median = L + [(N/2 − cf) ÷ f] × h

Calculation:

⇒ N/2 = 80 ÷ 2 = 40

⇒ Cumulative frequency:

0–10 → 9

10–30 → 9+19 = 28

30–60 → 28+34 = 62

⇒ Median class = 30–60

⇒ L = 30, cf = 28, f = 34, h = 30

⇒ Median = 30 + [(40 − 28) ÷ 34] × 30

⇒ = 30 + (12 ÷ 34) × 30

⇒ = 30 + 10.59

⇒ = 40.59

∴ Median = 40.59

Additional Information

Median Class: Class where cumulative frequency just exceeds N/2

Formula: Median = L + [(N/2 − cf) ÷ f] × h

Class Width: h = Upper limit − Lower limit

Shortcut Tip: Quickly find median class using cumulative frequency

Shortcut Trick

Second Number = (HCF × LCM) ÷ First Number

Second Number = (104 × 1040) ÷ 208

As 208 = 104 × 2, Second Number = 1040 ÷ 2 = 520

Sum = 208 + 520 = 728

∴ Answer = 728

Alternate Method 

Given:

HCF of two numbers = 104

LCM of two numbers = 1040

One of the numbers (a) = 208

Formula used:

Product of two numbers = HCF × LCM

Sum of numbers = a + b

Num 1: 208 + Num 2: 520 Sum = 728 Product Relation: 208 × 520 = 104 × 1040

Calculations:

Let the second number be b.

⇒ 208 × b = 104 × 1040

⇒ b = (104 × 1040) ÷ 208

⇒ b = 108160 ÷ 208

⇒ b = 520

⇒ Sum = 208 + 520 = 728

∴ The correct answer is 728.

Additional Information

Product Property

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

HCF and LCM of Fractions

HCF = (HCF of Numerators) ÷ (LCM of Denominators) and LCM = (LCM of Numerators) ÷ (HCF of Denominators).

Co-prime Numbers

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

Factor Property

The HCF of a group of numbers is always a factor of their LCM. If HCF does not divide LCM, such a set of numbers cannot exist.

Shortcut Trick

⇒ Let Arun = A, Mahesh = M

⇒ A(1.08)¹⁷ = M(1.08)¹⁸

⇒ ⇒ A = M × 1.08

⇒ Total = A + M = 1404 ⇒ 1.08M + M = 1404

⇒ 2.08M = 1404 ⇒ M = 1404 / 2.08 = 675

∴ Answer = 675

Alternate Method

Given:

Total amount = 1404

Rate = 8% per annum

Arun after 17 years = Mahesh after 18 years

Formula:

Amount = P(1 + r/100)ⁿ

Calculation:

⇒ A(1.08)¹⁷ = M(1.08)¹⁸

⇒ Divide both sides by (1.08)¹⁷

⇒ A = M × 1.08

⇒ A + M = 1404

⇒ 1.08M + M = 1404

⇒ 2.08M = 1404

⇒ M = 1404 / 2.08 = 675

Final Answer: 675

Additional Information

1. Compound Interest: A = P(1 + r/100)ⁿ

2. Equal Amount Trick: Divide powers to simplify

3. Ratio: A : M = 1.08 : 1

4. Faster Method: Use direct proportional relation

The logic followed here is:

So, 'HJO 19' will replace the question mark in the given series.

Hence, the correct answer is "Option 1".

The correct answer is Article 42.

Key Points

• Article 42 of the Constitution of India specifically mandates that the State shall make provisions for securing just and humane conditions of work and for maternity relief.
• This article is a part of the Directive Principles of State Policy (DPSP), which are contained in Part IV of the Constitution, spanning from Article 36 to Article 51.
• The primary objective of Article 42 is to ensure that the working environment for employees is safe, healthy, and respectful of human dignity, while also providing necessary support to women workers during and after pregnancy.
• It reflects the Socialist Principles of the Indian Constitution, aiming to bridge the gap between the capital and labor by protecting the welfare of the workforce.
• The State is expected to apply these principles while making laws and policies, although they are non-justiciable in a court of law, meaning they cannot be legally enforced like Fundamental Rights.

Additional Information

• Article 41: This article provides for the right to work, to education, and to public assistance in certain cases such as unemployment, old age, sickness, and disablement. It ensures that the State, within the limits of its economic capacity, makes effective provisions for these rights.
• Article 44: This article directs the State to endeavor to secure for the citizens a Uniform Civil Code (UCC) throughout the territory of India. It aims to replace personal laws based on the scriptures and customs of each major religious community with a common set of laws governing every citizen.
• Article 48: This article deals with the organization of agriculture and animal husbandry. It directs the State to organize these sectors on modern and scientific lines and, in particular, to take steps for preserving and improving the breeds, and prohibiting the slaughter of cows and calves and other milch and draught cattle.
• Directive Principles of State Policy (DPSP): These were borrowed from the Irish Constitution. They serve as guidelines to the Central and State governments of India, to be kept in mind while framing laws and policies.

Important Points

• Maternity Benefit Act, 1961: To give effect to the provisions of Article 42, the Parliament of India enacted the Maternity Benefit Act in 1961. This act regulates the employment of women in certain establishments for certain periods before and after childbirth and provides for maternity benefits and certain other benefits.
• 2017 Amendment: The Maternity Benefit (Amendment) Act, 2017 significantly increased the duration of paid maternity leave available for women employees from the existing 12 weeks to 26 weeks for the first two children.
• Applicability: The Maternity Benefit Act applies to all establishments employing 10 or more persons, including factories, mines, plantations, and shops.
• Crèche Facility: Under the 2017 amendment, every establishment having 50 or more employees is required to have a crèche facility within a prescribed distance.
• International Standards: These provisions align with the standards set by the International Labour Organization (ILO), specifically the Maternity Protection Convention.

Given number: 4528173

Logic:

Add 1 to each odd digit

Subtract 2 from each even digit

Original number: 4 5 2 8 1 7 3

New number: 2 6 0 6 2 8 4

Digits appearing more than once: 2 and 6 → total 2 digits

Hence, the correct answer is Option 2.

Shortcut Trick

⇒ Follow BODMAS → divide & multiply first

⇒ (−56) ÷ (−8) = 7

⇒ (−4) × 6 = −24

⇒ Expression = −9 − 7 − 24 = −40

∴ Answer = −40

Alternate Method

Given:

(−9) − (−56) ÷ (−8) + (−4) × 6

Formula:

BODMAS → Division and Multiplication first

Calculation:

⇒ (−56) ÷ (−8) = 7

⇒ (−4) × 6 = −24

⇒ Substitute:

⇒ −9 − 7 − 24

⇒ = −16 − 24 = −40

Final Answer: −40

Additional Information

1. BODMAS: Order → Bracket, Division, Multiplication, Addition, Subtraction

2. Sign Rules: (−) ÷ (−) = +, (−) × (+) = −

3. Simplification: Solve stepwise

4. Negative Numbers: Keep track of signs carefully

Shortcut Trick

⇒ If A is 13% more than B ⇒ A = 113, B = 100

⇒ % less of B from A = (13 / 113) × 100

⇒ ≈ 11.50%

∴ Answer = 0.115

Alternate Method

Given:

A is 13% more than B

Formula:

% decrease = (Difference / Larger value) × 100

Calculation:

⇒ Let B = 100

⇒ A = 113

⇒ Difference = 113 − 100 = 13

⇒ % less = (13 / 113) × 100

⇒ = 11.5044 ≈ 11.50%

Final Answer: 0.115

Additional Information

1. Important Rule: % increase and % decrease are not equal

2. Base Change: Always divide by the new base

3. Shortcut: x% more ⇒ decrease = x/(100+x) × 100

4. Example: 13/(113) × 100

Shortcut Trick

⇒ Total work = Men × Days = 100 × 27 = 2700

⇒ Remaining men = 100 − 46 = 54

⇒ Days = 2700 / 54 = 50

∴ Answer = 50 days

Alternate Method

Given:

100 men → 27 days

Remaining men = 54

Formula:

Men × Days = Constant

Calculation:

⇒ Total provisions = 100 × 27 = 2700 man-days

⇒ Days for 54 men = 2700 / 54

⇒ = 50 days

Final Answer: 50 days

Additional Information

1. Concept: Work = Men × Days

2. Inverse Relation: More men ⇒ fewer days

3. Unit: Man-days

4. Shortcut: Multiply first, then divide

Given: Seven people B, C, O, P, Q, R and S are sitting around a circular table facing the center of the table.

 S sits to the immediate right of Q.

C sits to the immediate right of R.

C sits second to the left of B.

O sits third to the left of S.

So, B sits fourth to the right of P.

Hence, the correct answer is "Option 2".

Shortcut Trick

⇒ 2 pages → 40 min ⇒ 1 page → 20 min

⇒ 95 pages → 95 × 20 = 1900 min

∴ Answer = 1900 minutes

Alternate Method

Given:

2 pages → 40 minutes

Formula:

Time ∝ Pages

Calculation:

⇒ Time for 1 page = 40 / 2 = 20 minutes

⇒ Time for 95 pages = 95 × 20 = 1900 minutes

Final Answer: 1900 minutes

Additional Information

1. Direct Proportion: More pages ⇒ more time

2. Unitary Method: First find value for 1 unit

3. Constant Speed: Same typing speed assumed

4. Shortcut: Divide then multiply

Given: Seven boxes K, L, O, P, S, T and W are kept one over the other.

Only three boxes are kept below T.

Only one box is kept between O and T.

Only two boxes are kept between T and W.

Only W is kept above O.

S is kept immediately below O.

L is kept above K and below P.

Now, boxes between T and L: 1

Hence, the correct answer is Option 3.

Family Chart:

Decoding the Symbols:

Given: R + J @ K + C

It means: R is the daughter of J, J is the husband of K, K is the daughter of C.

 

Hence, K is mother of R

Hence, the correct answer is "Option 3".

Shortcut Trick

4:12 = 1:3 ⇒ 2.1:x = 1:3 ⇒ x = 6.3

9:36 = 1:4 ⇒ 8:y = 1:4 ⇒ y = 32

⇒ x:y = 6.3:32

⇒ Multiply by 10 ⇒ 63:320

∴ Answer = 63 : 320

Alternate Method

Given:

4 : 12 :: 2.1 : x

9 : 36 :: 8 : y

Concept Used:

a : b :: c : d ⇒ a/b = c/d

Calculation:

⇒ 4/12 = 2.1/x

⇒ 1/3 = 2.1/x

⇒ x = 2.1 × 3 = 6.3

⇒ 9/36 = 8/y

⇒ 1/4 = 8/y

⇒ y = 8 × 4 = 32

⇒ x : y = 6.3 : 32

⇒ Multiply both by 10

⇒ = 63 : 320

∴ Ratio = 63 : 320

Additional Information

Proportion Rule: a : b :: c : d ⇒ ad = bc

Simplification: Reduce ratios before solving

Decimal Handling: Multiply to remove decimals

Shortcut Tip: Convert ratios to simplest form first

The logic followed here is:

So, 'ZSJ 32' will replace the question mark in the given series.

Hence, the correct answer is "Option 1".

Given Statements:

All pigs are jackals.

All pigs are cats.

All elephants are cats.

The least possible Venn diagram shows:

Conclusions:

(I) All elephants are jackals

This does not follow because elephants are only given inside cats, and there is no link between cats and jackals. So this is false.

(II) Some cats are jackals

Since all pigs are cats and also all pigs are jackals, pigs form a common subset of cats and jackals.

So, some cats are definitely jackals. Hence this follows.

Therefore, only conclusion (II) follows.

Hence, the correct answer is "Option 2".

Shortcut Trick

Highest freq = 72 ⇒ Modal class = 20–25

⇒ l = 20, f₁=72, f₀=48, f₂=36, h=5

⇒ Mode = 20 + [(72−48)/(2×72−48−36)]×5

⇒ = 20 + (24/60)×5 = 20 + 2

∴ Answer = 22

Alternate Method

Given:

Modal class = class with highest frequency = 20–25

Concept Used:

Mode = l + [(f₁ − f₀) ÷ (2f₁ − f₀ − f₂)] × h

Calculation:

⇒ l = 20, h = 5

⇒ f₁ = 72, f₀ = 48, f₂ = 36

⇒ Mode = 20 + [(72 − 48) ÷ (2×72 − 48 − 36)] × 5

⇒ = 20 + [24 ÷ (144 − 84)] × 5

⇒ = 20 + (24 ÷ 60) × 5

⇒ = 20 + 2

⇒ = 22

∴ Mode = 22

Additional Information

Modal Class: Class with highest frequency

Formula: Mode = l + [(f₁ − f₀) ÷ (2f₁ − f₀ − f₂)] × h

Class Width: h = upper − lower limit

Shortcut Tip: Always identify modal class first

The logic followed here is:

For, HEGK → DBEJ

Now, ILNP → EILO

Now, applying the same logic for FMRT:

So, FMRT → BJPS

Hence, the correct answer is Option 3.

Shortcut Trick

A:B = 3:5, B:C = 2:3, C:D = 3:4

⇒ Make B same ⇒ LCM(5,2)=10

⇒ A:B = 6:10, B:C = 10:15

⇒ Now C same ⇒ C:D = 15:20

⇒ A:B:C:D = 6:10:15:20

⇒ A:D = 6:20 = 3:10

∴ Answer = 3 : 10

Alternate Method

Given:

A : B = 3 : 5

B : C = 2 : 3

C : D = 3 : 4

Concept Used:

Chain ratio method

Calculation:

⇒ A : B = 3 : 5

⇒ B : C = 2 : 3

⇒ Make B equal (LCM of 5 and 2 = 10)

⇒ A : B = 6 : 10

⇒ B : C = 10 : 15

⇒ So A : B : C = 6 : 10 : 15

⇒ C : D = 3 : 4

⇒ Make C equal (LCM of 15 and 3 = 15)

⇒ C : D = 15 : 20

⇒ Final ratio A : B : C : D = 6 : 10 : 15 : 20

⇒ A : D = 6 : 20 = 3 : 10

∴ Ratio of A and D = 3 : 10

Additional Information

Chain Ratio: Equalize common terms step by step

LCM Trick: Use LCM to match middle terms

Final Ratio: Extract only required terms

Shortcut Tip: Always align ratios before combining

BODMAS Table: 

Given equation: 25 A 5 B 7 C 9 D 2 = ?

Now, replacing the symbols with their meanings ‘A = ÷’, ‘B = ×’, ‘C = +’, ‘D = −’, then:

⇒ 25 ÷ 5 × 7 + 9 − 2

⇒ (25 ÷ 5) × 7 + 9 − 2

⇒ 5 × 7 + 9 − 2

⇒ 35 + 9 − 2

⇒ 44 − 2

⇒ 42

Hence, the correct answer is "Option 4".

The correct answer is Calculation using formulas.

Key Points

• Calculation using formulas is the defining characteristic of spreadsheet software. While both word processors and spreadsheets can store data, only spreadsheets are built with a calculation engine that can process mathematical, statistical, and logical data through formulas and functions. Hence, this statement is correct.
• The ability to format text, such as making it bold or changing colors, is a feature present in both Microsoft Word (word processor) and Microsoft Excel (spreadsheet). Because it is a shared feature, it does not serve as a primary differentiator. Hence, this statement is incorrect.
• The ability to change font and size is a basic functional requirement for almost all Office Productivity Tools. Users can adjust typography in both spreadsheets and word processing documents to improve readability. Hence, this statement is incorrect.
• Creating slides is the primary application of presentation software, such as Microsoft PowerPoint or Google Slides. It involves visual storytelling rather than the document-heavy focus of word processors or the data-heavy focus of spreadsheets. Hence, this statement is incorrect.

Additional Information

• Spreadsheet Software:
• Structure: It is organized into a grid of rows (identified by numbers) and columns (identified by alphabetical letters). The intersection of a row and a column is known as a cell.
• Core Functions: It is used for data analysis, financial modeling, and budgeting. Examples include Microsoft Excel, Google Sheets, and Lotus 1-2-3.
• Features: It supports automatic recalculation. When a value in a referenced cell is changed, the formula automatically updates the result.
• Data Visualization: Spreadsheets can convert numerical data into charts, graphs, and pivot tables for better analytical insights.
• Word Processing Software:
• Structure: It provides a blank page (canvas) layout primarily designed for text entry and paragraph formatting.
• Core Functions: It is used for creating letters, reports, theses, and legal documents. Common examples are Microsoft Word, Apple Pages, and Google Docs.
• Features: It includes advanced typography tools, spell check, grammar correction, thesaurus, and mail merge capabilities for mass correspondence.

Important Points

• Historical Context: The first electronic spreadsheet was VisiCalc, released in 1979 for the Apple II computer, which revolutionized business accounting.
• File Extensions: Spreadsheet files typically use extensions like .xlsx, .xls, or .csv (Comma Separated Values), whereas word processing files use .docx, .doc, or .pdf.
• Data Handling: While a word processor treats a number as a piece of text, a spreadsheet treats a number as a value that can be manipulated through operators such as addition, subtraction, multiplication, and division.
• Interoperability: Modern Office Suites allow integration, where a spreadsheet table can be embedded into a word document or a presentation slide while maintaining its dynamic calculation properties.

The correct answer is One Hundredth Amendment.

Key Points

• The One Hundredth Amendment Act, 2015 of the Constitution of India was enacted to give effect to the acquiring of certain territories by India and the transfer of certain other territories to Bangladesh. This was done in pursuance of the Land Boundary Agreement (LBA) of 1974 and its Protocol of 2011. Hence, the option regarding the One Hundredth Amendment is correct.
• Through this amendment, India transferred 111 enclaves (covering approximately 17,160 acres) to Bangladesh, while Bangladesh transferred 51 enclaves (covering approximately 7,110 acres) to India. This exchange of enclaves (also known as Chitmahals) resolved a decades-old border dispute.
• The amendment modified the First Schedule of the Constitution of India, which defines the territorial extent of the states and union territories. The changes specifically impacted the territories of four Indian states: West Bengal, Assam, Meghalaya, and Tripura.
• The Land Boundary Agreement was originally signed on May 16, 1974, by Prime Ministers Indira Gandhi and Sheikh Mujibur Rahman. However, it required a constitutional amendment in India because the Supreme Court had ruled in the Berubari Union case (1960) that any cession of Indian territory to a foreign nation requires an amendment under Article 368.

Additional Information

• Ninety-Seventh Amendment (2011):
• This amendment gave constitutional status and protection to co-operative societies.
• It made the right to form co-operative societies a fundamental right under Article 19(1)(c).
• It inserted a new Directive Principle of State Policy (Article 43B) for the promotion of co-operative societies and added Part IXB to the Constitution.
• Ninety-Eighth Amendment (2012):
• It provided for special provisions for the Hyderabad-Karnataka region of the state of Karnataka.
• It inserted Article 371J to empower the Governor of Karnataka to take steps for the development of this backward region, including the creation of a separate development board and equitable allocation of funds.
• One Hundred and First Amendment (2016):
• This amendment paved the way for the introduction of the Goods and Services Tax (GST) in India.
• It replaced various indirect taxes levied by the Central and State Governments with a single unified tax system to create a common national market.
• It led to the insertion of Articles 246A, 269A, and 279A (relating to the GST Council).

Important Points

• Humanitarian Aspect: The 100^th Amendment was significant not just for geopolitics but for human rights. Around 51,000 residents living in these enclaves were previously "stateless" and lacked access to basic government services. Post-amendment, they were given the choice of citizenship in either India or Bangladesh.
• Un-demarcated Boundary: Besides the exchange of enclaves, the agreement also settled the demarcation of a 6.1-kilometer un-demarcated border stretch and the issue of adverse possessions (territories occupied by one country but legally belonging to another).
• Ratification: The Constitution (100^th Amendment) Bill was passed by the Rajya Sabha on May 6, 2015, and by the Lok Sabha on May 7, 2015, reflecting a rare political consensus in the Parliament of India.

The correct answer is High-capacity coal-based power plants.

Key Points

• The primary objective of the Ultra Mega Power Projects (UMPP) initiative is to develop high-capacity coal-based power plants, each having a capacity of approximately 4,000 MW or more.
• These projects are designed to deliver power at minimum cost to consumers through economies of scale and the use of supercritical technology.
• The initiative was launched by the Ministry of Power, Government of India, in association with the Power Finance Corporation (PFC), which acts as the nodal agency and bid process coordinator.
• The UMPP model involves International Competitive Bidding (ICB) to select developers who can build, own, and operate these massive energy infrastructures.
• Regarding the options provided in the question:
• Rooftop solar systems in rural areas: This refers to decentralized renewable energy initiatives like the PM-KUSUM or Grid-Connected Rooftop Solar Scheme, not UMPP. Hence, this statement is incorrect.
• Small-scale solar plants: These are typically handled under the National Solar Mission for localized energy needs. Hence, this statement is incorrect.
• Wind farms in rural areas: Wind energy development is governed by the National Offshore Wind Energy Policy and other renewable targets, distinct from the coal-centric UMPP. Hence, this statement is incorrect.
• High-capacity coal-based power plants: This is the core definition and objective of the Ultra Mega Power Projects to ensure energy security for the country. Hence, this statement is correct.

Additional Information

• History and Launch: The UMPP scheme was initiated in 2005-06 to facilitate rapid capacity addition in the Indian power sector and to attract private investment.
• Types of UMPPs:
• Pit-head projects: Located near coal mines, where coal is transported via conveyor belts (e.g., Sasan in Madhya Pradesh).
• Coastal projects: Located at coastal locations to utilize imported coal arriving via sea routes (e.g., Mundra in Gujarat).
• Mechanism of Development: For each project, a Special Purpose Vehicle (SPV) is incorporated as a wholly-owned subsidiary of PFC. This SPV is responsible for obtaining environmental clearances, land acquisition, and water allocation before handing over the project to the successful bidder.
• Key Examples:
• Mundra UMPP: Located in Gujarat, developed by Tata Power (Coastal).
• Sasan UMPP: Located in Madhya Pradesh, developed by Reliance Power (Pit-head).
• Krishnapatnam UMPP: Located in Andhra Pradesh (Coastal).
• Tilaiya UMPP: Located in Jharkhand (Pit-head).
• Features and Technology: UMPPs utilize supercritical technology, which operates at higher pressures and temperatures, leading to higher efficiency and lower carbon dioxide emissions per unit of electricity generated compared to subcritical plants.

Important Points

• Tariff-Based Bidding: The developers are selected based on the lowest levelized tariff offered over a period of 25 years, ensuring competitive pricing for state distribution companies (DISCOMs).
• Regulatory Framework: These projects fall under the Electricity Act, 2003, and the National Electricity Policy, which aim to provide "Power for All" across the Indian territory.
• Current Status: While several UMPPs were planned, some faced delays due to issues in coal block allocations, environmental concerns, and changes in international coal prices (especially for coastal projects).
• Data and Impact: A single 4,000 MW project can cater to the electricity needs of multiple states, significantly bridging the peak demand-supply gap in the national grid.

Shortcut Trick

(5/4)×2.4 = 1.25×2.4 = 3

⇒ Expression = 3.6 + 3 − 0.5

⇒ = 6.6 − 0.5 = 6.1

∴ Answer = 6.1

Alternate Method

Given:

3.6 + (5 ÷ 4) × 2.4 − (1 ÷ 2)

Concept Used:

BODMAS rule

Calculation:

⇒ (5 ÷ 4) × 2.4 = 1.25 × 2.4 = 3

⇒ 3.6 + 3 − 0.5

⇒ = 6.6 − 0.5

⇒ = 6.1

∴ The correct answer is 6.1

Additional Information

BODMAS: Solve multiplication/division before addition/subtraction

Fraction to Decimal: 5/4 = 1.25, 1/2 = 0.5

Shortcut: Simplify multiplication first to reduce steps

Tip: Convert fractions to decimals for faster calculation

The correct answer is To skill rural youth and promote wage employment opportunities.

Key Points

• The Deen Dayal Upadhyaya Grameen Kaushalya Yojana (DDU-GKY) was launched on 25^th September 2014 by the Ministry of Rural Development (MoRD). The primary objective is to transform rural poor youth into an economically independent and globally relevant workforce.
• It is a placement-linked skill training program that targets rural youth between the age of 15 and 35 years. For vulnerable groups like women, persons with disabilities (PWDs), and SC/ST candidates, the upper age limit is relaxed up to 45 years.
• The scheme is a critical part of the National Rural Livelihoods Mission (NRLM), focusing on adding diversity to the incomes of rural poor families and catering to the career aspirations of rural youth. Hence, the statement regarding skilling rural youth for wage employment is correct.
• DDU-GKY uniquely mandates that at least 70% of the trained candidates must be guaranteed placement with a minimum salary of ₹6,000 per month (or as per the minimum wages, whichever is higher). This ensures the scheme is outcome-oriented rather than just focusing on training.
• The scheme follows a three-tier implementation model, involving the Ministry of Rural Development at the national level, State Rural Livelihood Missions (SRLM) or State Skills Missions, and Project Implementing Agencies (PIAs) which are typically private or public sector training providers.

Additional Information

• Evolution of the Scheme: DDU-GKY is the successor to the Swarnjayanti Gram Swarozgar Yojana-Special Projects (SGSY-SP). It was revamped to focus specifically on wage employment in the formal sector rather than self-employment, which was the focus of earlier iterations.
• Funding Pattern: The funding for DDU-GKY is shared between the Central Government and the State Governments in a 60:40 ratio. However, for North-Eastern States, Himachal Pradesh, and Uttarakhand, the funding ratio is 90:10.
• Social Inclusion: To ensure the benefits reach the most marginalized, the scheme mandates earmarked coverage for specific groups: 50% for SC/ST, 15% for Minorities, and 33% for Women.
• Geographical Coverage: The scheme is implemented across all states and Union Territories of India. It specifically targets rural areas as defined by the Census of India.
• International Standards: The training provided under DDU-GKY is aligned with the National Skills Qualification Framework (NSQF), ensuring that the skills gained by the rural youth are recognized by employers across the country and even internationally.

Important Points

• Champion Employers: The program identifies "Champion Employers" who can provide training and career progression for at least 10,000 candidates over a 2-year period. This partnership helps in scaling up the impact of the yojana.
• Alumni Support: DDU-GKY provides post-placement support to candidates, such as migration support centers, to help rural youth adjust to urban work environments after their placement.
• Global Outlook: By 2020, India was predicted to have a surplus of 55 million working-age people, while the rest of the world faced a shortage. DDU-GKY aims to leverage this demographic dividend by preparing youth for global employment opportunities.

The logic followed here is:

For, WXPL → VZMP

Now, ZUQH → YWNL

Now, applying the same logic for TRKF:

So, TRKF → STHJ

Hence, the correct answer is Option 3.

The correct answer is Jharkhand.

Key Points

• Chhau dance is a formidable semi-classical Indian dance with martial, tribal, and folk traditions, which found its primary origin in the Seraikella region of Jharkhand. Hence, the statement regarding Jharkhand is correct.
• This dance form is deeply rooted in the local culture and is primarily performed by male dancers from families of traditional artists or from local communities.
• In 2010, UNESCO inscribed Chhau dance on the Representative List of the Intangible Cultural Heritage of Humanity, recognizing its cultural significance and unique artistic expression.
• The dance is traditionally performed during the spring festival known as Chaitra Parva, which typically falls in the month of April and lasts for thirteen days.
• It is characterized by its vigorous movements, acrobatics, and athleticism, which are derived from martial arts techniques (specifically Parikhanda) and mock combat.

Additional Information

• Regional Variations: There are three distinct styles of Chhau named after the locations where they are performed:
• Seraikella Chhau: Developed in the Seraikella Kharsawan district of Jharkhand. This style is known for its sophisticated use of masks to depict characters.
• Purulia Chhau: Developed in the Purulia district of West Bengal. This style also uses masks, which are typically larger and more theatrical than the Seraikella variety.
• Mayurbhanj Chhau: Developed in the Mayurbhanj district of Odisha. Unlike the other two, this style does not use masks, relying instead on facial expressions and body movements.
• Themes and Narratives: The dance performances usually depict episodes from great Hindu epics such as the Ramayana and Mahabharata, as well as stories from the Puranas and other Indian literature.
• Musical Accompaniment: The music is based on folk melodies and is played on traditional instruments such as the Dhol (a cylindrical drum), Dhumsa (a large kettle drum), and Mohuri (a reed instrument similar to the shehnai).
• Costumes and Masks: The masks are a central feature in the Jharkhand and West Bengal traditions, crafted by local artisans using clay, paper-mâché, and cloth. They are painted in vibrant colors to represent gods, goddesses, demons, and animals.

Important Points

• Uttarakhand: This state is famous for folk dances like Chholiya, which is a martial art dance performed during marriages and other celebrations. However, it is not the place of origin for Chhau. Hence, the statement regarding Uttarakhand is incorrect.
• Punjab: The state of Punjab is world-renowned for the Bhangra and Giddha dance forms, which are energetic folk dances associated with the harvest season (Vaisakhi). These are distinct from the semi-classical nature of Chhau. Hence, the statement regarding Punjab is incorrect.
• Haryana: Folk dances such as Loor, Phag, and Dhamal are native to Haryana. These dances are mostly related to agriculture and seasonal festivals like Holi. Hence, the statement regarding Haryana is incorrect.
• Cultural Impact: Chhau serves as a powerful medium for social cohesion, bringing together people from different social strata and ethnic backgrounds to participate in the performance and the festivities of Chaitra Parva.
• Modern Status: Today, Chhau is recognized as one of the classical-adjacent dances of India, and the Sangeet Natak Akademi provides significant support for its preservation and promotion across Jharkhand, Odisha, and West Bengal.

Shortcut Trick

Area = l × b = 10 × √5

⇒ √5 ≈ 2.236

⇒ Area ≈ 10 × 2.236 = 22.36

∴ Answer = 22.36 cm²

Alternate Method

Given:

Length = 10 cm

Width = √5 cm

Concept Used:

Area of rectangle = Length × Width

10  √5

Calculation:

⇒ Area = 10 × √5

⇒ √5 ≈ 2.236

⇒ Area ≈ 10 × 2.236 = 22.36 cm²

∴ Area ≈ 22.36 cm²

Additional Information

Rectangle Area: A = l × b

Square Root Approx: √5 ≈ 2.236

Rounding Rule: Round to 2 decimal places

Shortcut Tip: Memorize common √ values for speed

The logic followed here is based on the alphabetical positional difference between corresponding letters in each pair:

Option 1: EH − FI

Option 2: LO − PS

Option 3: AD − BE

Option 4: RU − SV

Thus, LO-PS is different from the rest.

Hence, the odd one out is Option 2.

The correct answer is 131.

Key Points

• The Global Gender Gap Index for the year 2025 (based on the latest comparative assessments of 148 nations) placed India at the 131^st rank, reflecting the nation's ongoing challenges and progress in achieving gender parity.
• The index is an annual publication released by the World Economic Forum (WEF), an international non-governmental organization based in Cologny, Geneva, Switzerland.
• The report evaluates countries across four critical dimensions: Economic Participation and Opportunity, Educational Attainment, Health and Survival, and Political Empowerment.
• In the 2025 assessment involving 148 countries, India showed slight fluctuations compared to the previous years (such as 129^th in 2024), highlighting specific gaps in Economic Participation and Health metrics.
• The Global Gender Gap Index scores range from 0 to 1, where 1 represents full gender parity and 0 represents complete imparity; the 131^st rank indicates that India has a significant journey ahead to close the gender gap.

Additional Information

• History and Origin: The Global Gender Gap Index was first introduced by the World Economic Forum in 2006. It was designed to measure gender-based gaps in access to resources and opportunities in countries rather than the actual level of the resources available.
• Top Performers: Historically, Nordic countries like Iceland, Norway, and Finland have consistently topped the index. Iceland has been the most gender-equal country in the world for over a decade, having closed more than 90% of its gender gap.
• The Four Pillars of Assessment:
• Economic Participation and Opportunity: This includes indicators like labour force participation rates, wage equality for similar work, and the ratio of women in senior-level positions.
• Educational Attainment: This measures the gap between women’s and men’s access to primary, secondary, and tertiary education levels.
• Health and Survival: This pillar looks at the sex ratio at birth and healthy life expectancy.
• Political Empowerment: This measures the ratio of women in parliament, ministerial positions, and the number of years with a female head of state.
• India's Context: While India often performs relatively well in Political Empowerment due to historical leadership roles and local government reservations, it consistently lags in Health and Survival and Economic Participation, where the female labour force participation rate (LFPR) remains a point of concern.
• Comparison with Other Indices: The Global Gender Gap Index is distinct from the Gender Inequality Index (GII), which is published by the United Nations Development Programme (UNDP). The GII also considers reproductive health and maternal mortality rates, where India ranked 108^th in the 2022 report (released in 2024).

Important Points

• Data and Trends: According to WEF reports, at the current rate of progress, it will take approximately 131 to 134 years to reach full global gender parity.
• Global Coverage: The index has grown from 115 countries in 2006 to 148 countries in the 2025 cycle, making it one of the most comprehensive benchmarks for gender equality worldwide.
• SDG 5: The findings of this index are crucial for monitoring progress toward Sustainable Development Goal 5 (SDG 5), which aims to achieve gender equality and empower all women and girls by the year 2030.
• Policy Influence: Governments use this data to draft legislation, such as the Women's Reservation Bill (Nari Shakti Vandan Adhiniyam) passed in India in September 2023, which seeks to reserve 33% of seats in the Lok Sabha and state assemblies for women.

The logic followed here is:

Given: (Left) B R © # # # W & S @ Z @ @ A & L @ @ I © O © (Right)

Now, we need letters which are immediately preceded by a letter and also immediately followed by a symbol.

So, Needed pattern is: Letter - Letter - Symbol

(Left) B R © # # # W & S @ Z @ @ A & L @ @ I © O © (Right)

Now, Total = 1.

Hence, the correct answer is Option 1.

Shortcut Trick

⇒ 2/sinA = 3/cosA

⇒ 2cosA = 3sinA

⇒ tanA = 2/3

⇒ Given expression:

= (1 − cos²A)/(1 − sin²A)

= sin²A / cos²A = tan²A

⇒ tan²A = (2/3)² = 4/9

Final Answer: 4/9

Alternate Method

Given:

2cosecA = 3secA

Formula:

cosecA = 1/sinA, secA = 1/cosA

1 − cos²A = sin²A, 1 − sin²A = cos²A

Calculation:

⇒ (1−cosA)(1+cosA) = 1 − cos²A = sin²A

⇒ (1−sinA)(1+sinA) = 1 − sin²A = cos²A

⇒ Expression = sin²A / cos²A = tan²A

⇒ Given: 2cosecA = 3secA

⇒ 2/sinA = 3/cosA ⇒ 2cosA = 3sinA

⇒ tanA = 2/3

⇒ tan²A = (2/3)² = 4/9

∴ Answer = 4/9

Additional Information

1. Identity: (1−a)(1+a) = 1−a²

2. Trig Identity: sin²A + cos²A = 1

3. Ratio: tanA = sinA/cosA

4. Trick: Reduce expression first, then substitute

The correct answer is Regulating Act, 1773.

Key Points

• The Regulating Act of 1773 was the first major step taken by the British Parliament to control and regulate the affairs of the East India Company in India. It recognized for the first time the political and administrative functions of the Company.
• This Act designated the Governor of Bengal as the Governor-General of Bengal and created an Executive Council of four members to assist him. Lord Warren Hastings was the first such Governor-General. Hence, the statement regarding regulation of Bengal's administration is correct.
• It provided for the establishment of a Supreme Court at Calcutta in the year 1774, comprising one Chief Justice and three other judges. Sir Elijah Impey was appointed as the first Chief Justice.
• The Act prohibited the servants of the Company from engaging in any private trade or accepting presents and bribes from the "natives," aiming to curb corruption within the administration.
• It strengthened the control of the British Government over the Company by requiring the Court of Directors (the governing body of the Company) to report on its revenue, civil, and military affairs in India.

Additional Information

• Pitt’s India Act, 1784:
• This Act was passed to rectify the defects of the Regulating Act of 1773. It established a system of double government by creating a Board of Control to manage political affairs while the Court of Directors managed commercial affairs.
• For the first time, the Company’s territories in India were called the “British possessions in India.”
• Charter Act, 1813:
• This Act ended the monopoly of the East India Company over trade in India, except for trade in tea and trade with China.
• It allotted an annual sum of one lakh rupees for the promotion of education and knowledge of sciences among the inhabitants of British India.
• Government of India Act, 1858:
• Enacted in the wake of the Revolt of 1857, this Act abolished the East India Company and transferred the powers of government, territories, and revenues to the British Crown.
• The designation of the Governor-General of India was changed to the Viceroy of India. Lord Canning became the first Viceroy.

Important Points

• The Regulating Act of 1773 laid the foundations of central administration in India by making the Governors of Bombay and Madras presidencies subordinate to the Governor-General of Bengal.
• Prior to this Act, the three Presidencies (Bengal, Bombay, and Madras) were independent of one another.
• The Executive Council members under the 1773 Act were Philip Francis, Richard Barwell, John Clavering, and George Monson.
• While the Act was a landmark, it had flaws, such as the lack of clarity between the jurisdiction of the Governor-General-in-Council and the Supreme Court, which eventually led to the passage of the Act of Settlement in 1781 and Pitt's India Act in 1784.