The correct answer is Sachindra Nath Bakshi.

Key Points

• The Kakori Conspiracy Case, also known as the Kakori Train Robbery, took place on 9 August 1925, in a small village called Kakori near Lucknow, Uttar Pradesh.
• Rajendra Lahiri was a prominent member of the Hindustan Republican Association (HRA). He was found guilty of participating in the robbery and was awarded the death sentence. He was hanged in Gonda Jail on 17 December 1927, two days before the scheduled date. Statement 1 is incorrect as he was sentenced to death.
• Ashfaqulla Khan was a key strategist and the first Muslim to be hanged in a conspiracy case against the British Raj. He was sentenced to a death sentence and was executed on 19 December 1927, in Faizabad Jail. Statement 2 is incorrect as he was sentenced to death.
• Sachindra Nath Bakshi was a revolutionary and a member of the HRA who participated in the robbery. Unlike his comrades, he was not sentenced to death; instead, he was awarded life imprisonment (transportation for life) and sent to the Cellular Jail in the Andaman and Nicobar Islands. Statement 3 is correct.
• Roshan Singh (Thakur Roshan Singh) was another revolutionary involved in the conspiracy. Although he was not directly involved in the train robbery itself but was associated with the Bamrauli action, he was convicted and given a death sentence. He was hanged in Naini Allahabad Jail on 19 December 1927. Statement 4 is incorrect as he was sentenced to death.

Additional Information

• Hindustan Republican Association (HRA):
• The HRA was a revolutionary organization established in October 1924 in Kanpur.
• The founding members included Sachindra Nath Sanyal, Ram Prasad Bismil, and Jogesh Chandra Chatterjee.
• The objective of the association was to establish a Federal Republic of United States of India through an armed revolution.
• The Kakori Train Robbery was planned to acquire funds from the British Treasury to purchase weapons and support the organization's activities.
• Ram Prasad Bismil:
• He was the primary leader and mastermind behind the Kakori robbery.
• He was a gifted poet who wrote under the pen names Bismil, Ram, and Agyat.
• He was awarded the death sentence and hanged on 19 December 1927, in Gorakhpur Jail.
• Evolution to HSRA:
• After the crackdown following the Kakori incident, the organization was reorganized as the Hindustan Socialist Republican Association (HSRA) in 1928 at Feroz Shah Kotla, Delhi.
• Leaders like Chandrashekhar Azad, Bhagat Singh, and Sukhdev played pivotal roles in this transition towards Socialist ideologies.

Important Points

• Chandrashekhar Azad was the only major leader involved in the Kakori Conspiracy who successfully evaded arrest by the British police. He continued the revolutionary struggle until his death in Alfred Park, Allahabad in February 1931.
• The British Government arrested approximately 40 revolutionaries from various cities across India for their alleged involvement in the conspiracy.
• The legal defense for the revolutionaries was led by prominent figures such as Govind Ballabh Pant and Chandra Bhanu Gupta, although the Special Magistrate's Court ultimately handed down severe punishments to suppress the uprising.
• Sachindra Nath Bakshi survived his imprisonment and was released in 1937 after the formation of the Congress governments in provinces. He later participated in the Quit India Movement in 1942.

Shortcut Trick

⇒ Highest frequency = 39 ⇒ Modal class = 60–70

⇒ l = 60, h = 10

⇒ f₁ = 39, f₀ = 28, f₂ = 10

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

⇒ = 60 + [(39−28)/(78 − 28 − 10)] × 10

⇒ = 60 + (11/40) × 10

⇒ = 60 + 2.75 = 62.75

∴ Answer = 62.75

Alternate Method

Given:

Class intervals: 20–30, 30–40, 40–50, 50–60, 60–70, 70–80, 80–90

Frequencies: 31, 29, 33, 28, 39, 10, 18

Formula:

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

Calculation:

⇒ Modal class = 60–70 (highest frequency = 39)

⇒ l = 60, h = 10

⇒ f₁ = 39, f₀ = 28, f₂ = 10

⇒ Mode = 60 + [(39 − 28)/(78 − 28 − 10)] × 10

⇒ = 60 + (11/40) × 10

⇒ = 60 + 2.75 = 62.75

Final Answer: 62.75

Additional Information

1. Modal Class: Highest frequency class

2. Formula Use: For grouped data

3. Terms: f₁ (modal), f₀ (previous), f₂ (next)

4. Class Width: h = 10

Shortcut Trick

⇒ Mode = value with highest frequency

⇒ Highest frequency = 12

⇒ Corresponding height = 21 cm

∴ Answer = 21 cm

Alternate Method

Given:

Heights: 14, 27, 23, 21, 19, 17

Frequencies: 1, 3, 6, 12, 7, 5

Formula:

Mode = Observation with highest frequency

Calculation:

⇒ Compare frequencies: 1, 3, 6, 12, 7, 5

⇒ Maximum frequency = 12

⇒ Corresponding height = 21 cm

Final Answer: 21 cm

Additional Information

1. Mode: Most frequently occurring value in data

2. Discrete Data: Mode is directly identified from frequency

3. Grouped Data: Mode calculated using formula

4. Use Case: Helps identify most common observation

The correct answer is Lala Lajpat Rai.

Key Points

• Lala Lajpat Rai was a prominent Indian nationalist leader who played a pivotal role in the Indian Independence Movement. He was popularly known as Punjab Kesari or the ‘Lion of Punjab’ due to his fierce advocacy for self-rule.
• He was a key member of the Extremist faction of the Indian National Congress, famously known as the Lal-Bal-Pal trio, which included Lala Lajpat Rai, Bal Gangadhar Tilak, and Bipin Chandra Pal.
• In 1894, he was instrumental in the founding of the Punjab National Bank (PNB), which was the first Swadeshi bank in India, and the Lakshmi Insurance Company.
• He led a non-violent protest against the Simon Commission in Lahore on 30 October 1928. During this protest, he was severely injured in a lathi charge ordered by the local police superintendent, James A. Scott.
• Following the injuries sustained during the protest, he passed away on 17 November 1928. His death sparked a wave of revolutionary activities among the youth of India, leading to the Saunders' murder case involving Bhagat Singh and his associates.

Additional Information

• Bhagat Singh:
• Commonly known as Shaheed-e-Azam, he was a charismatic Indian revolutionary who played a crucial role in the movement for independence.
• He founded the Naujawan Bharat Sabha in March 1926 and was a leading member of the Hindustan Socialist Republican Association (HSRA).
• He, along with Batukeshwar Dutt, threw non-lethal bombs into the Central Legislative Assembly in April 1929 to protest against the Public Safety Bill and the Trade Dispute Bill.
• He was executed on 23 March 1931 at the age of 23 in Lahore Jail.
• Bal Gangadhar Tilak:
• Known as Lokmanya (accepted by the people) and the 'Father of Indian Unrest' by British colonial authorities.
• He was a founding member of the All India Home Rule League established in 1916 alongside Annie Besant.
• He popularized the slogan, "Swaraj is my birthright and I shall have it!" and published influential newspapers such as Kesari (in Marathi) and The Mahratta (in English).
• Rajguru (Shivaram Hari Rajguru):
• A brave revolutionary from Maharashtra, he was a member of the HSRA and a close associate of Bhagat Singh and Sukhdev.
• He participated in the assassination of John P. Saunders in 1928 to avenge the death of Lala Lajpat Rai.
• He was hanged on 23 March 1931, and his sacrifice is commemorated annually as Shaheed Diwas (Martyrs' Day).

Important Points

• Literary Contributions: Lala Lajpat Rai was a prolific writer. His famous works include 'Unhappy India', 'The Political Future of India', and 'England’s Debt to India'. He also founded the Servants of the People Society in 1921.
• Religious and Social Work: He was deeply influenced by Swami Dayananda Saraswati and was a prominent leader of the Arya Samaj movement in Punjab.
• Role in Congress: He presided over the Special Session of the Indian National Congress in Calcutta in 1920, where the Non-Cooperation Movement resolution was passed.
• Legacy: To honor his legacy, Lala Lajpat Rai University of Veterinary and Animal Sciences was established in Hisar, Haryana, and his birthday on 28 January is celebrated in various parts of India.

The correct answer is Trafficking in human beings.

Key Points

• Article 23 of the Constitution of India is a significant provision that prohibits trafficking in human beings, begar, and other similar forms of forced labour.
• Statement 1: Compulsory service in the armed forces is not prohibited; rather, Article 23(2) allows the State to impose compulsory service for public purposes, such as military or social service, provided there is no discrimination based on religion, race, caste, or class. Hence, statement 1 is incorrect.
• Statement 2: The conferring of titles (except military and academic) is prohibited and regulated under Article 18 of the Indian Constitution to ensure social equality. Hence, statement 2 is incorrect.
• Statement 3: The prohibition of child employment in factories, mines, or any hazardous industries is specifically covered under Article 24 for children below the age of 14 years. Hence, statement 3 is incorrect.
• Statement 4: Trafficking in human beings and forced labour are explicitly prohibited under Article 23(1), and any violation is considered an offence punishable under the law. Hence, statement 4 is correct.
• The Right Against Exploitation is enshrined in Articles 23 and 24 to protect the dignity of the individual and prevent exploitation by the State or private persons.

Additional Information

• Legislative Actions: To implement the mandate of Article 23, the Parliament of India has enacted several laws, including the Immoral Traffic (Prevention) Act, 1956 and the Bonded Labour System (Abolition) Act, 1976.
• Scope of Article 23: This Fundamental Right is available to both citizens and foreigners, and it acts as a safeguard against exploitation by both State authorities and private individuals.
• Definition of Begar: The term 'Begar' specifically means involuntary work without payment or remuneration, which was traditionally practiced in India under the zamindari system.
• Human Trafficking: This involves the illegal trade of humans for sexual slavery, forced labour, or commercial sexual exploitation, which is strictly prohibited under the Constitution.
• The 44^th Amendment Act: While Fundamental Rights can be suspended during an Emergency, the Right Against Exploitation remains a crucial pillar of Indian democracy.

Important Points

• Article 35: Under this Article, the Parliament has the exclusive power to make laws to prescribe punishment for those acts declared as offences under Article 23.
• Article 23(2) Exception: The State can require compulsory service (like conscription) for national security or social service, but it cannot discriminate between citizens on religious or racial grounds while doing so.
• Forced Labour: The Supreme Court of India has interpreted 'forced labour' broadly to include labor arising from economic circumstances where a person is forced to work for less than minimum wages.
• International Context: Article 23 aligns with international standards like the Universal Declaration of Human Rights (UDHR) and International Labour Organization (ILO) conventions against forced labour.

The logic followed here is:

thus, "45" will replace the question mark in the given series.

Hence, the correct option is "Option 3".

The correct answer is 2015.

Key Points

• The Digital India programme was officially launched on July 1, 2015, by Prime Minister Narendra Modi. The initiative was designed to transform India into a digitally empowered society and a knowledge economy.
• It is an ambitious umbrella programme that covers multiple Government Ministries and Departments. It weaves together a large number of ideas and thoughts into a single, comprehensive vision so that each of them can be implemented as part of a larger goal.
• The Ministry of Electronics and Information Technology (MeitY) is the nodal agency responsible for the overall coordination and implementation of this flagship scheme.
• The motto of the programme is "Power To Empower," focusing on three key vision areas: Digital Infrastructure as a Core Utility to Every Citizen, Governance and Services on Demand, and Digital Empowerment of Citizens.
• The programme aims to provide high-speed internet connectivity to all Gram Panchayats and ensure that government services are available to citizens electronically, thereby improving efficiency and transparency.

Additional Information

• The Digital India initiative is centered on 9 Pillars of growth, which include:
• Broadband Highways: To cover all 2.5 lakh Gram Panchayats under the National Optical Fibre Network (NOFN).
• Universal Access to Mobile Connectivity: To ensure mobile coverage in the remaining uncovered villages in the country.
• Public Internet Access Programme: Strengthening Common Service Centres (CSCs) and transforming post offices into multi-service centers.
• e-Governance: Reforming government through technology by simplifying forms and tracking applications online.
• e-Kranti: Electronic delivery of services such as e-Education, e-Healthcare, and e-Justice.
• Information for All: Hosting data on Open Data platforms to facilitate transparency and accessibility for the public.
• Electronics Manufacturing: Aiming for Net Zero Imports in electronics by the year 2020 through domestic production.
• IT for Jobs: Training youth in smaller towns and villages for IT sector jobs and BPO operations.
• Early Harvest Programmes: Implementation of quick-result projects like Biometric Attendance and Wi-Fi in All Universities.

Important Points

• DigiLocker: A key initiative under the programme launched in 2015 to provide a secure cloud-based platform for storage, sharing, and verification of documents and certificates.
• BHIM (Bharat Interface for Money): Launched in December 2016, it is a mobile payment app based on Unified Payments Interface (UPI) that facilitated the digital payment revolution in India.
• UMANG (Unified Mobile Application for New-age Governance): A single mobile app that provides access to over 1,200 central and state government services, supporting the goal of mobile governance.
• Pradhan Mantri Gramin Digital Saksharta Abhiyan (PMGDISHA): One of the world's largest digital literacy programmes, aimed at making 6 crore rural households digitally literate.
• Impact and Data: As of recent reports, India has seen a massive surge in internet subscribers, exceeding 800 million, and has become the global leader in real-time digital transactions, accounting for nearly 46% of global digital payments in 2022.

The correct answer is 1955.

Key Points

• The National Small Industries Corporation (NSIC) was established in the year 1955 as a Government of India enterprise. Hence, the year 1955 is the correct answer.
• It functions under the administrative control of the Ministry of Micro, Small and Medium Enterprises (MSME). It was created to promote, aid, and foster the growth of small industries in the country.
• In 1955, the corporation started with the primary objective of facilitating the procurement of government orders for small-scale units and providing them with machinery on a hire-purchase basis.
• The NSIC acts as a nodal agency to implement various schemes of the Ministry of MSME, focusing on Marketing, Technology, and Finance support services for small enterprises.
• The establishment of NSIC in 1955 marked a significant step in India's industrial policy to encourage entrepreneurship and employment generation through the small-scale sector.

Additional Information

• Marketing Support: NSIC helps MSMEs through the Single Point Registration Scheme (SPRS), which allows small units to participate in Government Stores Purchase Programmes without paying earnest money deposits.
• Financial Assistance: It provides Raw Material Assistance by financing the purchase of raw materials (both indigenous and imported) and also has tie-ups with commercial banks to facilitate working capital for small units.
• Technology Support: The corporation manages several NSIC Technical Services Centres (NTSCs) across India (e.g., in New Delhi, Rajkot, Ludhiana, and Howrah) to provide technical training and common facility support.
• Exhibition and Trade Fairs: To provide international and domestic exposure, NSIC organizes and participates in various Trade Fairs and Exhibitions, helping MSMEs showcase their products to a global audience.
• B2B Portal: NSIC manages a specialized B2B Web Portal (MSMEMart) to facilitate e-commerce and marketing linkages for small-scale industries in the digital era.

Important Points

• Headquarters: The NSIC is headquartered in Okhla, New Delhi.
• Mini Ratna Status: The corporation has been recognized with the Mini Ratna Category-II status, reflecting its financial performance and operational efficiency as a Public Sector Undertaking (PSU).
• International Cooperation: NSIC has shared the Indian experience of Small Business Development with many developing nations in Africa and Asia, helping them set up similar institutional frameworks.
• ISO Certification: It is an ISO 9001:2015 certified company, ensuring that its service delivery and management systems meet international standards.
• Other Options Context: While 1954 saw the establishment of the Small Industries Development Organization (SIDO), NSIC was specifically incorporated in 1955. 1982 is notable for the establishment of NABARD and EXIM Bank, and 1975 marked the beginning of Regional Rural Banks (RRBs).

Shortcut Trick

⇒ Let original CSA = 2πrh and TSA = 2πrh + 2πr²

⇒ After cutting into 5 parts → CSA unchanged, flat surfaces increase

⇒ Given: total CSA = total flat area ⇒ 2πrh = 10πr²

⇒ ⇒ h = 5r

⇒ Each piece TSA = S = (2πr·h/5 + 2πr²) = (2πr² + 2πr²) = 4πr²

⇒ Original TSA = 2πr·5r + 2πr² = 12πr² = 3S

∴ Answer = 3S

Alternate Method

Given:

Cylinder cut into 5 equal parts

CSA (all pieces) = Flat surface area (all pieces)

Formula:

CSA = 2πrh

Flat area after cut = top + bottom + cuts = 2πr² + 8πr² = 10πr²

Calculation:

⇒ 2πrh = 10πr²

⇒ h = 5r

⇒ TSA of one piece = curved + top + bottom

⇒ = 2πr(h/5) + 2πr²

⇒ = 2πr(r) + 2πr² = 4πr² = S

⇒ Original TSA = 2πrh + 2πr²

⇒ = 2πr(5r) + 2πr² = 12πr²

⇒ = 3S

Final Answer: 3S

Additional Information

1. Cylinder CSA: 2πrh

2. Cylinder TSA: 2πrh + 2πr²

3. Cutting Effect: New flat surfaces increase, CSA unchanged

4. Key Insight: Use equality condition to find relation between r and h

Shortcut Trick

⇒ Circumference = 2πr = 5.5 ⇒ r = 5.5 × 7 / (2×22) = 0.875 cm

⇒ Thickness = 2 mm = 0.2 cm

⇒ Volume of coin = πr²h = (22/7)×(0.875)²×0.2 ≈ 0.48125 cm³

⇒ Volume of cuboid = 14×11×8 = 1232 cm³

⇒ Number = 1232 / 0.48125 ≈ 2560

∴ Answer = 2560

Alternate Method

Given:

Circumference = 5.5 cm

Thickness = 2 mm = 0.2 cm

Cuboid dimensions = 14, 11, 8 cm

Formula:

Volume of cylinder = πr²h

Volume of cuboid = l×b×h

   Coin     Cuboid

Calculation:

⇒ 2πr = 5.5 ⇒ r = (5.5×7)/(44) = 0.875 cm

⇒ Volume of one coin = (22/7)×(0.875)²×0.2 ≈ 0.48125 cm³

⇒ Volume of cuboid = 14×11×8 = 1232 cm³

⇒ Number of coins = 1232 / 0.48125 ≈ 2560

Final Answer: 2560

Additional Information

1. Circumference: 2πr

2. Unit Conversion: 1 cm = 10 mm

3. Volume Conservation: Total volume remains same after melting

4. Cylinder Concept: Coin treated as small cylinder

Shortcut Trick

⇒ Let a = 7^2/3, b = 7^-2/3

⇒ x = a − b

⇒ Use identity: (a − b)³ + 3(a − b) = a³ − b³

⇒ = 7² − 7^-2 = 49 − 1/49

∴ Answer = 2400/49

Alternate Method

Given:

x = 7^2/3 − 7^-2/3

Formula:

(a − b)³ = a³ − b³ − 3ab(a − b)

Calculation:

⇒ Let a = 7^2/3, b = 7^-2/3

⇒ x = a − b

⇒ x³ = a³ − b³ − 3ab(a − b)

⇒ x³ = a³ − b³ − 3abx

⇒ x³ + 3x = a³ − b³ − 3abx + 3x

⇒ Since ab = 1 ⇒ −3abx + 3x = 0

⇒ x³ + 3x = a³ − b³

⇒ = 7² − 7^-2 = 49 − 1/49

⇒ = (2401 − 1)/49 = 2400/49

Final Answer: 2400/49

Additional Information

1. Exponent Rule: a^m × a^-m = 1

2. Identity: (a − b)³ + 3(a − b) = a³ − b³ if ab = 1

3. Negative Power: a^-n = 1/aⁿ

4. Simplification Tip: Convert powers to simple base before solving

Shortcut Trick

Prime factorize LCM 240 = 2⁴ × 3¹ × 5¹.

Exponents for 2: gcd(a,b)=2³, gcd(b,c)=2², gcd(c,a)=2², LCM=2⁴ → powers are {4, 3, 2}.

Exponents for 3: gcd(b,c)=3¹, gcd(a,b)=3⁰, gcd(c,a)=3⁰, LCM=3¹ → a has 3⁰, b and c have 3¹.

Exponents for 5: Only one number can have 5¹ (as all gcd pairs lack 5).

Test case 1: a = 2³×5, b = 2⁴×3, c = 2²×3 → 40 + 48 + 12 = 100.

Test case 2: a = 2⁴, b = 2³×3, c = 2²×3×5 → 16 + 24 + 60 = 100.

∴ Answer = 100

Alternate Method 

Given:

gcd(a, b) = 8, gcd(b, c) = 12, gcd(c, a) = 4, LCM(a, b, c) = 240

Formula used:

gcd(x, y) = Product of common prime factors with lowest powers.

LCM(x, y, z) = Product of all prime factors with highest powers.

a=40 b=48 c=12  gcd=8  gcd=4  gcd=12 LCM (a, b, c) = 240 Min Sum = 40+48+12 = 100

Calculations:

Let a = 2^a1 × 3^a2 × 5^a3, b = 2^b1 × 3^b2 × 5^b3, c = 2^c1 × 3^c2 × 5^c3.

⇒ For prime 2: min(a1, b1)=3, min(b1, c1)=2, min(c1, a1)=2, max(a1, b1, c1)=4. This gives c1=2 and {a1, b1}={3, 4}.

⇒ For prime 3: min(a2, b2)=0, min(b2, c2)=1, min(c2, a2)=0, max(a2, b2, c2)=1. This gives a2=0, b2=1, c2=1.

⇒ For prime 5: min(a3,b3)=0, min(b3,c3)=0, min(c3,a3)=0, max(a3,b3,c3)=1. One of them is 1, others 0.

⇒ Case 1 (a3=1): a = 2³×5=40, b = 2⁴×3=48, c = 2²×3=12. Sum = 40+48+12 = 100.

⇒ Case 2 (c3=1): a = 2⁴=16, b = 2³×3=24, c = 2²×3×5=60. Sum = 16+24+60 = 100.

∴ The correct answer is 100.

Additional Information

LCM and GCD Property

For two numbers x and y, LCM(x, y) × GCD(x, y) = x × y. This does not directly apply to three numbers.

Prime Exponent Rule

The exponent of a prime p in GCD is the minimum of its exponents in the numbers, while in LCM, it is the maximum.

Coprime Numbers

If gcd(a, b) = 1, then a and b are called coprime or relatively prime numbers.

Shortcut Trick

2 pages ⇒ 40 min

⇒ 1 page ⇒ 20 min

⇒ 84 pages ⇒ 84 × 20

⇒ = 1680 min

∴ Answer = 1680 minutes

Alternate Method

Given:

2 pages = 40 minutes

Formula:

Time ∝ Pages

Calculations:

⇒ Time for 1 page = 40 ÷ 2 = 20 min

⇒ Time for 84 pages = 84 × 20 = 1680 min

∴ Required time = 1680 minutes

Additional Information

Direct Proportion: Time increases directly with work if speed is constant

Unitary Method: Find value of 1 unit, then multiply

Rate Concept: Pages per minute = Work ÷ Time

Shortcut Tip: Always reduce to per unit for faster calculation

The correct answer is 2024.

Key Points

• The Pradhan Mantri Janjatiya Unnat Gram Abhiyaan (PMJUGA) was launched in 2024. It was initially announced by the Union Finance Minister Nirmala Sitharaman during the Union Budget 2024-25 presentation. Hence, the statement regarding 2024 is correct.
• The Union Cabinet, chaired by Prime Minister Narendra Modi, formally approved the mission on September 18, 2024, with a total outlay of Rs. 79,156 crore.
• This ambitious campaign is designed to improve the socio-economic condition of tribal-majority villages and Scheduled Tribe (ST) families across the country.
• The Abhiyaan aims to cover around 63,000 villages in 549 districts and 2,740 blocks across 30 States and Union Territories, benefiting approximately 5 crore tribal people.
• It focuses on 25 interventions implemented through 17 Central Ministries to ensure saturation of government schemes in tribal areas.

Additional Information

• Funding Structure: The total financial commitment of Rs. 79,156 crore involves a Central Share of Rs. 48,083 crore and a State Share of Rs. 31,073 crore. This highlights the cooperative federalism approach to tribal development.
• Target Criteria: The mission identifies villages where the Scheduled Tribe population is at least 50% or where there are at least 500 ST residents in a cluster. This ensures that the benefits reach the most concentrated tribal pockets.
• Livelihood and Infrastructure: Key focus areas include providing pucca houses under PM Awas Yojana, piped water supply, electricity, all-weather roads, and high-speed internet to remote tribal hamlets.
• Sustainable Goals: The mission aligns with the Sustainable Development Goals (SDGs) by focusing on health, quality education, and poverty reduction specifically for the indigenous communities of India.
• Tribal Health and Education: It includes specific goals for Sickle Cell Anaemia screening and the strengthening of Eklavya Model Residential Schools (EMRS) to boost literacy rates and wellness among tribal youth.

Important Points

• Comparison with PM-JANMAN: In 2023, the government launched the PM-JANMAN (Pradhan Mantri Janjati Adivasi Nyaya Maha Abhiyan) specifically for Particularly Vulnerable Tribal Groups (PVTGs). While PM-JANMAN focuses on 75 PVTGs, the PMJUGA launched in 2024 has a much broader scope covering a larger Scheduled Tribe population.
• Implementation Strategy: The Ministry of Tribal Affairs acts as the nodal ministry, but the mission is a convergence of various schemes like Jal Jeevan Mission, PMGSY, and Ayushman Bharat.
• Tribal Entrepreneurship: The scheme also promotes tribal homestays and village-level entrepreneurship to integrate tribal economies with the mainstream market through Van Dhan Vikas Kendras.
• Monitoring: Progress is tracked using the PM-Gati Shakti portal to ensure spatial planning and transparency in the development of physical infrastructure in tribal regions.

Shortcut Trick

LCM of 4, 30, 30 = 60 (Total Work)

⇒ A = 60 ÷ 4 = 15, B = 60 ÷ 30 = 2, C = −2

⇒ Net = 15 + 2 − 2 = 15 units/hr

⇒ 1/4 work = 60 ÷ 4 = 15 units

⇒ Time = 15 ÷ 15 = 1 hr

∴ Answer = 1 hour

Alternate Method

Given:

Tap A fills in 4 hours

Tap B fills in 30 hours

Tap C empties in 30 hours

Calculations:

⇒ Work required = 1 ÷ 4 of 60 = 15 units

⇒ Net efficiency = 15 units/hr

⇒ Time = 15 ÷ 15 = 1 hour

∴ Required time = 1 hour

Additional Information

LCM Method: Converts total work into integer units for easier calculation

Negative Efficiency: Emptying pipe has negative work rate

Net Work: Add all efficiencies considering sign

Partial Work: Required fraction = (Fraction) × Total Work

Family Chart:

Decoding the Symbols:

Given: W % A $ C + J

It means: W is the mother of A, A is the father of C, C is the brother of J.

Here, C is related to W as Son’s son

Hence, the correct answer is "Option 3".

The correct answer is Government of NCT of Delhi Act, 1991.

Key Points

• The Government of National Capital Territory of Delhi Act, 1991 was enacted by the Parliament to supplement the provisions of the Constitution relating to the Legislative Assembly and a Council of Ministers for the National Capital Territory of Delhi.
• This Act was passed following the 69^th Constitutional Amendment Act, 1991, which inserted Article 239AA and Article 239AB into the Constitution of India, providing a special status to the Union Territory of Delhi. Hence, the statement regarding the 1991 Act is correct.
• The Legislative Assembly of Delhi was granted the power to make laws for the whole or any part of the NCT with respect to any of the matters enumerated in the State List or in the Concurrent List, except for three specific subjects: Public Order, Police, and Land.
• The Act specifies that the total number of seats in the Legislative Assembly shall be 70, and these members are chosen by direct election from territorial constituencies.
• The 1991 Act provides the operational framework for the functioning of the Delhi Government, including the conduct of business, the role of the Speaker, and the relationship between the Lieutenant Governor and the Council of Ministers.

Additional Information

• 69^th Constitutional Amendment Act, 1991: This amendment officially designated the Union Territory of Delhi as the National Capital Territory of Delhi and provided for a Legislative Assembly and a Council of Ministers headed by a Chief Minister.
• Article 239AA: This specific article describes the special provisions with respect to Delhi. It mandates that the Administrator of Delhi shall be designated as the Lieutenant Governor (LG).
• Delhi Administration Act, 1966: Prior to the 1991 Act, Delhi was governed under the Delhi Administration Act, 1966, which provided for a Metropolitan Council and an Executive Council, but these bodies had limited recommendatory powers and were not a fully functional Legislative Assembly.
• Comparison with other UTs: Among the Union Territories in India, only Delhi, Puducherry, and Jammu & Kashmir (as per the J&K Reorganisation Act, 2019) are provided with their own Legislative Assemblies. Puducherry received its assembly through the 14^th Amendment Act, 1962.
• Recent Amendments: The Government of National Capital Territory of Delhi (Amendment) Act, 2021, and the 2023 Amendment further clarified the powers of the Lieutenant Governor, stating that the expression "Government" referred to in any law made by the Legislative Assembly shall mean the Lieutenant Governor.

Important Points

• Composition of the Council: The Council of Ministers in Delhi is restricted to 10% of the total number of members in the Legislative Assembly. Since there are 70 seats, the Council of Ministers (including the Chief Minister) cannot exceed 7 members.
• Appointment: The Chief Minister of Delhi is appointed by the President of India (not the Lieutenant Governor), and other Ministers are appointed by the President on the advice of the Chief Minister.
• Year of Implementation: While the Act was passed in 1991, the first elections to the 70-member Delhi Legislative Assembly were held in 1993.
• Responsibility: The Council of Ministers is collectively responsible to the Legislative Assembly of the National Capital Territory.
• Difference from States: Unlike regular states where the Governor acts on the "aid and advice" of the ministers on most matters, in Delhi, the Lieutenant Governor has broader discretionary powers, particularly concerning matters outside the assembly's legislative competence (Police, Land, and Public Order).

The logic followed here is:

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

Only four people sit between D and C when counted from the right of D.

R sits third to the right of D.

P is an immediate neighbor of both C and R.

B sits third to the left of Q.

So, the people between O and P are: 3 people

Hence, the correct answer is Option 3.

The correct answer is 89^th Amendment.

Key Points

• The 89^th Amendment Act of 2003 is the legislation that bifurcated the erstwhile combined National Commission for Scheduled Castes and Scheduled Tribes into two separate bodies. Hence, statement 4 is correct.
• This amendment resulted in the creation of the National Commission for Scheduled Tribes (NCST) under a newly inserted Article 338A of the Constitution of India.
• The 65^th Amendment Act of 1990 had previously replaced the single-member Special Officer for Scheduled Castes and Scheduled Tribes with a multi-member high-level National Commission. Hence, statement 3 is incorrect.
• The 97^th Amendment Act of 2011 is related to the constitutional status and protection of co-operative societies, adding Part IXB to the Constitution. Hence, statement 2 is incorrect.
• The 102^nd Amendment Act of 2018 granted constitutional status to the National Commission for Backward Classes (NCBC) by inserting Article 338B. Hence, statement 1 is incorrect.

Additional Information

• Historical Evolution: Originally, Article 338 of the Constitution provided for a Special Officer (designated as the Commissioner for SCs and STs) to investigate all matters relating to the safeguards provided for them.
• The 89^th Amendment Rationale: The separation was done to provide more focused attention on the development and protection of Scheduled Tribes, acknowledging that their geographical and cultural needs differ significantly from those of Scheduled Castes.
• Establishment Date: Following the 89^th Amendment, the National Commission for Scheduled Tribes officially came into existence on 19 February 2004.
• Constitutional Status: As it is established directly by Article 338A, the NCST is a Constitutional Body, which gives it higher authority and autonomy compared to statutory bodies.
• Geographical Focus: The commission works across India, with specific focus on areas with high tribal populations, including the Fifth Schedule and Sixth Schedule areas mentioned in the Constitution.

Important Points

• Composition of the Commission: The NCST consists of a Chairperson, a Vice-Chairperson, and three other members. It is mandatory that at least one of the members is a woman.
• Appointment and Tenure: All members are appointed by the President of India by warrant under his hand and seal. Their tenure of office and conditions of service are determined by the President, usually fixed at 3 years.
• Powers: The Commission has the power to regulate its own procedure and possesses all the powers of a civil court while investigating any matter. This includes summoning witnesses, requiring the production of documents, and receiving evidence on affidavits.
• Functions: Its primary duties include investigating and monitoring safeguards for Scheduled Tribes, inquiring into specific complaints regarding the deprivation of rights, and participating in the planning process of socio-economic development.
• Reporting Mechanism: The Commission submits annual reports to the President. The President causes these reports to be laid before each House of Parliament along with a memorandum explaining the action taken on the recommendations.

Given Statements:

Some lakes are oceans.

All planets are oceans.

All lakes are roads.

The least possible Venn diagram shows:

Conclusions:

(I) Some oceans are roads

Since some lakes are oceans and all lakes are roads, that overlapping part of lakes (which are oceans) must also be roads.

So, some oceans are definitely roads.

Hence, conclusion I follows.

(II) Some planets are lakes

Planets are inside oceans, and lakes are also inside oceans, but there is no necessary overlap between planets and lakes.

So, conclusion II does not follow.

Therefore, only conclusion I follows.

Hence, the correct answer is "Option 2".

Shortcut Trick

Amount doubles in 7 years

⇒ 8 times = 2³

⇒ So time = 3 × 7 = 21 years

∴ Answer = 21 years

Alternate Method

Given:

Amount doubles in 7 years

Formula:

A = P(1 + r)^t

Calculations:

⇒ After 7 years: A = 2P ⇒ (1 + r)⁷ = 2

⇒ For 8 times: A = 8P ⇒ (1 + r)^t = 8

⇒ 8 = 2³

⇒ (1 + r)^t = (1 + r)^7×3

⇒ t = 21 years

∴ Required time = 21 years

Additional Information

Compound Growth: A = P(1 + r)^t

Doubling Concept: If money doubles in T years, then 4 times in 2T, 8 times in 3T

Exponential Rule: a^m × aⁿ = a^m+n

Shortcut Insight: Convert multiples into powers of 2 for quick solving

The correct answer is Imagine, Innovate, Inspire for Viksit Bharat 2047.

Key Points

• The Emerging Science, Technology, and Innovation Conclave (ESTIC) held in November 2025 adopted the theme "Imagine, Innovate, Inspire for Viksit Bharat 2047". This theme reflects India's long-term vision of becoming a developed nation by the 100^th year of its independence.
• The conclave serves as a premier platform for scientists, policymakers, industry leaders, and academia to deliberate on the future of Science, Technology, and Innovation (STI) in India. The focus was on creating a roadmap that aligns scientific research with national economic goals.
• The "Imagine" component of the theme focuses on visionary thinking and foresight in disruptive technologies, while "Innovate" emphasizes the transition of ideas from laboratories to the market through Research and Development (R&D).
• The "Inspire" element aims to cultivate a scientific temper among the youth and start-up ecosystem, ensuring a steady pipeline of talent to drive the Viksit Bharat agenda.
• During the event, various National Missions were reviewed to assess their progress toward making India a global hub for manufacturing and technology by 2047.

Additional Information

• Viksit Bharat 2047:
• This is a comprehensive vision by the Government of India to transform the country into a developed economy by 2047. It involves key pillars such as economic growth, social progress, environmental sustainability, and good governance.
• In the context of science, it envisions India as a top three global power in scientific publications and patent filings.
• Department of Science and Technology (DST):
• Established in May 1971, the DST functions under the Ministry of Science and Technology. It is the nodal agency for organizing and promoting science and technology activities in India.
• It plays a critical role in funding scientific research and implementing high-end technology missions like the National Quantum Mission.
• Key Technological Focus Areas:
• The conclave highlighted several emerging fields such as Artificial Intelligence (AI), Quantum Computing, Semiconductor manufacturing, and Green Hydrogen.
• These sectors are identified as "Sunrise Sectors" that will drive the $30 trillion economy goal targeted for 2047.
• Anusandhan National Research Foundation (ANRF):
• The ANRF, established under the Anusandhan National Research Foundation Act, 2023, aims to provide high-level strategic direction for scientific research in the country.
• It seeks to bridge the gap between academic research and industrial application, which is a core objective of the ESTIC 2025.

Important Points

• Global Innovation Index (GII): India has shown a significant jump in the GII, moving from the 81^st rank in 2015 to within the top 40 in recent years. Events like ESTIC are instrumental in maintaining this trajectory.
• Net Zero Goal: Technological innovations discussed at the conclave are vital for India to achieve its Net Zero emissions target by 2070, as pledged at COP26.
• Science and Technology Policy: The discussions at ESTIC 2025 are often used to refine the Science, Technology, and Innovation Policy (STIP) to ensure it remains relevant to changing global dynamics$.

The correct answer is C. Rajagopalachari.

Key Points

• C. Rajagopalachari, also known as Rajaji, was a prominent leader of the Indian National Congress and a close confidant of Mahatma Gandhi.
• During the Civil Disobedience Movement in 1930, he was chosen to lead the salt protest in the Madras Presidency, mirroring Gandhi’s Dandi March in Gujarat.
• The protest, known as the Vedaranyam Salt March, commenced from Trichinopoly (now Tiruchirappalli) on April 13, 1930, and concluded at Vedaranyam in the Tanjore district.
• The march covered a total distance of approximately 150 miles (240 kilometers) and lasted for about 15 days, ending on April 28, 1930.
• By picking up salt at the Vedaranyam coast, Rajaji symbolically broke the British Salt Laws, leading to his subsequent arrest and imprisonment by the colonial authorities.

Additional Information

• K. Kamaraj: He was a legendary leader from Tamil Nadu, known as the "Kingmaker" in Indian politics. Although he participated in the Vedaranyam March under Rajaji’s leadership, he is best known for serving as the Chief Minister of Madras from 1954 to 1963 and introducing the Mid-day Meal Scheme in schools.
• Sardar Vallabhbhai Patel: Known as the "Iron Man of India," he led the Bardoli Satyagraha in 1928. He was instrumental in the political integration of India after 1947, ensuring the merger of over 560 princely states into the Indian Union.
• Sarojini Naidu: Known as the "Nightingale of India," she played a pivotal role in the Civil Disobedience Movement. Following Gandhi’s arrest, she led the Dharasana Satyagraha in May 1930, a non-violent raid on the Dharasana Salt Works in Gujarat.
• Civil Disobedience Movement (1930): This nationwide movement was launched by Mahatma Gandhi with the Dandi March (March 12 – April 6, 1930). It aimed at total non-cooperation with the British Government by refusing to pay taxes, especially the Salt Tax, which affected the poorest citizens.

Important Points

• Political Career: C. Rajagopalachari served as the last Governor-General of India from 1948 to 1950. He was the only Indian-born individual to hold this high constitutional designation.
• Bharat Ratna: In 1954, he was among the first three recipients of India’s highest civilian award, the Bharat Ratna, along with S. Radhakrishnan and C.V. Raman.
• Swatantra Party: In 1959, he founded the Swatantra Party, which advocated for free-market policies and opposed the Socialist agenda of the Jawaharlal Nehru-led Congress government.
• Literary Contributions: He was a prolific writer and translated the Ramayana and Mahabharata into English and Tamil, which remain highly popular versions of these epics today.
• Legacy in Madras: He served as the Premier of the Madras Presidency (1937–1939) and later as the Chief Minister of Madras State (1952–1954), where he introduced controversial reforms like the Kula Kalvi Thittam (Modified Scheme of Elementary Education).

The logic followed here is:

For, RUB → WSG

For, BQL → GOQ

Now, checking the options:

Option 1) BCG → GYL

Option 2) KDH → NZK

Option 3) MHV → OCX

Option 4) LMV → QKA

Hence, the correct answer is Option 4.

p>The correct answer is February 2.

Key Points

• World Wetlands Day is observed globally every year on February 2. In 2026, this day is dedicated to highlighting the synergy between nature and human history.
• The specific theme for the year 2026 is “Wetlands and traditional knowledge: Celebrating cultural heritage”. This theme emphasizes how indigenous communities and local traditions have historically contributed to the sustainable management and protection of wetland ecosystems.
• The date marks the anniversary of the signing of the Convention on Wetlands of International Importance, commonly known as the Ramsar Convention. It was adopted on February 2, 1971, in the Iranian city of Ramsar.
• The primary objective of this observance is to raise global awareness about the vital role wetlands play for people and our planet. Wetlands are essential for biodiversity, climate mitigation, and water security.
• The celebration in 2026 marks the 55^th anniversary of the Ramsar Convention, serving as a reminder of the long-standing international commitment to preserving these "biological supermarkets."

Additional Information

• The Ramsar Convention: It is an intergovernmental treaty that provides the framework for national action and international cooperation for the conservation and wise use of wetlands and their resources. It is one of the oldest global environmental agreements.
• Wetlands in India: India became a party to the Ramsar Convention on February 1, 1982. Since then, the country has significantly increased its number of Ramsar Sites. As of 2024, India has 85 designated wetlands of international importance, covering a vast geographical area across various states.
• Ecological Importance: Wetlands are often referred to as the “Kidneys of the Earth” because they filter pollutants from water. They also act as massive carbon sinks, helping to sequester carbon dioxide and mitigate the effects of climate change.
• Biodiversity Support: Although they cover only about 6% of the Earth’s land surface, 40% of all plant and animal species live or breed in wetlands. They are crucial for migratory birds, providing essential stopover points during their long-distance travels.
• Economic Value: Millions of people depend on wetlands for their livelihoods, including fishing, agriculture, and tourism. They provide natural flood defense, saving billions of dollars in disaster management costs annually.

Important Points

• UN Recognition: On August 30, 2021, the United Nations General Assembly adopted resolution 75/317, which officially established February 2 as World Wetlands Day on the UN international calendar.
• Types of Wetlands: These include marine and coastal areas (like mangroves and coral reefs), estuaries, rivers, lakes, marshes, and even human-made sites like rice paddies and reservoirs.
• Cultural Connection: The 2026 theme focuses on the spiritual and historical value of wetlands. Many ancient civilizations thrived near wetlands, and traditional knowledge systems (like ancient irrigation or sustainable fishing) are now being recognized as keys to modern conservation.
• Threats to Wetlands: Despite their value, wetlands are disappearing three times faster than forests. Major threats include urbanization, industrial pollution, over-extraction of water, and invasive species.
• Global Participation: World Wetlands Day was first celebrated in 1997. Since then, government agencies, NGOs, and community groups use the day to undertake restoration projects, educational seminars, and nature walks to promote environmental stewardship.

The correct answer is Kudankulam Atomic Power Plant.

Key Points

• The Kudankulam Atomic Power Plant (KKNPP), located in the Tirunelveli district of Tamil Nadu, is the highest-capacity nuclear power station in India as of 2023. It currently has an installed capacity of 2000 MW, consisting of two VVER-1000 units of 1000 MW each. This makes it the leading contributor to India's nuclear energy grid. Hence, statement 2 is correct.
• The Tarapur Atomic Power Station (TAPS) is located in Palghar, Maharashtra. It was the first commercial nuclear power station built in India, starting in 1969. As of 2023, its total capacity is 1400 MW, comprising two older 160 MW units and two newer 540 MW units. While significant, its capacity is lower than Kudankulam. Hence, statement 4 is incorrect.
• The Kakrapar Atomic Power Station (KAPS) is situated in Gujarat. With the recent commissioning of Unit 3 and Unit 4 (each 700 MW), the total capacity has significantly increased. However, its total operational capacity as of early 2023 remained below the 2000 MW mark set by Kudankulam. Hence, statement 3 is incorrect.
• The Narora Atomic Power Plant (NAPS) is located in the Bulandshahr district of Uttar Pradesh. It operates two PHWR units with a total capacity of 440 MW (220 MW each). It has the lowest capacity among the four options provided. Hence, statement 1 is incorrect.

Additional Information

• Nuclear Power Corporation of India Limited (NPCIL):
• NPCIL is a Public Sector Enterprise under the Department of Atomic Energy (DAE), Government of India. It was incorporated in September 1987 under the Companies Act, 1956.
• Its primary objective is the design, construction, operation, and maintenance of atomic power stations for the generation of electricity in pursuance of the schemes and programs of the Government of India under the Atomic Energy Act, 1962.
• International Cooperation in Nuclear Energy:
• The Kudankulam project is a result of an inter-governmental agreement between India and the former Soviet Union (now Russia) signed in 1988. Russia provides the technical expertise and VVER (Water-Water Energetic Reactor) technology.
• Tarapur was initially built with the help of the United States (General Electric), utilizing Boiling Water Reactors (BWR), which were later supplemented by indigenous Pressurized Heavy Water Reactors (PHWR).
• India's Three-Stage Nuclear Power Programme:
• Formulated by Dr. Homi J. Bhabha in the 1950s, the program aims to utilize India's vast Thorium reserves.
• Stage 1: Uses Pressurized Heavy Water Reactors (PHWR) fueled by Natural Uranium.
• Stage 2: Uses Fast Breeder Reactors (FBR) fueled by Plutonium-239.
• Stage 3: Aims to use Thorium-232 in Advanced Heavy Water Reactors to produce Uranium-233.
• Geographic Distribution of Major Plants:
• Kaiga Generating Station: Located in Karnataka with a capacity of 880 MW.
• Rajasthan Atomic Power Station (RAPS): Located in Rawatbhata, Rajasthan, with a capacity of approximately 1180 MW.
• Madras Atomic Power Station (MAPS): Located in Kalpakkam, Tamil Nadu, with a capacity of 440 MW.

Important Points

• Expansion Plans: India aims to increase its nuclear power capacity to 22,480 MW by the year 2031. This involves the construction of more 700 MW PHWR units and additional 1000 MW VVER units at Kudankulam (Units 3, 4, 5, and 6).
• Safety Features: Modern Indian nuclear plants, especially the Kudankulam units, incorporate Generation III+ safety features, including passive cooling systems that can function even in the event of a total power failure.
• Clean Energy Contribution: Nuclear energy is a critical part of India's strategy to achieve Net Zero emissions by 2070, as it provides a stable "base load" of electricity without the carbon emissions associated with coal or gas.

Given Statements:

Some beds are pillows.

All pillows are towels.

All towels are cushions.

The least possible Venn diagram shows:

Conclusions:

(I) All cushions are pillows

This does not follow because only pillows are inside cushions, not the reverse. Cushions can exist beyond pillows. So this conclusion is false.

(II) Some towels are beds

Some beds are pillows, and all pillows are towels. So those beds (which are pillows) must also be towels.

Therefore, some towels are definitely beds. So this conclusion follows.

Hence, only conclusion (II) follows.

Hence, the correct answer is "Option 2".

The correct answer is They encourage thrift and extend micro-credit facilities to poor rural women.

Key Points

• Self-Help Groups (SHGs) are informal associations of people who choose to come together to find ways to improve their living conditions. They are primarily designed to encourage thrift (savings) and provide micro-credit to their members. Hence, the statement that they encourage thrift and extend micro-credit facilities to poor rural women is correct.
• These groups typically consist of 10 to 20 members, mostly from similar socio-economic backgrounds, who pool their small savings regularly. This pooled resource is then used to give small interest-bearing loans to members for their emergency or consumption needs.
• Statement 1 suggests they provide large-scale industrial loans to farmers. This is inaccurate as SHGs focus on micro-finance and small-scale livelihood activities rather than heavy industrial credit. Hence, statement 1 is incorrect.
• Statement 3 claims they operate as regional offices of the Reserve Bank of India (RBI). The RBI is India's central bank and a regulatory body; SHGs are community-based organizations and do not function as administrative arms of the RBI. Hence, statement 3 is incorrect.
• Statement 4 mentions they function as government-owned cooperative banks. While SHGs may link with banks, they are self-governed and informal in nature, unlike cooperative banks which are statutory bodies registered under the Cooperative Societies Act. Hence, statement 4 is incorrect.

Additional Information

• Origin and Growth: The SHG movement in India gained momentum in the 1980s, pioneered by NGOs like MYRADA in Karnataka. It was formalized when NABARD (National Bank for Agriculture and Rural Development) launched the SHG-Bank Linkage Project in 1992, which has since become the world's largest micro-finance project.
• Government Schemes: The National Rural Livelihoods Mission (NRLM), renamed Deendayal Antyodaya Yojana (DAY-NRLM) in 2015, is the flagship central scheme that promotes SHGs across India to alleviate poverty and promote women's empowerment.
• Features and Functions: SHGs work on the principle of "Mutual Help". They help members overcome the lack of collateral, which is the biggest hurdle for the poor in obtaining bank loans. The peer pressure within the group ensures timely repayment of loans.
• Social Impact: Beyond finance, SHGs act as a platform for rural women to discuss social issues like health, nutrition, domestic violence, and education, leading to significant social empowerment and gender equality in rural areas.

Important Points

• Economic Significance: SHGs reduce the dependence of rural households on informal moneylenders who often charge usurious interest rates. By providing affordable credit, they enable income-generating activities such as poultry, tailoring, and small-scale farming.
• Financial Inclusion: They are a vital tool for financial inclusion in India, bringing the "unbanked" population into the formal banking system. The SBLP (SHG-Bank Linkage Program) allows groups to open savings accounts in commercial banks, Regional Rural Banks (RRBs), and cooperative banks.
• Membership Criteria: Usually, only one person from a family can join a particular SHG. Most groups are all-women groups, as research shows that credit provided to women has a more positive impact on family welfare and child education.
• Lakhpati Didi Initiative: In recent years (specifically in 2023-2024), the Government of India set a target to create 3 crore "Lakhpati Didis" (SHG members earning at least Rs. 1 lakh per annum) through skill development and market linkages.

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

Option 1: PLO

Option 2: LHK

Option 3: JFH

Option 4: NJM

Thus, JFH is different from the rest.

Hence, the odd one out is Option 3.

The correct answer is Mission LiFE.

Key Points

• Mission LiFE (Lifestyle for Environment) is an India-led global mass movement that encourages individual and community action to protect and preserve the environment. It was highlighted as a central theme by India at the Seventh session of the United Nations Environment Assembly (UNEA-7) held in December 2025.
• The initiative is designed to nudge individuals to adopt simple, environment-friendly actions in their daily lives, which collectively lead to a significant impact on Climate Action and Sustainable Development.
• It directly contributes to SDG 12 (Responsible Consumption and Production) by promoting mindful utilization of resources and SDG 13 (Climate Action) by reducing carbon footprints through sustainable lifestyle choices.
• The core philosophy of the mission is to replace the prevalent "use-and-dispose" economy with a Circular Economy, defined by mindful and deliberate utilization instead of mindless and destructive consumption.
• The mission envisions a global network of individuals known as "Pro-Planet People" (P3), who share a common commitment to adopting and promoting environment-friendly lifestyles.

Additional Information

• Origin and Evolution: Mission LiFE was first introduced by the Prime Minister of India during the COP26 summit in Glasgow in 2021. It was later formally launched at Kevadia, Gujarat, in October 2022 in the presence of the UN Secretary-General.
• Implementation Strategy: The mission is implemented in three distinct phases:
• Phase I (Change in Demand): Encouraging individuals to practice simple yet effective environment-friendly actions.
• Phase II (Change in Supply): Inducing industries and markets to respond to the shift in demand by providing sustainable products.
• Phase III (Change in Policy): Influencing government and industrial policy to support sustainable consumption and production.
• Swachh Bharat Abhiyan: Launched on October 2, 2014, this mission focuses on universal sanitation coverage and making India Open Defecation Free (ODF). While related to the environment, its primary focus is hygiene and waste management rather than the broader lifestyle changes of Mission LiFE.
• Make in India: Launched in September 2014, this initiative aims to transform India into a global design and manufacturing hub. It focuses on 25 sectors of the economy to create jobs and enhance skill sets.
• Digital India: Launched in July 2015, this campaign aims to ensure that government services are made available to citizens electronically by improving online infrastructure and increasing Internet connectivity.

Important Points

• The United Nations Environment Assembly (UNEA) is the world’s highest-level decision-making body on the environment. It meets biennially in Nairobi, Kenya, to set the global environmental agenda.
• The UNEA-7 session in 2025 emphasized the "Triple Planetary Crisis": Climate Change, Biodiversity Loss, and Pollution.
• NITI Aayog is the nodal agency in India for coordinating the implementation of Mission LiFE, working alongside the Ministry of Environment, Forest and Climate Change (MoEFCC).
• Specific actions under Mission LiFE include saving energy (switching off lights), saving water, reducing single-use plastic, sustainable food systems, and waste reduction (e-waste and food waste).

The correct answer is Alleles.

Key Points

• Alleles are defined as the alternative or different forms of a gene that occupy the same locus (position) on homologous chromosomes. They are responsible for the variations in a specific hereditary characteristic. Hence, the statement regarding Alleles is correct.
• Every individual inherits two alleles for each gene, one from each parent. These alleles can be identical or different, determining the genetic diversity within a species.
• The function of alleles is to encode for slightly different versions of the same protein, which ultimately results in different phenotypic traits such as eye color or blood type.
• In classical genetics, alleles are categorized as dominant or recessive. A dominant allele masks the expression of a recessive allele in a heterozygous state.
• The numerical value of alleles for a single gene in a diploid organism is 2, but in a population, there can be multiple alleles for a single trait.

Additional Information

• Genotypes: This term refers to the complete genetic makeup or DNA sequence of an organism. It is the internal hereditary information that contributes to the physical expression of traits. Hence, the statement regarding Genotypes is incorrect.
• Phenotypes: This refers to the observable physical characteristics or traits of an organism, such as height, skin color, and behavior. It is the result of the interaction between the genotype and the environment. Hence, the statement regarding Phenotypes is incorrect.
• Chromosomes: These are long, thread-like structures located in the nucleus of animal and plant cells. Each chromosome is made of protein and a single molecule of deoxyribonucleic acid (DNA). Humans have 46 chromosomes arranged in 23 pairs. Hence, the statement regarding Chromosomes is incorrect.
• Gregor Mendel: Often called the "Father of Genetics," he conducted experiments on pea plants in the year 1865, which led to the discovery of the laws of inheritance involving what we now call alleles.
• Homozygous and Heterozygous: When an individual has two identical alleles (e.g., AA or aa), they are homozygous; when they have two different alleles (e.g., Aa), they are heterozygous.

Important Points

• Multiple Alleles: While an individual carries only two alleles, a population can have multiple alleles for a gene. A prime example is the ABO blood group system in humans, which is controlled by three alleles: IA, IB, and i.
• Incomplete Dominance: This occurs when the phenotype of the heterozygote is an intermediate between the phenotypes of the two homozygotes. An example is the pink flowers produced by crossing red and white snapdragons.
• Co-dominance: In this genetic scenario, both alleles in a heterozygote are fully expressed. For example, in AB blood type, both the A and B antigens are present on the surface of red blood cells.
• Mutation: New alleles are created through mutations, which are permanent changes in the DNA sequence. This is a key feature of evolution and biological adaptation.

The correct answer is Madayagari Mallana.

Key Points

• Madayagari Mallana was a distinguished Telugu poet of the 16^th century and a vital member of the Ashtadiggajas. This group comprised eight legendary poets who adorned the court of Emperor Krishnadevaraya during the Vijayanagara Empire.
• He is best known for composing the Rajashekharacharitra, a significant work in the Prabandha genre of Telugu literature. This literary piece intricately describes the life, military expeditions (wars), and romantic pursuits (loves) of Rajashekhara, the King of Avanti. Hence, the statement regarding Madayagari Mallana as the author is correct.
• The Rajashekharacharitra is highly regarded for its stylistic elegance and vivid descriptions. Madayagari Mallana dedicated this work to Nadiru Timmarusu, who was the Mahapradhani (Prime Minister) of Krishnadevaraya and a major political figure of that era.
• His writing reflects the cultural zenith of the Tuluva Dynasty, emphasizing themes of chivalry, governance, and courtly love, which were characteristic of the Golden Age of Telugu Literature.

Additional Information

• Allasani Peddana:
• Known as the Andhra Kavita Pitamaha (Grandfather of Telugu Poetry), he was the most prominent of the Ashtadiggajas.
• His most famous work is Manucharitra (Swarochisha Manu Sambhavamu), which is considered the first Prabandha in Telugu.
• Krishnadevaraya:
• He was the Emperor of the Vijayanagara Empire from 1509 to 1529 and a great patron of arts and letters.
• A scholar himself, he authored Amuktamalyada in Telugu and the play Jambavati Kalyanam in Sanskrit.
• Nachana Somanatha:
• A famous poet from the 14^th century, he preceded the Vijayanagara golden era but influenced many later poets.
• His masterpiece is Uttara Harivamsam, and he held the title Sakalagama Chakravarti for his vast knowledge.
• Ashtadiggajas:
• The eight pillars of the literary assembly in Krishnadevaraya's court included Allasani Peddana, Nandi Thimmana, Dhurjati, Madayagari Mallana, Ayyalaraju Ramabhadrudu, Pingali Surana, Ramarajabhushanudu, and Tenali Ramakrishna.

Important Points

• The Prabandha style is a form of Telugu poetry that revolves around a specific theme, usually a puranic story or a historical legend, embellished with descriptions of nature, battles, and weddings.
• The reign of Krishnadevaraya saw the transition of Telugu literature from mere translations of Sanskrit epics to original, creative Prabandhas.
• The historical context of the Rajashekharacharitra suggests that poets like Mallana used fictionalized versions of kings (like the King of Avanti) to mirror the bravery and virtues of their contemporary patrons in Hampi.

The correct answer is Article 243 J and Article 243 Z.

Key Points

• Article 243 J of the Indian Constitution specifically mandates the Audit of accounts of Panchayats. It states that the Legislature of a State may, by law, make provisions with respect to the maintenance of accounts by the Panchayats and the auditing of such accounts. Hence, the first part of the statement in the option is correct.
• Article 243 Z deals with the Audit of accounts of Municipalities. Similar to the provisions for rural bodies, it empowers the State Legislature to frame laws regarding the maintenance and auditing of accounts for urban local bodies to ensure financial transparency. Hence, the second part of the statement in the option is correct.
• These articles were incorporated into the Constitution through the 73^rd Constitutional Amendment Act and the 74^th Constitutional Amendment Act of 1992, respectively.
• The primary function of these audits is to ensure that the funds allocated to Local Self-Governments (both rural and urban) are utilized for their intended applications and to prevent financial irregularities.
• Under these provisions, the State Government determines the authority or organization responsible for conducting the audit, which often involves the Director of Local Fund Audit or the Comptroller and Auditor General (CAG) in some states.

Additional Information

• Article 243 I and Article 243 Y:
• Article 243 I provides for the constitution of a Finance Commission at the State level every five years to review the financial position of the Panchayats.
• Article 243 Y performs the same function for Municipalities, ensuring that taxes, duties, and tolls are properly distributed between the State and the urban local bodies.
• Article 243 G and Article 243 W:
• Article 243 G outlines the powers, authority, and responsibilities of Panchayats, enabling them to function as institutions of self-government.
• Article 243 W details the powers and responsibilities of Municipalities regarding the preparation of plans for economic development and social justice.
• Article 243 M and Article 243 ZA:
• Article 243 M specifies locations and areas where the provisions of Part IX (Panchayats) do not apply, such as certain Scheduled Areas and Tribal Areas.
• Article 243 ZA deals with the elections to the Municipalities, vesting the superintendence, direction, and control of elections in the State Election Commission.
• Article 243 ZB:
• This article specifies the application of the provisions of Part IXA (Municipalities) to Union Territories of India.

Important Points

• The 73^rd Amendment Act added Part IX to the Constitution, titled "The Panchayats," and the Eleventh Schedule, which contains 29 functional items.
• The 74^th Amendment Act added Part IXA, titled "The Municipalities," and the Twelfth Schedule, which contains 18 functional items.
• The State Election Commission, established under Article 243 K, is responsible for conducting elections for both Panchayats and Municipalities, ensuring democratic decentralization at the grassroots level.
• The minimum age to contest elections for these local bodies is 21 years, as per Article 243 F and Article 243 V.
• A mandatory reservation of one-third (33%) of the total number of seats is provided for women in both rural and urban local bodies to promote gender inclusion in governance.

The logic followed here is:

Logic: Second number = First number + 51

107 → 158

⇒ 107 + 51 = 158

122 → 173

⇒ 122 + 51 = 173

Now, applying the same logic:  154 → 154 + 51 = 205

Now, checking options:

Option 1) 213 → not matching

Option 2) 218 → not matching

Option 3) 198 → not matching

Option 4) 205 → matches 

Hence, the correct answer is Option 4.

Shortcut Trick

Winning margin = 52% − 48% = 4% of valid votes

⇒ 4% = 291 ⇒ 1% = 291 ÷ 4 = 72.75

⇒ Valid votes = 72.75 × 100 = 7275

⇒ Polled votes = 7275 ÷ 0.97 = 7500

⇒ Registered voters = 7500 ÷ 0.8 = 9375

∴ Answer = 9375

Alternate Method

Given:

Votes polled = 80% of registered voters

Invalid votes = 3%

Valid votes = 97%

Winner gets 52%, loser gets 48%

Margin = 291 votes

Formula:

Margin = Difference% of valid votes

Calculations:

⇒ Difference = 52% − 48% = 4%

⇒ 4% of valid votes = 291

⇒ Valid votes = (291 × 100) ÷ 4 = 7275

⇒ Valid = 97% of polled

⇒ Polled = 7275 ÷ 0.97 = 7500

⇒ Polled = 80% of registered

⇒ Registered = 7500 ÷ 0.8 = 9375

∴ Total registered voters = 9375

Additional Information

Margin Trick: Margin = Difference% of valid votes

Reverse Percentage: Total = Part ÷ (Percentage ÷ 100)

Vote Breakdown: Always move stepwise → Valid → Polled → Registered

Shortcut Tip: Convert % difference directly into votes to save time

The logic followed here is:

Given:

COOK → 8245

HOOK → 5429

Here, H = 9

Hence, the correct answer is "Option 1".

Shortcut Trick

⇒ Total ratio = 2 + 3 + 4 = 9

⇒ Largest angle share = 4/9

⇒ Percentage = (4/9) × 100 ≈ 44.44%

∴ Answer = 44%

Alternate Method

Given:

Ratio of angles = 2 : 3 : 4

Formula:

Sum of angles in triangle = 180°

Calculation:

⇒ Total ratio = 2 + 3 + 4 = 9

⇒ Largest angle = (4/9) × 180 = 80°

⇒ Percentage = (80 / 180) × 100 ≈ 44.44%

⇒ Rounded value = 44%

Final Answer: 44%

Additional Information

1. Triangle Sum: Sum of all angles = 180°

2. Ratio Method: Actual value = (part/total parts) × total

3. Percentage: (part/whole) × 100

4. Shortcut: Largest % = largest ratio / total ratio × 100

Shortcut Trick

⇒ Number of meeting points = Difference in laps when they meet

⇒ LCM of 85 and 90 = 1530 seconds

⇒ Laps by Shahrukh = 1530 ÷ 85 = 18

⇒ Laps by Amir = 1530 ÷ 90 = 17

⇒ Difference = 18 − 17 = 1

∴ Answer = 1

Alternate Method

Given:

Time of Shahrukh = 85 s

Time of Amir = 90 s :contentReference[oaicite:0]{index=0}

Formula:

Relative speed = (1 ÷ T₁) − (1 ÷ T₂)

Meeting time = 1 ÷ Relative speed

Calculations:

⇒ Relative speed = (1 ÷ 85) − (1 ÷ 90)

⇒ = (90 − 85) ÷ (85 × 90)

⇒ = 5 ÷ 7650

⇒ = 1 ÷ 1530

⇒ Meeting time = 1 ÷ (1 ÷ 1530) = 1530 s

⇒ Laps by Shahrukh = 1530 ÷ 85 = 18

⇒ Laps by Amir = 1530 ÷ 90 = 17

⇒ Difference in laps = 1

∴ Final Answer = 1

Additional Information

Relative Speed Concept: For same direction, subtract speeds → V_rel = V₁ − V₂

Meeting Time: Time between meetings = Track length ÷ relative speed

LCM Method: First meeting occurs at LCM of individual times

Circular Motion Insight: Meeting points = difference in number of laps completed

The correct answer is Dubai.

Key Points

• The 7^th Future Food Forum 2025 is scheduled to be hosted in Dubai, United Arab Emirates (UAE). This forum has established itself as the leading regional platform for the Food and Beverage (F&B) industry to discuss the future of food manufacturing and distribution.
• The event is organized by the UAE Food & Beverage Manufacturers Group (FBMG), an organization that operates under the Dubai Chamber of Commerce. It serves as a critical bridge between government regulators and private sector manufacturers.
• The primary focus of the 2025 forum is on food security and sustainability, aligning with the UAE's broader vision to become a global leader in food innovation. It addresses the challenges of global supply chains, climate change, and the need for nutritional security.
• The forum facilitates high-level discussions involving the Ministry of Economy, the Ministry of Climate Change and Environment, and various international food agencies. It aims to foster innovation and digital transformation within the food production cycle.
• By hosting this event, Dubai reinforces its position as a global re-export hub and a central node for the Middle East and North Africa (MENA) region's food trade, supporting the Dubai Economic Agenda D33.

Additional Information

• UAE National Food Security Strategy 2051:
• This strategy aims to put the UAE at the top of the Global Food Security Index by the year 2051.
• It focuses on facilitating the global food trade, diversifying food import sources, and identifying alternative supply schemes to ensure resilience against geopolitical risks.
• The strategy also promotes sustainable local food production through the use of modern technologies such as hydroponics and vertical farming.
• Role of the UAE Food & Beverage Manufacturers Group (FBMG):
• The FBMG represents a diverse range of companies, from multinational corporations to Small and Medium Enterprises (SMEs), providing them a voice in policy-making.
• It helps in implementing standards for food safety and labeling, ensuring that products manufactured in Dubai meet international quality benchmarks.
• Sustainability and the Circular Economy:
• The forum emphasizes the Circular Economy, specifically targeting the reduction of food waste and the repurposing of resources within the manufacturing process.
• In line with the COP28 legacy held in the UAE, the food sector is under pressure to reduce its carbon footprint and adopt eco-friendly packaging solutions.
• Innovation in AgTech:
• Dubai has become a testing ground for Agricultural Technology (AgTech), utilizing Artificial Intelligence (AI) and Internet of Things (IoT) to optimize crop yields and water consumption in desert environments.
• The 7^th Future Food Forum showcases advancements in alternative proteins and lab-grown meat, reflecting changing consumer preferences and environmental concerns.

Important Points

• Economic Impact: The food sector is one of the largest non-oil sectors in the UAE economy. Events like the Future Food Forum help attract Foreign Direct Investment (FDI) into the industrial sector.
• Regional Significance: While Singapore is a leader in AgTech in Asia and New Delhi is a major agricultural hub, Dubai serves as the strategic link for the Global South, facilitating trade between Africa, Europe, and Asia.
• Consumer Safety: A key theme of the forum is food traceability. Using Blockchain technology, the UAE aims to ensure that every food item can be traced back to its source, enhancing public health and consumer trust.
• Data and Facts: The UAE imports approximately 80-90% of its food, making the discussions at the Future Food Forum vital for the nation's strategic reserves and price stability.

Shortcut Trick

⇒ (n − 2)×180 = 1620 ⇒ n = 11

⇒ Interior = 1620/11, Exterior = 360/11

⇒ Difference = (1620 − 360)/11 = 1260/11

⇒ = $114\frac{6}{11}$

∴ Answer = $114\frac{6}{11}$

Alternate Method

Given:

Sum of interior angles = 1620°

Formula:

(n − 2) × 180 = 1620

Interior angle = 1620 / n

Exterior angle = 360 / n

Calculation:

⇒ (n − 2) × 180 = 1620

⇒ n − 2 = 9 ⇒ n = 11

⇒ Interior angle = 1620 / 11

⇒ Exterior angle = 360 / 11

⇒ Difference = (1620/11 − 360/11)

⇒ = 1260/11

⇒ = $114\frac{6}{11}$

Final Answer: $114\frac{6}{11}$

Additional Information

1. Interior Sum: (n − 2) × 180

2. Exterior Angle: 360 / n

3. Relation: Interior + Exterior = 180°

4. Mixed Fraction: Improper fraction → a b/c

The correct answer is Grid system of town planning.

Key Points

• The Harappan Civilization, also known as the Indus Valley Civilization, is world-renowned for its advanced urban planning. The most striking feature of these cities was the Grid system, where streets and lanes were laid out to cut each other at right angles (90 degrees), dividing the city into rectangular blocks.
• Unlike many contemporary civilizations, Harappan cities like Mohenjo-daro and Harappa were divided into two distinct parts: a raised Citadel (or Acropolis) on the western side, which housed important public buildings, and a larger Lower Town on the eastern side, where the common citizens resided.
• The use of standardized burnt bricks for construction was a hallmark of their engineering. These bricks followed a uniform ratio of 1:2:4 (thickness:width:length), ensuring structural integrity across various sites located hundreds of miles apart.
• Every house was connected to a highly sophisticated drainage system. These drains were made of mortar, lime, and gypsum and were covered with stone slabs or large bricks that could be removed for cleaning, indicating a high level of concern for sanitation and hygiene.
• The Great Granaries found at Harappa and Mohenjo-daro suggest a centralized system for storing surplus grains, which was a critical economic feature of their urban lifestyle.

Additional Information

• Geographical Extent and Age: The civilization flourished during the Bronze Age, roughly between 3300 BCE and 1300 BCE, with its mature phase occurring between 2600 BCE and 1900 BCE. It spread across present-day India, Pakistan, and Afghanistan.
• Mohenjo-daro: Located in the Larkana district of Sindh, Pakistan, on the banks of the Indus River. It is famous for the Great Bath, a large rectangular tank used for ritual bathing, and the discovery of the Dancing Girl bronze statue.
• Harappa: The first site to be excavated in 1921 by Daya Ram Sahni. It is located on the banks of the Ravi River in the Sahiwal district of Punjab, Pakistan.
• Lothal: Situated in Gujarat, India, this site featured the world's earliest known artificial dockyard, connecting the city to an old course of the Sabarmati River, facilitating maritime trade with Mesopotamia.
• Dholavira: Located in the Rann of Kutch, Gujarat, it is unique for its three-part city division (Citadel, Middle Town, and Lower Town) and an extraordinary water management system consisting of giant reservoirs.
• Kalibangan: Found in Hanumangarh, Rajasthan, it provides the earliest evidence of ploughed fields and contains both Pre-Harappan and Harappan cultural phases.

Important Points

• Wooden houses: While timber was used for roofs and doors, Harappan houses were primarily built with baked bricks and mud bricks. They did not rely on wooden structures as their primary architectural feature. Hence, this statement is incorrect.
• Stone palaces: The Harappans focused on functional civic architecture rather than monumental stone palaces or temples. While stone was used in sites like Dholavira, the concept of "stone palaces" as seen in later empires was absent. Hence, this statement is incorrect.
• Irregular street patterns: The Harappan cities were the antithesis of irregular patterns. They are celebrated specifically for their planned, systematic layout and geometric precision. Hence, this statement is incorrect.
• Grid system of town planning: This was the most defining characteristic of the Indus Valley Civilization, showcasing their expertise in geometry and urban management. Hence, this statement is correct.

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

Option 1: LK − IK

Option 2: ZY − XW

Option 3: YX − WV

Option 4: RQ − PO

Thus, LK − IK is different from the rest.

Hence, the odd one out is Option 1.

Shortcut Trick

Profit = 25% ⇒ SP : CP = 5 : 4

⇒ 48 SP = x CP

⇒ 48 × 5 = x × 4

⇒ x = (48 × 5) ÷ 4 = 60

∴ Answer = 60

Alternate Method

Given:

SP of 48 items = CP of x items

Profit = 25%

Concept Used:

Profit% = [(SP − CP) ÷ CP] × 100

Calculation:

⇒ Profit = 25%

⇒ SP = 1.25 CP

⇒ SP of 48 items = CP of x items

⇒ 48 × SP = x × CP

⇒ 48 × 1.25CP = x × CP

⇒ 48 × 1.25 = x

⇒ x = 60

∴ The correct answer is 60.

Additional Information

Profit Formula: Profit% = (Profit ÷ CP) × 100

SP-CP Relation: SP = CP × (1 + Profit%)

Ratio Trick: 25% profit ⇒ SP : CP = 5 : 4

Shortcut Tip: Use ratio instead of decimals for faster solving

The correct answer is Sulphur dioxide.

Key Points

• Sulphur dioxide (SO2) is a colorless gas with a pungent smell, primarily produced from the burning of fossil fuels like coal and oil in power plants and industrial boilers. It is the most significant pollutant closely linked to the formation of acid rain. Hence, option 2 is correct.
• When sulphur dioxide is released into the atmosphere, it reacts with water vapor, oxygen, and other oxidants to form sulphuric acid (H2SO4), which then mixes with rain, snow, or fog.
• Ammonia (NH3) is a nitrogen-based compound often released from agricultural activities and livestock waste; while it can contribute to nitrogen deposition in soil, it is not the primary chemical driver for acid rain formation. Hence, option 1 is incorrect.
• Ozone (O3) is a secondary pollutant found in the troposphere, formed by the reaction of Nitrogen Oxides and Volatile Organic Compounds in the presence of sunlight. It is a major component of smog but does not directly cause acid rain. Hence, option 3 is incorrect.
• Methane (CH4) is a powerful greenhouse gas responsible for global warming and climate change, but it does not possess the chemical properties required to increase the acidity of precipitation. Hence, option 4 is incorrect.

Additional Information

• Definition of Acid Rain: It refers to any form of precipitation—rain, snow, fog, or hail—that is unusually acidic, meaning it possesses elevated levels of hydrogen ions. Normal rain has a pH of about 5.6, whereas acid rain typically has a pH between 4.2 and 4.4.
• Nitrogen Oxides (NOx): Along with sulphur dioxide, nitrogen oxides (emitted from motor vehicles and electric utilities) are the other major precursors. They react in the air to form nitric acid (HNO3).
• Environmental Impact: Acid rain causes the acidification of lakes and streams, which can be toxic to fish and other aquatic animals. It also leaches aluminum from the soil, which is harmful to forest ecosystems and plants.
• Effect on Infrastructure: It accelerates the corrosion of metals (such as bronze) and the deterioration of paint and stone (such as marble and limestone). Famous monuments like the Taj Mahal in India have faced threats of yellowing due to pollutants like SO2 from nearby industries.

Important Points

• Chemical Reaction: The oxidation of sulphur dioxide to form sulphuric acid often occurs on the surface of aerosol particles or through liquid-phase reactions in cloud droplets.
• Natural Sources: While human activity is the leading cause, natural events like volcanic eruptions and decaying vegetation also release sulphur dioxide into the atmosphere.
• Historical Context: The phenomenon of acid rain was first observed by Robert Angus Smith in 1852 in Manchester, England, which was a hub during the Industrial Revolution.
• Global Mitigation: Many countries have signed international treaties and enacted laws like the Clean Air Act to reduce emissions of SO2 and NOx through the use of scrubbers in power plants and catalytic converters in vehicles.

The correct answer is PM-SVANidhi.

Key Points

• The PM-SVANidhi (Pradhan Mantri Street Vendor’s AtmaNirbhar Nidhi) was launched by the Ministry of Housing and Urban Affairs on June 1, 2020. It aims to provide affordable working capital loans to street vendors to resume their livelihoods that were adversely affected by the COVID-19 lockdown. Hence, this option is correct.
• Under this scheme, vendors can avail of a collateral-free working capital loan of up to ₹10,000 with a tenure of one year. On timely or early repayment, the vendor is eligible for the next cycle of working capital loan with an enhanced limit of ₹20,000 and ₹50,000 respectively.
• The scheme provides an interest subsidy at the rate of 7% per annum, which is credited to the beneficiary's bank account through Direct Benefit Transfer (DBT) on a quarterly basis.
• To promote digital transactions, the scheme offers a monthly cashback ranging from ₹50 to ₹100 for vendors who accept or make digital payments.
• The Small Industries Development Bank of India (SIDBI) acts as the Implementation Partner for the scheme's administration, ensuring smooth coordination between Lending Institutions like Scheduled Commercial Banks, Non-Banking Financial Companies (NBFCs), and Micro-Finance Institutions (MFIs).

Additional Information

• Jal Shakti Abhiyan:
• Launched in 2019, this is a water conservation campaign focused on rainwater harvesting and groundwater recharge. It does not provide financial support to informal workers. Hence, this statement is incorrect.
• The campaign covers 256 water-stressed districts across India, promoting intensive afforestation and watershed development.
• PM Ujjwala Yojana (PMUY):
• Launched in May 2016 in Ballia, Uttar Pradesh, its primary goal is to provide clean cooking fuel (LPG) to women from Below Poverty Line (BPL) households. Hence, this statement is incorrect.
• It aims to protect the health of women and children by replacing unclean cooking fuels like coal and firewood with smoke-free LPG connections.
• PM-KISAN (Pradhan Mantri Kisan Samman Nidhi):
• Launched in February 2019 (retroactive from December 2018), it is a Central Sector Scheme that provides income support to all landholding farmer families in India. Hence, this statement is incorrect.
• Under the scheme, an amount of ₹6,000 per year is released in three equal installments of ₹2,000 directly into the bank accounts of the beneficiaries.

Important Points

• The informal sector in India accounts for a significant portion of the urban workforce. Street vendors, often referred to as thelewalas or rehri-patri walas, are vital to the urban economy, providing essential goods at affordable prices.
• Eligibility for PM-SVANidhi: The scheme is available to all street vendors engaged in vending in urban areas on or before March 24, 2020. This includes vendors from surrounding peri-urban or rural areas who vend within the city limits.
• Lending Institutions: The scheme leverages a wide network of lenders, including Regional Rural Banks (RRBs) and Cooperative Banks, to reach the last mile of the unorganized sector.
• Socio-economic profiling: Under the SVANidhi se Samriddhi program, the government also conducts socio-economic profiling of beneficiaries and their families to link them to other welfare schemes like PM Suraksha Bima Yojana and PM Jeevan Jyoti Bima Yojana.

Shortcut Trick

Total amount = (12×160) + (55×109) + (89×181)

⇒ = 1920 + 5995 + 16109 = 24024

Total members = 12 + 55 + 89 = 156

⇒ Average = 24024 ÷ 156 = 154

∴ Answer = 154

Alternate Method

Given:

Group A: 12 members, avg = 160

Group B: 55 members, avg = 109

Group C: 89 members, avg = 181

Concept Used:

Overall Average = Total Amount ÷ Total Members

Calculation:

⇒ Total of A = 12 × 160 = 1920

⇒ Total of B = 55 × 109 = 5995

⇒ Total of C = 89 × 181 = 16109

⇒ Total amount = 1920 + 5995 + 16109 = 24024

⇒ Total members = 12 + 55 + 89 = 156

⇒ Average = 24024 ÷ 156 = 154

∴ Overall average = 154

Additional Information

Average Formula: Average = Total Sum ÷ Number of items

Weighted Average: Used when groups have different sizes

Shortcut: Multiply each average by its frequency

Tip: Add totals first, divide once at end

Shortcut Trick

Use the Pacific-Atlantic Rule for significant figures:

1. If a decimal is Present, count from the Pacific (Left) side.
2. Skip all zeros until you hit the first non-zero digit.
3. Count every digit from that point until the end.

In $0.00\mathbf{200}$, we start counting at '2' and include the trailing zeros. Total = 3.

∴ Answer = 3

Detailed Method

Concept of Significant Figures:

Significant figures represent the precision of a measurement. Every digit that is known with certainty plus one last digit that is somewhat uncertain is included.

Rules Applied to 0.00200:

• Rule 1 (Leading Zeros): Zeros to the left of the first non-zero digit (0.00) are never significant. They are simply placeholders to indicate the position of the decimal point.

• Rule 2 (Non-zero Digits): The digit '2' is non-zero, so it is significant.

• Rule 3 (Trailing Zeros with Decimal): Zeros at the end of a number are significant if a decimal point is present. These zeros ($...00$) indicate that the measurement was precise to that many decimal places.

0.00200Leading Zeros (Placeholders)                                            Significant Figures→ 3 Sig Figs

Conclusion:

Number = $0.00200$

Significant digits = $2, 0, 0$

Total count = $3$

∴ The number of significant figures present in 0.00200 is 3.

Additional Information

Scientific Notation Check

A foolproof way to find significant figures is to convert the number to scientific notation: $0.00200 = 2.00 \times 10^{-3}$. All digits in the coefficient part ($2.00$) are significant.

Significant Figures in Calculations

When multiplying or dividing, the result should have the same number of significant figures as the measurement with the fewest significant figures.

Shortcut Trick

Compare fractions using benchmark values or division estimation.

3 ÷ 17 ≈ 0.17 (Much less than 0.5)

13 ÷ 67 ≈ 0.19 (Much less than 0.5)

10 ÷ 37 ≈ 0.27 (Much less than 0.5)

5 ÷ 9 ≈ 0.55 (More than 0.5)

∴ Answer = 5 : 9

Alternate Method 

Given:

Ratios are 3 : 17, 13 : 67, 10 : 37, and 5 : 9.

Formula used:

To compare ratios, convert them to equivalent decimals by dividing the antecedent by the consequent.

Ratio Comparison Chart 3 : 17 0.176 13 : 67 0.194 10 : 37 0.270 5 : 9 0.555 (Max) 0.0 1.0

Calculations:

⇒ 3 ÷ 17 ≈ 0.1764

⇒ 13 ÷ 67 ≈ 0.1940

⇒ 10 ÷ 37 ≈ 0.2702

⇒ 5 ÷ 9 ≈ 0.5555

⇒ Comparing values: 0.5555 > 0.2702 > 0.1940 > 0.1764

∴ The correct answer is 5 : 9.

Additional Information

Cross-Multiplication Method

For two fractions a/b and c/d, if ad > bc, then a/b > c/d. This avoids division entirely for small numbers.

Benchmark Comparison

Compare fractions to standard values like 1/2, 1/3, or 1/4. Since 5/9 > 1/2 and all others are less than 1/2, 5/9 is automatically the largest.

Same Difference Rule

In proper fractions, if the difference between numerator and denominator is the same, the fraction with the largest values is the greatest.

Reciprocal Method

If a/b is hard to calculate, compare b/a. The fraction with the smallest reciprocal value is the largest original fraction.

The correct answer is Rigidity.

Key Points

• Rigidity is the property of a substance to maintain its shape when an external force is applied. In solids, the constituent particles (atoms, ions, or molecules) are closely packed, leaving very little space between them. Hence, statement 2 is correct.
• Compressibility refers to the capacity of a substance to decrease in volume under pressure. Because particles in a solid are already in close proximity and have strong intermolecular forces, they possess negligible compressibility. Hence, statement 1 is incorrect.
• Transparency is an optical property that allows light to pass through a material without being scattered. While some solids like glass are transparent, many others like wood or iron are opaque; therefore, it is not a property possessed by solids solely due to the packing of particles. Hence, statement 3 is incorrect.
• Fluidity is the ability of a substance to flow, which is characteristic of liquids and gases. In solids, particles are held in fixed positions and can only vibrate about their mean positions, preventing them from flowing. Hence, statement 4 is incorrect.
• The strong intermolecular forces of attraction in solids keep the particles so tightly bound that they exhibit a definite shape and definite volume, which are the fundamental aspects of rigidity.

Additional Information

• Characteristics of Solids: Solids are characterized by high density, low kinetic energy of particles, and incompressibility. They do not expand to fill their container like gases do.
• Crystalline Solids: These solids have a long-range order with a regular repeating pattern of particles. Examples include Diamond, Quartz, and Sodium Chloride. They have sharp melting points.
• Amorphous Solids: Also known as pseudo-solids or super-cooled liquids, these lack a regular arrangement of particles. Examples include Glass, Rubber, and Plastic. They soften over a range of temperatures.
• Density and Packing: In a solid, the packing efficiency determines how much of the total space is occupied by particles. For instance, in a Face-Centered Cubic (FCC) structure, the packing efficiency is 74%, which is quite high compared to other states.
• Applications: The rigidity of solids is utilized in civil engineering for construction (using steel and concrete), in manufacturing for creating durable tools, and in aerospace for structural components that must withstand high mechanical stress.

Important Points

• Kinetic Molecular Theory: According to this theory, the particles in a solid are in constant motion, but this motion is limited to vibrations because the potential energy of attraction is much greater than the kinetic energy of the particles.
• Diffusion: The process of diffusion (movement of particles from high to low concentration) is extremely slow in solids compared to liquids or gases because the intermolecular spaces are almost absent.
• Thermal Expansion: When a solid is heated, the vibrations of its particles increase, leading to a slight increase in volume known as thermal expansion. However, the rigidity remains until the melting point is reached.
• Elasticity vs. Rigidity: While rigidity is the resistance to change in shape, elasticity is the property of a solid to return to its original shape after the deforming force is removed (e.g., a steel spring).

The logic followed here is:

Given: (Left) M K L $ F % G & # @ S ! S + ? K > H V G (Right)

Now, all letters are dropped and only symbols are kept.

So, first we remove all letters:

Remaining symbols: $ % & # @ ! + ? >

Now we rewrite the reduced series (left to right):  $ % & # @ ! + ? >

Now, we need the 7^th from the right: $ % & # @ ! + ? >

So, the 7^th symbol from the right is &

Hence, the correct answer is Option 3.

Shortcut Trick

Apply BODMAS quickly:

⇒ 16 + 5 − 2 × 4 ⇒ 16 + 5 − 8

⇒ 21 − 8 ⇒ 13

∴ Answer = 13

Alternate Method

Given:

16 + 20 ÷ 4 − 2 × 4

Concept Used:

BODMAS rule

Calculation:

16 + 20 ÷ 4 - 2 × 4

⇒ 16 + 5 − 2 × 4

⇒ 16 + 5 − 8

⇒ 21 − 8

⇒ 13

∴ The correct answer is 13.

Additional Information

BODMAS Rule: Solve Division and Multiplication before Addition and Subtraction

Left to Right: Same priority operations are solved from left to right

Common Error: Adding before division leads to wrong answer

Speed Tip: Always simplify ÷ and × first

The correct answer is Siachen Glacier.

Key Points

• The Siachen Glacier is located in the Eastern Karakoram range in the Himalayan Mountains, at approximately 35.42°N 77.10°E.
• It is the longest glacier in the Karakoram Range and the second-longest in the world's non-polar regions, with a total length of about 76 kilometers (47 miles).
• The only glacier longer than Siachen outside the polar regions is the Fedchenko Glacier, which is 77 kilometers long and situated in the Pamir Mountains of Tajikistan.
• The Siachen Glacier lies just south of the great drainage divide that separates the Eurasian Plate from the Indian subcontinent.
• The altitude of the glacier ranges from approximately 5,753 meters (18,875 feet) above sea level at its head at Indira Col to 3,620 meters (11,875 feet) at its snout.

Additional Information

• Baltoro Glacier:
• Located in the Gilgit-Baltistan region of the Karakoram range.
• It has a length of 63 kilometers (39 miles) and is one of the longest glaciers outside the polar regions.
• It is a major source of the Shigar River, which is a tributary of the Indus River.
• It is famous for its proximity to four of the world's fourteen "eight-thousanders," including K2 (8,611 meters).
• Gangotri Glacier:
• Located in the Uttarkashi District of Uttarakhand, India, within the Garhwal Himalayas.
• It is one of the largest glaciers in the Himalayas with an estimated volume of over 27 cubic kilometers.
• The glacier is about 30 kilometers long and 2 to 4 kilometers wide.
• The snout of the glacier is known as Gaumukh, which is the source of the Bhagirathi River, one of the main headstreams of the Ganga.
• Pindari Glacier:
• Situated in the Kumaon region of the Himalayas in the Bageshwar district of Uttarakhand.
• This glacier has a length of roughly 3.2 kilometers and is the source of the Pindar River.
• It is a popular trekking destination in India due to its relatively easy accessibility compared to other Himalayan glaciers.

Important Points

• The Siachen Glacier is famously known as the highest battlefield in the world, where India and Pakistan have maintained a military presence since 1984.
• In April 1984, the Indian Army launched Operation Meghdoot, a military operation to seize control of the glacier, which was successful.
• The Nubra River originates from the snout of the Siachen Glacier and flows into the Shyok River.
• Administratively, the entire Siachen Glacier is part of the Union Territory of Ladakh in India since the reorganization of the state in October 2019.
• The Saltoro Ridge serves as a natural divide that separates the Siachen Glacier from Pakistan-occupied territory.

The correct answer is Task Manager.

Key Points

• The Task Manager is a system monitor and startup manager utility included with Microsoft Windows systems that allows users to monitor processor utilization, memory usage, and network activity. Hence, the statement regarding Task Manager is correct.
• To view the total processor utilization across all cores, a user must navigate to the Performance tab within the Task Manager. This section provides real-time graphical data on the CPU (Central Processing Unit), showing the percentage of processing power currently being utilized.
• The utility allows users to see a single overall graph or right-click to change the view to "Logical processors," which displays the utilization of every individual core and thread in the system.
• It serves as a critical diagnostic tool for identifying applications or background processes that are consuming excessive resources, potentially slowing down the computer.
• The Task Manager can be quickly accessed by pressing the keyboard shortcut Ctrl + Shift + Esc or by right-clicking the Taskbar in most Windows versions.

Additional Information

• My Computer (This PC):
• This is a system folder and file management interface used to access drives like the C: Drive, D: Drive, and external storage devices.
• It provides information about disk space and file hierarchy but does not show real-time CPU utilization. Hence, this statement is incorrect.
• Settings:
• This is a universal app in Windows 10 and Windows 11 designed to replace the legacy Control Panel for configuring system preferences.
• While it contains "About" information showing the processor model and RAM capacity, it is not the primary tool for monitoring live utilization across all cores. Hence, this statement is incorrect.
• Recycle Bin:
• The Recycle Bin is a directory where deleted files are temporarily stored before being permanently removed from the hard drive.
• It has no function related to hardware monitoring or system performance tracking. Hence, this statement is incorrect.

Important Points

• History of Task Manager: It was significantly overhauled in Windows 8 and Windows 10, introducing a cleaner "Processes" tab that groups applications and background tasks separately for better management.
• Metrics Tracked: Beyond CPU, the Performance tab tracks GPU (Graphics Processing Unit) utilization, Disk Read/Write speeds, and Ethernet/Wi-Fi throughput.
• Process Management: If a software program becomes unresponsive, the Task Manager allows a user to "End Task," which forcefully terminates the process to free up system resources.
• Uptime: The utility also displays the System Uptime (in Days:Hours:Minutes:Seconds), which indicates how long the computer has been running since the last reboot or startup.

Given: X, Y, Z, S, T and U live on six different floors of the same building.

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

Only two people live between T and Y.

Only S lives above U.

Z lives on an even numbered floor.

T lives on the lowermost floor. 

Now, people between X and T: 1 person

Hence, the correct answer is Option 3.

Given: J, K, L, R, S and T 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 is numbered 6.

Only three people live between R and S, where R lives below S.

J lives on an odd numbered floor and immediately above R.

L lives on one of the floors below K and on one of the floors above T.

Now, person on Floor 4 = L

Hence, the correct answer is Option 4.

The logic followed here is:

thus, "94" will replace the question mark in the given series.

Hence, the correct option is "Option 3".

The correct answer is M.S. Subbulakshmi and T. Sadasivam.

Key Points

• The biography titled "Sivam Subham: The Biography of a Couple" chronicles the intertwined lives of the legendary Carnatic vocalist M.S. Subbulakshmi and her husband, the freedom fighter and journalist T. Sadasivam.
• Highlighted in October 2025 current affairs, this book provides an in-depth look at how T. Sadasivam played a pivotal role in shaping the career of M.S. Subbulakshmi, moving beyond a standard biography to explore their spiritual and professional partnership.
• The book is authored by S. Janaki, a noted researcher and writer, who captures the essence of their life in Chennai and their contributions to Indian classical music and the Independence movement.
• It details the couple's immense philanthropic work, noting that they donated a significant portion of their lifetime earnings from concerts to various charitable causes, including hospitals and educational institutions.
• The narrative emphasizes T. Sadasivam’s role as a visionary who managed Subbulakshmi’s public persona, ensuring her music reached global audiences while maintaining the traditional roots of Carnatic music.

Additional Information

• M.S. Subbulakshmi (1916–2004):
• Born in Madurai, Tamil Nadu, she became the first musician ever to be awarded the Bharat Ratna, India's highest civilian honor, in 1998.
• In 1966, she became the first Indian musician to perform at the United Nations General Assembly, an event that brought international recognition to Indian classical music.
• She was the first Indian musician to receive the Ramon Magsaysay Award in 1974, often referred to as Asia's Nobel Prize, for her contribution to public service through music.
• T. Sadasivam (1902–1997):
• He was a leading freedom fighter and a close associate of C. Rajagopalachari. He co-founded the popular Tamil magazine Kalki in 1941.
• His management skills were legendary, as he successfully organized massive benefit concerts that raised millions of rupees for national and social causes.
• Significance of the Title:
• The title "Sivam Subham" is a play on their names—Sivam for Sadasivam and Subham representing the auspiciousness associated with Subbulakshmi.
• It symbolizes the harmony (Sruthi) that existed between them, which was essential for the preservation of cultural heritage in post-independence India.

Important Points

• Cultural Impact: The couple was instrumental in the Tamil Isai Movement, which promoted the singing of Tamil compositions in Carnatic concerts.
• Iconic Renditions: M.S. Subbulakshmi is world-renowned for her renditions of the Venkateswara Suprabhatam, Vishnu Sahasranamam, and Bhajans by Meera and Kabir, which remain staple recordings in Indian households.
• Acting Career: Before dedicating herself entirely to music, Subbulakshmi acted in several films, most notably Meera (1945), which was produced by Sadasivam and gained national acclaim.
• Historical Context: Their home in Madras (now Chennai) served as a meeting point for many political leaders and artists during the mid-20^th century, making them central figures in India's socio-cultural history.

The correct answer is Pallavas.

Key Points

• Vijayalaya was the founder of the Imperial Chola Empire in South India during the 9^th century. He belonged to the ancient Chola family of Uraiyur, which had a glorious past during the Sangam Age but had later declined into a minor power.
• Before establishing an independent kingdom, Vijayalaya served as a feudatory (vassal) of the Pallavas of Kanchipuram. This relationship highlights the political structure of the era where smaller local chieftains owed allegiance to dominant regional powers like the Pallavas.
• Around the year 850 AD, Vijayalaya took advantage of the constant warfare between the Pallavas and the Pandyas. He defeated the Muttharaiyars, who were subordinates to the Pandya kings and controlled the Kaveri delta.
• After capturing Thanjavur from the Muttharaiyars, he established it as the capital of the rising Chola kingdom. He also constructed a magnificent temple dedicated to the goddess Nishumbhasudini (a form of Durga) in Thanjavur to commemorate his victory.
• His reign lasted from 850 AD to 871 AD, laying the essential groundwork for his successors, particularly Aditya I, to expand the empire and eventually overthrow their Pallava overlords.

Additional Information

• Pallava Dynasty:
• The Pallavas ruled from Kanchipuram from the 3^rd century to the 9^th century AD.
• They were pioneers of Dravidian architecture, famously known for the rock-cut temples at Mahabalipuram and the Shore Temple.
• The Pallava power finally declined when the Chola ruler Aditya I defeated the last Pallava king, Aparajita, in 897 AD.
• Chalukya Dynasty:
• The Chalukyas were a major power in the Deccan region, with their capital at Badami (Vatapi).
• Pulakeshin II (610–642 AD) was their most famous ruler, known for defeating Harshavardhana on the banks of the Narmada River.
• They were persistent rivals of the Pallavas, often engaging in long-drawn conflicts over the fertile Raichur Doab.
• Western Ganga Dynasty:
• The Gangas ruled the southern part of modern-day Karnataka, a region known as Gangavadi, from the 4^th to the 10^th century.
• They often maintained their sovereignty by playing the role of a buffer state between the Pallavas, Chalukyas, and Rashtrakutas.
• They are well-known for the monolithic statue of Lord Bahubali (Gommateshwara) at Shravanabelagola, commissioned during the 10^th century.
• Vakataka Dynasty:
• The Vakatakas were a powerful dynasty in the Deccan (modern Maharashtra and Madhya Pradesh) from the 3^rd to 5^th century AD.
• They were contemporaries of the Guptas and entered into matrimonial alliances with them (e.g., Prabhavatigupta).
• They were significant patrons of the Ajanta Caves, particularly during the reign of Harisena.

Important Points

• The Imperial Chola dynasty established by Vijayalaya reached its zenith under Rajaraja I (985–1014 AD) and Rajendra I (1014–1044 AD).
• Rajaraja I constructed the world-famous Brihadisvara Temple in Thanjavur around 1010 AD, which is a UNESCO World Heritage Site.
• The Cholas are celebrated for their highly efficient local self-government system, as evidenced by the Uttaramerur Inscription, and for their maritime expeditions to Sri Lanka and Southeast Asia (Srivijaya empire).
• The transition from a Pallava feudatory to an independent empire showcases the Cholas' strategic ability to exploit political vacuums in the medieval South Indian landscape.

The logic followed here is:

So, 'MAR 27 ' will replace the question mark in the given series.

Hence, the correct answer is "Option 1".

Shortcut Trick

Sum of digits = 2+3+0+A+7+8+0+7 = 27 + A

⇒ For divisibility by 3 → sum must be multiple of 3

⇒ 27 is divisible by 3 ⇒ A must be divisible by 3

⇒ Max digit satisfying = 9

∴ Answer = 9

Alternate Method

Given:

Number = 230A7807

Concept Used:

A number is divisible by 3 if sum of its digits is divisible by 3

Calculation:

⇒ Sum of digits = 2 + 3 + 0 + A + 7 + 8 + 0 + 7

⇒ = 27 + A

⇒ For divisibility by 3:

⇒ (27 + A) must be divisible by 3

⇒ 27 is already divisible by 3

⇒ So A must be divisible by 3

⇒ Possible values: 0, 3, 6, 9

⇒ Maximum value = 9

∴ The correct answer is 9.

Additional Information

Divisibility Rule (3): Sum of digits divisible by 3

Digit Range: A can take values from 0 to 9

Shortcut: Ignore already divisible part and focus on variable digit