Shortcut Trick

Given: a + 1/a = 3

Shortcut: Use the identity: a⁶ + 1/a⁶ = (a² + 1/a²)³ − 3(a² + 1/a²).

First, a² + 1/a² = (a + 1/a)² − 2 = 3² − 2 = 7.

Now, a⁶ + 1/a⁶ = 7³ − 3(7) = 343 − 21 = 322.

∴ Answer = 322

Alternate Method

Given:

a + 1/a = 3

Formula used:

a⁶ + 1/a⁶ = (a² + 1/a²)³ − 3(a² + 1/a²)

Calculations:

Step 1: a² + 1/a² = (a + 1/a)² − 2

⇒ a² + 1/a² = 3² − 2 = 9 − 2 = 7

Step 2: a⁶ + 1/a⁶ = (a² + 1/a²)³ − 3(a² + 1/a²)

⇒ a⁶ + 1/a⁶ = 7³ − 3(7) = 343 − 21 = 322

∴ The correct answer is 322.

Additional Information

Formula for Higher Powers

For any n, aⁿ + 1/aⁿ can be derived using lower powers and substitution.

Key Identity Used

a⁶ + 1/a⁶ = (a² + 1/a²)³ − 3(a² + 1/a²).

Shortcut for a² + 1/a²

a² + 1/a² = (a + 1/a)² − 2 — useful for intermediate steps.

The correct answer is 1 and 3 only.

Key Points

• Before the Prime Minister enters upon his office, the President administers to him the oaths of office and secrecy. In his oath of office, the Prime Minister swears to bear true faith and allegiance to the Constitution of India, to uphold the sovereignty and integrity of India, and to faithfully discharge the duties of his office. In his oath of secrecy, he swears that he will not directly or indirectly communicate or reveal any matter that is brought under his consideration. Hence, statement 1 is correct.
• The President can dismiss the Prime Minister at any time in an arbitrary way. This is a misunderstanding of the constitutional provision. Although Article 75 states that the Prime Minister shall hold office during the pleasure of the President, this pleasure is not arbitrary. So long as the Prime Minister enjoys the majority support in the Lok Sabha (the Lower House of Parliament), the President cannot dismiss him. Hence, statement 2 is incorrect.
• If the Prime Minister loses the confidence of the Lok Sabha, he must resign or the President can dismiss him. This is based on the principle of Collective Responsibility mentioned in Article 75 of the Constitution of India. If a No-Confidence Motion is passed against the government in the Lok Sabha, the entire Council of Ministers, including the Prime Minister, must resign. If they fail to do so, the President has the constitutional power to dismiss the government. Hence, statement 3 is correct.
• The Prime Minister is the real executive authority (de facto executive) while the President is the nominal executive authority (de jure executive). The Prime Minister acts as the head of the Union Council of Ministers.

Additional Information

• Constitutional Provisions:
• Article 74: There shall be a Council of Ministers with the Prime Minister at the head to aid and advise the President who shall, in the exercise of his functions, act in accordance with such advice.
• Article 75: The Prime Minister shall be appointed by the President and the other Ministers shall be appointed by the President on the advice of the Prime Minister.
• Article 78: It defines the duties of the Prime Minister in respect of the furnishing of information to the President, including communicating all decisions of the Council of Ministers relating to the administration of the affairs of the Union.
• Eligibility and Appointment:
• To become the Prime Minister of India, a person must be a citizen of India and a member of either the Lok Sabha or the Rajya Sabha.
• If the person is a member of the Lok Sabha, the minimum age should be 25 years, and if he/she is a member of the Rajya Sabha, the age should be 30 years.
• A person who is not a member of either House of Parliament can also be appointed as Prime Minister for 6 months, within which he/she must get elected to either House.
• Powers and Functions:
• The Prime Minister allocates and reshuffles various portfolios among the Ministers.
• He presides over the meeting of the Council of Ministers and influences its decisions.
• He is the principal channel of communication between the President and the Council of Ministers.
• He advises the President with regard to the appointment of important officials like the Attorney General of India, Comptroller and Auditor General of India (CAG), and Chairmen of the UPSC.

Important Points

• Term of Office: The term of the Prime Minister is not fixed by the Constitution. He holds office as long as he enjoys the support of the majority in the Lok Sabha. Generally, this coincides with the life of the Lok Sabha, which is 5 years.
• Ex-officio Positions: The Prime Minister is the Chairman of the NITI Aayog (which replaced the Planning Commission on January 1, 2015), the National Development Council, the National Integration Council, the Inter-State Council, and the National Water Resources Council.
• Historical Context: Jawaharlal Nehru was the first Prime Minister of India, serving from 1947 to 1964. Gulzarilal Nanda was the first Acting Prime Minister. Indira Gandhi was the first woman Prime Minister.
• Salary and Allowances: The salary and allowances of the Prime Minister are determined by the Parliament from time to time. He receives the same salary and allowances as are payable to a Member of Parliament, plus a sumptuary allowance and other perks.

Shortcut Trick

⇒ √2601 = 51

⇒ 816 ÷ 51 = 16

⇒ 22 × 3 × 16 = 22 × 48 = 1056

⇒ y = 1056 − 794 = 262

∴ Answer = 262

Alternate Method

Given:

22 × 3 × 816 ÷ √2601 = y + 794

Concept Used:

BODMAS rule

Calculation:

⇒ 22 × 3 × 816 ÷ 51 = y + 794

⇒ 22 × 3 × 16 = y + 794

⇒ 22 × 48 = y + 794

⇒ 1056 = y + 794

⇒ y = 1056 − 794

⇒ y = 262

∴ The correct answer is 262.

Additional Information

Perfect Square: √2601 = 51, useful for fast simplification.

BODMAS Rule: Follow correct order: division and multiplication before addition.

Cancellation: 816 ÷ 51 simplifies early to reduce calculation load.

Linear Equation: Solve y + constant = value by shifting constant to RHS.

Shortcut Trick

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

⇒ Remaining men = 50

⇒ Days = 2700 ÷ 50 = 54

∴ Answer = 54 days

Alternate Method

Given:

100 men → 27 days

50 men → ? days

Concept Used:

Men × Days = Constant (Total work/food)

Calculation:

⇒ 100 × 27 = 50 × x

⇒ 2700 = 50x

⇒ x = 2700 ÷ 50

⇒ x = 54

∴ The correct answer is 54 days.

Additional Information

Man-Days Concept: Total work = Men × Days remains constant.

Inverse Proportion: More men → fewer days, fewer men → more days.

LCM Method: Assume total work as LCM for faster calculation in exams.

Shortcut Tip: Directly divide total man-days by remaining men.

Shortcut Trick

⇒ Assume CP of 1 kg = 100

⇒ 45% loss ⇒ SP = 55

⇒ Overall gain = 50% ⇒ Effective SP = 150

⇒ So, 55 price is actually for weight = 55/150 kg

⇒ = 0.3667 kg = 366.7 gm

∴ Answer = 366.7 gm

Alternate Method

Given:

Loss = 45%

Gain due to false weight = 50%

Concept Used:

Net gain when false weight is used

Calculation:

⇒ Assume CP of 1 kg = 100

⇒ Due to 45% loss, SP of 1 kg = 55

⇒ Let actual weight given = x kg

⇒ CP of x kg = 100x

⇒ Profit % = 50%

⇒ SP = 1.5 × CP = 1.5 × 100x = 150x

⇒ But SP = 55

⇒ 150x = 55

⇒ x = 55 ÷ 150

⇒ = 0.3667 kg = 366.7 gm

∴ The correct answer is 366.7 gm

Additional Information

False Weight Trick: Profit % = (SP − CP)/CP × 100

Shortcut Formula: Actual weight = (Apparent SP)/(Real SP after profit)

Common Trap: Loss shown is fake; actual profit comes from less quantity.

Exam Tip: Always assume CP = 100 for easier percentage calculations.

The logic followed here is:

So, 'NQO 57' will replace the question mark in the given series.

Hence, the correct answer is "Option 3".

The correct answer is A socio-political movement for Dalit rights and social equality.

Key Points

• The Mahar Movement was a significant organized struggle in Maharashtra primarily led by Dr. B.R. Ambedkar in the early 20^th century. It was fundamentally a socio-political movement aimed at achieving human rights, social equality, and the destruction of the caste system. Hence, the first statement is correct.
• A landmark event of this movement was the Mahad Satyagraha on March 20, 1927, where Dr. Ambedkar led the Mahar community to drink water from the Chardar Tank in Mahad, asserting their right to use public water resources.
• The movement also involved the symbolic burning of the Manusmriti in December 1927, representing a rejection of ancient texts that justified untouchability and social discrimination.
• The movement was not just social but also political, as it demanded separate electorates for the Depressed Classes, which eventually led to the Poona Pact of 1932.
• Unlike tribal uprisings that fought against British forest laws or peasant movements against landlords, the Mahar movement focused on internal social reform and constitutional safeguards for the Dalit population. Hence, statements 2 and 4 are incorrect.

Additional Information

• Historical Context: The Mahars were a traditionally untouchable community in Maharashtra with a history of military service in the British Indian Army (notably the Mahar Regiment). This military background provided them with early exposure to education and discipline, fostering a sense of self-respect.
• Early Pioneers: Before Dr. Ambedkar, leaders like Gopal Baba Walangkar (who founded the Anarya Dosha-Parihar Mandali in 1888) and Shivram Janba Kamble initiated efforts to organize the community and demand government jobs.
• Satyashodhak Samaj: While Jyotirao Phule’s Satyashodhak Samaj (founded in 1873) influenced the movement by critiquing Brahmanical hegemony, the Mahar movement under Ambedkar specifically transitioned from seeking Sanskritization (adopting upper-caste rituals) to radical political mobilization.
• Contrast with Other Movements:
• Tribal Movements: Examples include the Santhal Rebellion (1855) and Munda Uprising (1899), which were primarily anti-colonial and agrarian in nature.
• Peasant Movements: Examples include the Champaran Satyagraha (1917) or the Tebhaga Movement (1946), focusing on rent reduction and land rights.
• Religious Reform: Movements like the Arya Samaj aimed at purifying rituals, whereas the Mahar movement eventually moved away from Hinduism entirely.

Important Points

• Conversion to Buddhism: A major culmination of the movement occurred on October 14, 1956, at Deekshabhoomi in Nagpur, where Dr. B.R. Ambedkar along with nearly 365,000 followers converted to Buddhism (Navayana), seeking a religious identity free from the caste hierarchy.
• Education and Publication: The movement utilized journalism as a tool, with publications like Mooknayak (1920) and Bahishkrit Bharat (1927) playing a pivotal role in mass mobilization and public awareness.
• Impact on Modern India: The Mahar movement laid the foundation for Reservation Policy in the Indian Constitution and continues to influence the Dalit Panther movement and modern Ambedkarite politics in India.

The correct answer is Fergusson College Grounds.

Key Points

• The Pune Book Festival 2025 is organized at the Fergusson College Grounds, which is a prominent landmark located on Fergusson College Road (FC Road) in Pune, Maharashtra. This venue is historically significant and provides the vast open space required for such a large-scale literary gathering.
• The event is primarily organized by the National Book Trust (NBT), an autonomous organization under the Ministry of Education, Government of India, in collaboration with the Government of Maharashtra and the Pune Municipal Corporation (PMC).
• The main objective of the festival is to promote a reading culture and literature in various languages, including Marathi, Hindi, English, Sanskrit, and other regional Indian languages, aligning with the goals of the National Education Policy (NEP) 2020.
• The festival serves as a platform for thousands of publishers and booksellers to showcase millions of books, catering to all age groups, from children to senior citizens.
• The selection of Fergusson College as the venue is significant because the college itself is a symbol of the Renaissance in Western India and has been a hub for educational and cultural activities since its inception.

Additional Information

• National Book Trust (NBT), India:
• It was established in the year 1957 by the Government of India.
• The NBT works under the Department of Higher Education, Ministry of Education.
• Its primary mandate is to produce and encourage the production of good literature and to make such literature available at moderate prices to the public.
• Fergusson College:
• Founded in 1885 by the Deccan Education Society (DES).
• It was named after Sir James Fergusson, the then Governor of Bombay.
• Founding members included legendary figures such as Bal Gangadhar Tilak, Gopal Ganesh Agarkar, and Mahadev Ballal Namjoshi.
• Pune's Literary Heritage:
• Pune is widely recognized as the 'Cultural Capital of Maharashtra' and the 'Oxford of the East' due to its high density of educational institutions and literary history.
• The city hosts various other literary events like the Pune International Literary Festival (PILF) and several Marathi Sahitya Sammelans.
• Guinness World Records:
• During the 2023 edition of the Pune Book Festival, the city set a Guinness World Record for the 'Largest Reading Activity', where 3,066 parents read to their children simultaneously, surpassing the previous record held by China.

Important Points

• The Pune Book Festival typically includes a 'Bal Sahitya Melawa' (Children's Literature Festival) to engage young readers through storytelling, workshops, and interactive sessions.
• The venue, Fergusson College Grounds, allows for the setup of hundreds of stalls, separate stages for literary discussions, and dedicated zones for food and cultural performances.
• The festival reflects India's G20 Presidency themes of 'Vasudhaiva Kutumbakam' (The World is One Family) by showcasing books that promote global knowledge and Indian heritage.
• It also emphasizes digital literacy by featuring sections on e-books and digital libraries alongside traditional printed media.

The correct answer is Four: income, welfare, minimum needs, and capabilities approaches.

Key Points

• The Income Approach is one of the oldest methods used to measure human development. It links the level of development directly to income, under the assumption that higher income reflects a higher level of human development and greater freedom. Hence, statement 1 is incorrect as it includes participatory and rights-based approaches which are not part of the four "main" traditional classifications.
• The Welfare Approach views human beings as beneficiaries or targets of all development activities. This approach argues for higher government expenditure on education, health, and other social sectors to improve the quality of life. Hence, statement 2 is incorrect.
• The Basic Needs Approach was initially proposed by the International Labour Organisation (ILO). It identifies six basic needs: health, education, food, water supply, sanitation, and housing. This approach ignores the question of human choices and focuses primarily on the provision of these necessities. Hence, statement 3 is incorrect.
• The Capability Approach is closely associated with the work of Prof. Amartya Sen, the Indian Nobel Laureate. It focuses on building human capabilities in the areas of health, education, and access to resources as the key to increasing human development. Hence, statement 4 is correct.
• Collectively, these four methods represent the primary framework through which human development has been historically analyzed and implemented by global organizations.

Additional Information

• Concept of Human Development: The concept was introduced by Dr. Mahbub ul Haq, a Pakistani economist, in 1990. He described it as development that enlarges people's choices and improves their lives.
• United Nations Development Programme (UNDP): Since 1990, the UNDP has published the Human Development Report (HDR) annually. This report provides the Human Development Index (HDI), which ranks countries based on their progress in key dimensions.
• Dimensions of HDI: The index is a composite statistic of life expectancy (Health), education (Mean years of schooling and Expected years of schooling), and per capita income (Standard of living) indicators.
• Amartya Sen’s Contribution: Prof. Amartya Sen emphasized that the objective of development is to increase freedom. He argued that the lack of capabilities (like illiteracy or poor health) limits the choices people can make, thereby hindering development.
• Global Trends: Modern reports, such as the 2023-24 HDR, now also consider factors like planetary pressures and inequality (IHDI) to provide a more holistic view of global progress.

Important Points

• Linguistic and Cultural Factors: While not part of the "four main approaches," factors like gender empowerment and political freedom are often measured through supplementary indices like the Gender Inequality Index (GII).
• Income vs. Capability: A crucial distinction in these approaches is that while the Income Approach focuses on what people have, the Capability Approach focuses on what people are capable of doing with what they have.
• Government Policy: The Welfare Approach is often the basis for Social Security programs and Universal Healthcare initiatives in many countries, including India.
• ILO Standards: The Basic Needs Approach remains relevant for developing nations striving to meet the Sustainable Development Goals (SDGs) set by the United Nations for 2030.

The correct answer is Microsoft Word.

Key Points

• Microsoft Word is a prime example of Application Software. This type of software is designed to perform specific tasks for the end-user, such as word processing, document creation, and formatting.
• Application software like Microsoft Word depends entirely on System Software (the Operating System) to function because it cannot interact directly with the computer's Hardware (such as the CPU, RAM, or Hard Drive). Hence, the option Microsoft Word is the correct answer.
• BIOS (Basic Input/Output System) is a type of Firmware and System Software that initializes hardware during the Booting process. It does not depend on other system software to start; rather, it is the first software to run when a computer is powered on. Hence, the statement regarding BIOS as an application software is incorrect.
• Ubuntu is a popular Linux-based Operating System. It is categorized as System Software because its primary function is to manage computer resources and provide a platform for application programs. Hence, the statement regarding Ubuntu being an application software is incorrect.
• The Linux Kernel is the core component of the Linux Operating System. It acts as a bridge between Software and Hardware. It is the most fundamental part of System Software and manages low-level tasks like Memory Management and Process Scheduling. Hence, the statement regarding Linux Kernel being an application software is incorrect.

Additional Information

• Application Software:
• These are programs developed to assist users in performing specific personal, educational, or business tasks.
• Functions: Includes Data Manipulation, Image Editing, Web Browsing, and Communication.
• Examples: Google Chrome (Web Browser), Adobe Photoshop (Graphics Editor), VLC Media Player, and Microsoft Excel (Spreadsheet).
• Characteristics: They are usually written in High-Level Languages like Java, C++, or Python and require an Operating System to execute their instructions.
• System Software:
• This software acts as an interface between the user, the application software, and the computer's hardware.
• Categories: It includes Operating Systems (like Windows 11, macOS, and Android), Language Translators (Compilers and Interpreters), and Device Drivers.
• Utility Software: A sub-category of system software used for maintenance, such as Antivirus software, Disk Defragmenters, and Compression tools (like WinZip).

Important Points

• Dependency Layer: In a computing environment, the hierarchy of operation starts with the Hardware at the bottom, followed by the System Software (OS), then the Application Software, and finally the User at the top.
• Interaction: When a user types a character in Microsoft Word, the application sends a request to the Operating System, which then instructs the Hardware (Keyboard and Monitor) to process and display the input.
• Installation: System Software is typically installed when the computer is set up, whereas Application Software is installed by the user based on their specific needs.
• Execution: System Software starts running as soon as the computer is turned on and stays active until the system is shut down, whereas Application Software only runs when triggered by the user.

Shortcut Trick

⇒ Convert everything into same base: (28/9) and (9/28)

⇒ (9/28) = (28/9)⁻¹

⇒ Total power of (28/9) = 11 + 17 − 16 = 12

⇒ RHS: (9/28)^2m+8 = (28/9)^−(2m+8)

⇒ 12 = −(2m + 8) ⇒ 2m = −20 ⇒ m = −10

∴ Answer = −10

Alternate Method

Given:

(28/9)¹¹ × (9/28)¹⁶ × (28/9)¹⁷ = (9/28)^{2m + 8}

Concept Used:

Laws of exponents

Calculation:

⇒ (9/28)¹⁶ = (28/9)⁻¹⁶

⇒ LHS = (28/9)¹¹ × (28/9)⁻¹⁶ × (28/9)¹⁷

⇒ = (28/9)^{11 − 16 + 17}

⇒ = (28/9)¹²

⇒ RHS = (9/28)^2m+8 = (28/9)^−(2m+8)

⇒ (28/9)¹² = (28/9)^−(2m+8)

⇒ 12 = −(2m + 8)

⇒ 12 = −2m − 8

⇒ 2m = −20

⇒ m = −10

∴ The correct answer is −10.

Additional Information

Exponent Rule: a^m × aⁿ = a^m+n

Negative Power: a⁻ⁿ = 1/aⁿ

Base Conversion: (a/b) = (b/a)⁻¹

Equality Rule: If bases are same, equate exponents directly.

The correct answer is It converts light energy into chemical energy.

Key Points

• Photosynthesis is the biological process by which green plants, algae, and certain bacteria transform light energy into chemical energy. This energy is stored in the bonds of sugar (glucose).
• It occurs in the chloroplasts of plant cells, specifically within the thylakoid membranes and the stroma, not in the mitochondria. Mitochondria are primarily responsible for cellular respiration. Hence, statement 1 is incorrect.
• The core function of this process is the conversion of solar radiation into stable chemical energy. This process supports almost all life on Earth by providing the primary energy source in the food chain. Hence, statement 2 is correct.
• The process involves the synthesis of glucose from carbon dioxide and water, rather than the breakdown of glucose. The breakdown of glucose to release ATP is a characteristic of respiration. Hence, statement 3 is incorrect.
• Photosynthesis consists of light-dependent reactions which require direct sunlight to split water molecules. While the light-independent reactions (Calvin Cycle) can occur without light, they rely on ATP and NADPH produced during the day. It does not primarily take place at night. Hence, statement 4 is incorrect.

Additional Information

• Chlorophyll: This is the primary pigment involved in photosynthesis. It is located in the chloroplast and is responsible for absorbing blue and red light while reflecting green light, which gives plants their color.
• The Chemical Equation: The generalized balanced equation for photosynthesis is 6CO2 + 6H2O + Light Energy → C6H12O6 + 6O2. This shows that six molecules of carbon dioxide and six molecules of water are converted into one molecule of glucose and six molecules of oxygen.
• Stomata: These are microscopic pores located on the epidermis of leaves. Their primary function is to allow the entry of CO2 and the exit of O2 and water vapor through transpiration.
• Organisms: While terrestrial plants are the most visible photosynthesizers, phytoplankton in the oceans contribute to nearly 50% of the oxygen produced on Earth.
• History: The discovery of photosynthesis evolved over centuries, with significant data contributed by Jan Ingenhousz in 1779, who demonstrated that light is necessary for plants to purify air.

Important Points

• Light-Dependent Reaction: This stage takes place in the grana of the chloroplast. It involves photolysis of water, where water is split into oxygen, protons, and electrons.
• Calvin Cycle (C3 Cycle): Named after Melvin Calvin, who won the Nobel Prize in 1961. This stage occurs in the stroma and utilizes CO2 to produce sugar.
• Limiting Factors: The rate of photosynthesis is influenced by factors such as light intensity, carbon dioxide concentration, and temperature (optimally between 25°C to 35°C for many species).
• C4 and CAM Pathways: Certain plants in arid locations have evolved specialized features to minimize photorespiration and water loss, such as Crassulacean Acid Metabolism (CAM) where CO2 is taken up at night.
• Applications: Understanding photosynthesis is crucial for agriculture, forestry, and developing artificial photosynthesis technologies to produce clean fuels like hydrogen.

The correct answer is Mohenjodaro.

Key Points

• Mohenjodaro, which literally translates to the "Mound of the Dead" in the Sindhi language, was one of the largest and most prominent settlements of the ancient Indus Valley Civilization. It flourished around 2500 BCE.
• The city is famously known for the Great Bath, which was a large rectangular tank situated in the Citadel area. It was constructed using burnt bricks, coated with bitumen (natural tar) to ensure it was watertight, and featured changing rooms and a sophisticated drainage system. It is believed to have been used for religious or ritualistic bathing.
• Another hallmark of Mohenjodaro was its advanced urban planning. The city was laid out in a grid-pattern where streets were broad and intersected each other at 90-degree angles (right angles), dividing the residential areas into neat rectangular blocks.
• The site was discovered in 1922 by R. D. Banerji, an officer of the Archaeological Survey of India (ASI), just a year after the discovery of Harappa.
• Located in the Larkana district of Sindh, Pakistan, on the right bank of the Indus River, it served as a major political and commercial hub during the Bronze Age.

Additional Information

• Dholavira: Located in the Kutch district of Gujarat, India, this site was discovered by J.P. Joshi in 1967-68. It is unique for its three-part city division (Citadel, Middle Town, and Lower Town) and its highly sophisticated water management system, including giant reservoirs and a stadium.
• Kalibangan: Situated on the banks of the now-dry Ghaggar River in Hanumangarh, Rajasthan, it was identified by A. Ghosh in 1953. It is significant for providing the earliest evidence of a ploughed field and the presence of fire altars, suggesting fire worship.
• Lothal: Located in the Saurashtra region of Gujarat, it served as a vital maritime trade center. Its most distinguishing feature is the world's earliest known artificial brick dockyard, which connected the city to the Gulf of Khambhat through the Bhogava River.
• Indus Valley Civilization (IVC): Also known as the Harappan Civilization, it spanned parts of modern-day India, Pakistan, and Afghanistan. It is known for its standardized weights and measures, steatite seals, and a drainage system that was far more advanced than many contemporary civilizations.

Important Points

• Mohenjodaro yielded several iconic artifacts, including the bronze "Dancing Girl" statue, the steatite "Bearded Man" (often called the Priest-King), and the Pashupati Seal depicting a proto-Shiva figure.
• The city was divided into a Citadel (built on a raised platform for the ruling elite) and a Lower Town (where the common citizens resided).
• The Harappan script used in these cities consisted of approximately 400 to 600 symbols and was written in a boustrophedon style (right to left, then left to right), though it remains undeciphered to this day.
• Most Harappan cities, including Mohenjodaro, utilized burnt bricks with a standard ratio of 1:2:4 (thickness:width:length) for construction, demonstrating high architectural standardization.

The correct answer is Steatite.

Key Points

• Steatite, also commonly referred to as soapstone, was the primary material utilized by the craftsmen of the Harappan Civilization (also known as the Indus Valley Civilization) for the production of seals and beads.
• The choice of steatite was largely due to its physical properties; it is a soft mineral (composed mainly of talc) that is exceptionally easy to carve into intricate designs and scripts using copper tools.
• Once the carving process was complete, the Harappan artisans would often apply a whitening paste or silica coating to the steatite and then fire it in a kiln. This heating process caused the stone to harden significantly, giving it a durable, white, and lustrous finish.
• The Harappan seals were typically square or rectangular in shape, with dimensions often around 2x2 centimeters or 5x5 centimeters. These seals usually featured an animal motif (such as the unicorn, bull, elephant, or tiger) and a short inscription in the Indus script.
• In the context of bead-making, steatite was used to create a variety of shapes, including disc, cylindrical, and spherical forms. The civilization is particularly noted for its micro-beads made of steatite, which required high levels of technical precision.

Additional Information

• Significance of Seals: The seals served as vital tools for long-distance trade. They were used to stamp clay tags on bundles of goods. If the impression remained intact upon reaching its destination, it served as proof that the package had not been tampered with and authenticated the identity of the sender.
• Diverse Materials: While steatite was the most common, other materials used for making beads and seals included terracotta (fired clay), faience (a glazed ceramic material), agate, chert, carnelian, jasper, copper, gold, and ivory.
• Manufacturing Centers: Archeological excavations have identified specific industrial hubs for bead and seal production. Chanhudaro and Lothal (in present-day Gujarat) were renowned centers for bead-making, featuring specialized drills and workshops.
• The Pashupati Seal: One of the most famous steatite artifacts is the Pashupati Seal found at Mohenjo-daro. It depicts a figure sitting in a yogic posture, surrounded by animals like a rhino, buffalo, elephant, and tiger, providing insights into the religious beliefs of the period.
• Indus Script: Most steatite seals carry inscriptions in the Indus script, which remains undeciphered to this day. The script is usually written from right to left (boustrophedon style).

Important Points

• Chronology: The Harappan Civilization flourished during the Bronze Age, primarily between 2600 BCE and 1900 BCE (the Mature Harappan phase).
• Geographical Extent: The civilization covered a vast area including modern-day Pakistan, Northwest India (states like Rajasthan, Gujarat, Haryana, and Punjab), and parts of Afghanistan.
• Bead Varieties: The Harappans were masters of lapidary work. For instance, carnelian (a beautiful red stone) was sourced from Bharuch in Gujarat to make highly prized beads.
• Standardization: The production of steatite seals shows a high degree of standardization in weight and measure across different cities like Harappa, Mohenjo-daro, and Kalibangan, indicating a centralized or highly organized administrative system.
• Artistic Legacy: The use of steatite allowed for realistic carvings of animals, which are considered some of the finest examples of proto-historic art in the world.

The logic followed here is:

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

Only one person sits between P and R when counted from the right of R.

P sits third to the left of S.

O sits third to the left of B.

C is an immediate neighbor of both R and S.

So, There are  2 people in between Q and C.

 

Hence, the correct answer is "Option 3".

Given: C, D, N, O, P and Q live on six different floors of the same building.

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

No one lives above D.

Only two people live between D and C.

Only two people live between O and Q.

Q lives below C but above N.

Now, people between P and N: 2 people

Hence, the correct answer is Option 3.

Shortcut Trick

⇒ TSA of hemisphere = 3πr²

⇒ 3 × (22/7) × r² = 200

⇒ (66/7)r² = 200

⇒ r² = (200 × 7) ÷ 66 = 1400/66 = 700/33

⇒ r = $\sqrt{\frac{700}{33}}$

∴ Answer = $\sqrt{\frac{700}{33}}$

Alternate Method

Given:

Total surface area of hemisphere = 200 cm²

π = 22/7

Formula:

Total surface area of solid hemisphere = 3πr²

Calculation:

⇒ 3 × (22/7) × r² = 200

⇒ (66/7)r² = 200

⇒ r² = (200 × 7) ÷ 66

⇒ r² = 1400/66 = 700/33

⇒ r = √(700/33)

∴ The correct answer is $\sqrt{\frac{700}{33}}$ cm.

Additional Information

Hemisphere TSA: Total surface area = 3πr²

CSA of Hemisphere: Curved surface area = 2πr²

Base Area: Circular base = πr²

Exam Tip: Always remember TSA = CSA + base area.

The correct answer is Gujarat.

Key Points

• Gujarat emerged as the leading state in groundnut production and exports in India during the financial year 2020-2021. The state consistently accounts for a massive share, often exceeding 40%, of the total groundnut production in the country.
• The Ministry of Commerce and Industry, through its nodal agency APEDA (Agricultural and Processed Food Products Export Development Authority), reported that India exported a total of 6.38 lakh metric tonnes of groundnuts worth USD 727 million (approximately Rs. 5,381 crores) during 2020-21.
• The major groundnut-producing regions in Gujarat are concentrated in the Saurashtra belt, including districts like Junagadh, Rajkot, Amreli, and Bhavnagar. The presence of well-drained sandy loam soil in these areas makes it ideal for cultivation.
• During the year 2020-2021, despite the global pandemic, Gujarat maintained its dominance due to its robust supply chain infrastructure and proximity to major ports like Kandla and Mudra, which facilitate easy international trade.
• The state’s success is attributed to the adoption of high-yielding varieties and modern irrigation techniques, which have significantly improved the productivity per hectare compared to other states.

Additional Information

• Groundnut Characteristics and Uses:
• Groundnut (Arachis hypogaea) is a unique crop as it is a legume that matures its fruit underground. It is a rich source of protein (approx 25%), edible oil (48-50%), and vitamins.
• In India, it is primarily grown as a Kharif crop (sown in June-July and harvested in October-November), but in states like Tamil Nadu and Andhra Pradesh, it is also grown as a Rabi crop.
• The uses of groundnut range from direct human consumption (as table nuts), extraction of peanut oil for cooking, and the manufacture of peanut butter and confectionery products.
• Global and National Standing:
• India is the second-largest producer of groundnuts in the world, following China.
• The major export destinations for Indian groundnuts in 2020-21 included Indonesia, Vietnam, Philippines, Thailand, and Malaysia.
• Other significant groundnut-producing states in India include Rajasthan, Tamil Nadu, Andhra Pradesh, and Karnataka, but Gujarat remains the undisputed leader in export volume.

Important Points

• Export Varieties: The two main varieties of groundnuts exported from India are Bold and Java. The Java variety is smaller and rounder, while the Bold variety is larger and elongated.
• Quality Control: To maintain its status as a major exporter, India follows strict guidelines regarding Aflatoxin levels. APEDA has established monitoring laboratories to ensure that the produce meets European Union and South East Asian safety standards.
• Climate Requirements: The crop requires a temperature between 20°C and 30°C and a moderate rainfall of 50 cm to 100 cm. Excessive rain during the ripening stage can damage the pods.
• Economic Impact: In 2020-2021, the groundnut sector provided significant employment to millions of farmers in Gujarat and contributed substantially to the foreign exchange reserves of India.

The correct answer is The Legal Services Authorities Act, 1987.

Key Points

• The Lok Adalat (People's Court) is one of the Alternative Dispute Resolution (ADR) mechanisms in India, which serves as a forum where disputes or cases pending in the court of law or at the pre-litigation stage are settled or compromised amicably.
• Lok Adalats have been given statutory status under the Legal Services Authorities Act, 1987. This specific legislation provides a legal framework for the organization and functioning of these forums across the country. Hence, the statement regarding the Legal Services Authorities Act, 1987 is correct.
• Under this Act, the award (decision) made by the Lok Adalats is deemed to be a decree of a civil court and is final and binding on all parties involved. No appeal lies to any court against such an award.
• The primary objective of this Act is to fulfill the mandate of Article 39A of the Constitution of India, which directs the State to provide free legal aid to the weaker sections of society and ensure justice for all.
• The organization of Lok Adalats is handled by the National Legal Services Authority (NALSA) along with other legal services institutions at the State, District, and Taluk levels.

Additional Information

• The Indian Constitution: While the Constitution contains Article 39A (inserted by the 42^nd Amendment Act, 1976) which provides the philosophical basis for legal aid, it is not the specific Act that provides the operational statutory status to Lok Adalats. Hence, this statement is incorrect.
• The Arbitration and Conciliation Act, 1996: This legislation primarily deals with domestic arbitration, international commercial arbitration, and conciliation. While it is a part of the ADR family, it does not govern the Lok Adalat system. Hence, this statement is incorrect.
• The Civil Procedure Code (CPC), 1908: Section 89 of the CPC was amended to allow courts to refer pending cases to ADR methods like mediation and Lok Adalats to reduce the burden on the judiciary. However, the CPC itself is not the source of statutory status for Lok Adalats. Hence, this statement is incorrect.
• Historical Context: The first Lok Adalat in post-independence India was held on March 14, 1982, at Junagadh in Gujarat. It was a voluntary and conciliatory agency without any statutory backing at that time, before the 1987 Act was implemented.
• Benefits: One of the major features of Lok Adalats is that there is no court fee. If a case already filed in a regular court is settled in a Lok Adalat, the fee paid to the court is refunded to the parties.

Important Points

• Composition: A Lok Adalat generally consists of a judicial officer (sitting or retired) as the chairman, along with two other members, usually a lawyer and a social worker.
• Jurisdiction: They can deal with civil cases, matrimonial disputes, land acquisition cases, labour disputes, compoundable criminal offences, and bank recovery cases.
• Permanent Lok Adalats: The Legal Services Authorities Act was amended in 2002 to provide for the establishment of Permanent Lok Adalats to deal with Public Utility Services such as transport, postal, telegraph, power, and water supply. Unlike regular Lok Adalats, Permanent Lok Adalats have the power to decide a case on merits even if the parties fail to reach a compromise.
• National Lok Adalats: These are held on a single day throughout the country in all courts from the Supreme Court to the Taluk levels at regular intervals to dispose of a massive number of cases.

Family Chart:

Decoding the Symbols:

Given: D − F + G ÷ H × J

It means: D is the brother of F, F is the daughter of G, G is the father of H, H is the wife of J

So, D is wife’s brother of J

Hence, the correct answer is "Option 4".

The correct answer is Freely transferable Duty Credit Scrips.

Key Points

• The Merchandise Exports from India Scheme (MEIS) was introduced in the Foreign Trade Policy (FTP) 2015-20. It aimed to provide financial incentives to exporters to offset infrastructural inefficiencies and associated costs involved in exporting goods manufactured or produced in India.
• Under this scheme, exporters are rewarded in the form of Duty Credit Scrips. These scrips are a type of certificate that allows the holder to pay various customs duties using the credit balance instead of cash.
• A defining feature of these scrips is that they are freely transferable. This means an exporter who receives a scrip but does not need to import any goods can sell the scrip in the open market to another importer at a discounted rate. Hence, the statement regarding freely transferable duty credit scrips is correct.
• The value of the reward is calculated as a percentage (typically 2%, 3%, or 5%) of the Free on Board (FOB) value of the exported goods in free foreign exchange.
• The scheme merged five earlier incentive programs, including the Focus Product Scheme (FPS) and the Focus Market Scheme (FMS), into a single, streamlined program to simplify the export process.
• The rewards are not provided in the form of equity shares, as the scheme is designed for immediate fiscal relief rather than long-term capital investment in Export Oriented Units (EOUs). Hence, statement 1 is incorrect.
• The scrips are transferable and are not cash vouchers, which differentiates them from direct cash subsidies. Hence, statement 2 is incorrect.
• While the scrips are used to offset taxes, they are specifically tradable instruments rather than just rebates that expire on a single use by the original exporter. Hence, statement 3 is incorrect.

Additional Information

• Transition to RoDTEP: Due to challenges at the World Trade Organization (WTO), where MEIS was viewed as a prohibited export subsidy, the Government of India replaced it with the Remission of Duties and Taxes on Exported Products (RoDTEP) scheme. This transition took effect from January 1, 2021.
• Directorate General of Foreign Trade (DGFT): The DGFT, under the Ministry of Commerce and Industry, is the primary body responsible for formulating the Foreign Trade Policy and issuing Duty Credit Scrips to eligible exporters.
• Utilization of Scrips: These scrips can be used for the payment of Basic Customs Duty (BCD) on imports of inputs or goods, including capital goods. However, they generally cannot be used to pay Integrated Goods and Services Tax (IGST) or Compensation Cess under the GST regime.
• Eligibility Criteria: The scheme covers a vast range of products, including agricultural goods, textiles, electronics, and pharmaceuticals. Exporters must have an IEC (Importer Exporter Code) and must submit their claims online through the DGFT portal within a specified time limit from the date of export.
• Market Categorization: Initially, MEIS categorized global markets into three groups (Group A, B, and C) to determine the level of incentive, with higher rewards often provided for exports to markets with higher logistics costs or strategic importance.

Important Points

• WTO Compliance: The shift from MEIS to RoDTEP was necessary because RoDTEP is a tax-neutral scheme that refunds internal taxes (like electricity duty or fuel tax) that were previously not refunded, making it WTO-compliant.
• Digital Transformation: Under the Digital India initiative, the process of applying for and receiving Duty Credit Scrips was made entirely paperless. The scrips are issued in an electronic form (e-MEIS), which are then recorded in the ICEGATE system of the Customs Department.
• Validity of Scrips: Usually, these scrips have a validity period of 24 months from the date of issue, within which they must be utilized or transferred.
• Impact on Economy: By providing these incentives, the Government of India aimed to increase India's share in global exports and generate employment in labor-intensive sectors. The scheme played a vital role in supporting Micro, Small, and Medium Enterprises (MSMEs) in reaching international markets.

Shortcut Trick

⇒ Let younger brother = x

⇒ Sharad = 2x, other brother = x − 3

⇒ 3 years ago total = (2x − 3) + (x − 3) + (x − 6) = 28

⇒ 4x − 12 = 28 ⇒ 4x = 40 ⇒ x = 10

⇒ Sharad = 2x = 20

∴ Answer = 20 years

Alternate Method

Given:

Sharad = 2 × younger brother

Other brother = younger brother − 3

Sum of ages 3 years ago = 28

Concept Used:

Linear equation (age relation)

Calculation:

⇒ Let younger brother = x

⇒ Sharad = 2x

⇒ Other brother = x − 3

⇒ 3 years ago ages:

Sharad = 2x − 3

Younger = x − 3

Other = x − 6

⇒ (2x − 3) + (x − 3) + (x − 6) = 28

⇒ 4x − 12 = 28

⇒ 4x = 40

⇒ x = 10

⇒ Sharad = 2x = 20

∴ The correct answer is 20 years.

Additional Information

Age Concept: Present age − past years gives past age.

Linear Equations: Used to solve age relation problems.

Common Trick: Assume variable for youngest to simplify relations.

Exam Tip: Always shift all ages to same timeline before forming equation.

The correct answer is Windows Media Audio format.

Key Points

• Windows Media Audio (WMA) is a proprietary audio data compression technology developed by Microsoft. It is both an audio codec and its corresponding audio format.
• The .wma file extension is used to identify these audio files, which are part of the broader Windows Media framework.
• The format was first released in 1999 by Microsoft as a competitor to the widely popular MP3 and RealAudio formats, claiming to offer better compression efficiency.
• Wired Media Audio format is a non-existent technical term in computer science and does not correspond to any standard file extension. Hence, this statement is incorrect.
• Windows Media Audio format is the correct expansion for the .wma extension, representing the suite of audio codecs developed for the Windows ecosystem. Hence, this statement is correct.
• Wireless Media Audio format refers generally to audio transmitted over wireless protocols (like Bluetooth or RF), but it is not a specific file format name. Hence, this statement is incorrect.
• WiFi Media Audio format refers to networking standards (IEEE 802.11) used for data transfer, but there is no such audio file format under this name. Hence, this statement is incorrect.

Additional Information

• Types of WMA: The WMA family consists of four distinct codecs: WMA (Standard), WMA Pro (supports multi-channel and high-resolution audio), WMA Lossless (compresses audio without losing data), and WMA Voice (optimized for low-bitrate speech).
• Container Format: A .wma file is typically encapsulated in the Advanced Systems Format (ASF) container, which is a proprietary Microsoft container for digital audio and video streams.
• Digital Rights Management (DRM): One of the significant features of the WMA format is its support for DRM. This allows content providers to protect their music from unauthorized copying or playback on non-licensed devices.
• Compatibility: While natively supported on Windows via Windows Media Player, users on macOS or Linux often require third-party software like VLC Media Player or specific codecs to play these files.
• Compression Algorithm: It uses a lossy compression method (except for the Lossless version) that removes certain parts of the audio data that the human ear cannot easily perceive to reduce file size.

Important Points

• Bitrate Performance: In its early years, Microsoft claimed that WMA could provide CD-quality audio at a lower bitrate (e.g., 64 kbps) compared to MP3 (which typically required 128 kbps for similar quality).
• Licensing: Unlike the MP3 format, which became royalty-free in 2017, WMA remains a proprietary technology owned by Microsoft Corporation.
• Device Support: Many hardware portable media players and car stereos from the early 2000s and 2010s were marketed with "WMA Support" as a key feature alongside MP3 compatibility.
• Year of Launch: The initial version of WMA was introduced in Windows 98 Second Edition and became more prominent with the launch of Windows XP and Windows Media Player 7 in the year 2000.

Shortcut Trick

⇒ 3A = 4B = 8C = k

⇒ A = k/3, B = k/4, C = k/8

⇒ A : B : C = 1/3 : 1/4 : 1/8

⇒ Multiply by LCM 24 ⇒ 8 : 6 : 3

∴ Answer = 8 : 6 : 3

Alternate Method

Given:

3A = 4B = 8C

Concept Used:

Equal ratio method

Calculation:

⇒ Let 3A = 4B = 8C = k

⇒ A = k/3

⇒ B = k/4

⇒ C = k/8

⇒ A : B : C = 1/3 : 1/4 : 1/8

⇒ Taking LCM of 3, 4, 8 = 24

⇒ (1/3)×24 : (1/4)×24 : (1/8)×24

⇒ 8 : 6 : 3

∴ The correct answer is 8 : 6 : 3.

Additional Information

Ratio Trick: If aA = bB = cC, then A : B : C = 1/a : 1/b : 1/c

LCM Use: Multiply ratios by LCM to remove fractions.

Proportionality: Equal expressions can be assumed as a constant.

Exam Tip: Always convert into simplest integer ratio.

Given:

: NRL :: GKE : %

Option 1) # = MKN, % = EMK

For # (MKN) to NRL

For GKE to % (EMK)

Since the patterns do not match, Option 1 is incorrect.

Option 2) # = PTN, % = EIC

For # (PTN) to NRL

For GKE to % (EIC)

Since the pattern for PTN to NRL (-2, -2, -2) is the same as the pattern for GKE to EIC (-2, -2, -2), Option 2 is correct.

Option 3) # = LTN, % = EMK

For # (LTN) to NRL

 

For GKE to % (EMK)

Since the pattern for LTN to NRL (+2, -2, -2) is not the same as the pattern for GKE to EMK (-2, +2, +6), Option 3 is incorrect.

Option 4) # = IUN, % = EMJ

For # (IUN) to NRL

For GKE to % (EMJ)

Since the pattern for IUN to NRL (+5, -3, -2) is not the same as the pattern for GKE to EMJ (-2, +2, +5), Option 4 is incorrect.

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: Second number = (First number × 5) − 1

Pattern check:

14 × 5 = 70 → 70 − 1 = 69

18 × 5 = 90 → 90 − 1 = 89

Now check all options:

1. 21, 109 = 21×5−1 = 105−1 = 104 ≠ 109
2. 22, 108 = 22×5−1 = 110−1 = 109 ≠ 108
3. 21, 108 = 21×5−1 = 104 ≠ 108
4. 22, 109 = 22×5−1 = 109 = 109

Correct: Option 4 (22, 109)

Only option 4 follows the pattern.

Hence, the correct answer is Option 4.

The correct answer is Ernest Rutherford.

Key Points

• Ernest Rutherford, a New Zealand-born physicist, is credited with the discovery of the atomic nucleus. He supervised the alpha-particle scattering experiment, also known as the Gold Foil Experiment, which was performed by his students Hans Geiger and Ernest Marsden in 1909.
• In this experiment, high-energy alpha particles (doubly charged helium ions with a mass of 4u) were directed at a very thin gold foil, which was approximately 1000 atoms thick. This was done to observe how the particles interacted with the matter inside the gold atoms.
• Rutherford observed that most of the alpha particles passed straight through the gold foil without any deflection. This led to the conclusion that most of the space inside an atom is empty. Hence, the experiment fundamentally changed the understanding of atomic structure.
• A small fraction of particles were deflected by small angles, and about 1 in 12,000 particles rebounded almost 180 degrees back. This indicated that the positive charge and nearly all the mass of the atom were concentrated in a very small, dense region called the nucleus.
• Based on these observations, Ernest Rutherford proposed the Nuclear Model of an Atom, which states that an atom has a positively charged center where the electrons revolve around it in circular paths.

Additional Information

• John Dalton: He was an English chemist and physicist who proposed the first modern Atomic Theory in 1803. He suggested that atoms were indivisible and indestructible spheres. However, Rutherford's experiment later proved that atoms are divisible and consist of subatomic particles.
• Niels Bohr: A Danish physicist who improved upon Rutherford’s model in 1913. Bohr postulated that electrons move in specific discrete orbits or energy levels around the nucleus without radiating energy, thus addressing the stability issues in Rutherford's model.
• William Henry: He was an English chemist known for Henry's Law, which relates the amount of gas dissolved in a liquid to its partial pressure. He did not play a direct role in the discovery of the atomic nucleus or the scattering experiment.
• Alpha Particles: These are positively charged particles consisting of two protons and two neutrons. They are identical to the nucleus of a helium-4 atom. Because of their positive charge, they were repelled by the nucleus during the experiment.

Important Points

• The experiment utilized a Zinc Sulfide (ZnS) screen placed around the gold foil. When an alpha particle struck the screen, it produced a tiny flash of light, allowing the researchers to track the location and angle of the particles after they passed through or hit the foil.
• The radius of the nucleus was calculated to be about 10 to the power of 5 times smaller than the radius of the atom. If an atom were the size of a football stadium, the nucleus would be about the size of a small marble in the center.
• Ernest Rutherford received the Nobel Prize in Chemistry in 1908 for his investigations into the disintegration of elements and the chemistry of radioactive substances.
• This experiment famously disproved J.J. Thomson’s Plum Pudding Model, which suggested that positive charge was spread uniformly throughout the atom like a pudding with electrons embedded like plums.

The logic followed here is based on the alphabetical difference between letters:

Option 1: JNT

Option 2: WAF 

Option 3: LPU 

Option 4: DHM 

Thus, JNT does not follow this pattern.

Hence, the odd one out is Option 1.

Shortcut Trick

⇒ Income ratio = 6 : 7, Expenditure ratio = 1 : 3

⇒ Saving same ⇒ Difference between income and expenditure equal

⇒ Take income = 6x, 7x and expenditure = y, 3y

⇒ 6x − y = 7x − 3y

⇒ x = 2y

⇒ Saving = 6x − y = 66000

⇒ 6(2y) − y = 66000 ⇒ 11y = 66000 ⇒ y = 6000

⇒ x = 12000

⇒ Vipul income = 6x = 72000

∴ Answer = 72000

Alternate Method

Given:

Income ratio = 6 : 7

Expenditure ratio = 1 : 3

Savings of each = 66000

Concept Used:

Income − Expenditure = Savings

Calculation:

⇒ Let incomes be 6x and 7x

⇒ Let expenditures be y and 3y

⇒ For Vipul: 6x − y = 66000

⇒ For Vijay: 7x − 3y = 66000

⇒ 6x − y = 7x − 3y

⇒ x = 2y

⇒ Substitute in first equation:

⇒ 6(2y) − y = 66000

⇒ 12y − y = 66000

⇒ 11y = 66000

⇒ y = 6000

⇒ x = 2y = 12000

⇒ Vipul income = 6x = 72000

∴ The correct answer is 72000.

Additional Information

Basic Formula: Income = Expenditure + Savings

Equal Savings Trick: Set both savings equal to form equation.

Ratio Conversion: Assume variables for ratios to simplify.

Exam Tip: Solve using elimination when two equations are formed.

The correct answer is One-third of the seats.

Key Points

• The Constitution (One Hundred and Sixth Amendment) Act, 2023, popularly known as the Nari Shakti Vandan Adhiniyam, seeks to reserve one-third (approximately 33%) of all seats for women in the Lok Sabha (House of the People) and the State Legislative Assemblies.
• The bill for this amendment was introduced as the Constitution (One Hundred and Twenty-Eighth Amendment) Bill, 2023, in the Lok Sabha on September 19, 2023, during a special session of Parliament held in the new Parliament building.
• The Act mandates that one-third of the total number of seats filled by direct election in the Lok Sabha shall be reserved for women. This includes seats reserved for women within the existing quotas for Scheduled Castes (SCs) and Scheduled Tribes (STs).
• The reservation will also apply to the Legislative Assembly of the National Capital Territory of Delhi. The implementation of this reservation is contingent upon the conduct of a Census and the subsequent delimitation exercise (readjustment of constituencies) based on that census data.
• This historic legislation received the President's assent on September 28, 2023, marking a significant milestone in India's legislative history regarding gender representation and women's empowerment.

Additional Information

• Constitutional Articles Inserted: The amendment introduced new articles into the Constitution of India, including Article 330A (for Lok Sabha reservation), Article 332A (for State Assemblies), and Article 334A (regarding the sunset clause).
• Duration and Sunset Clause: The reservation is initially set for a period of 15 years from the date of its commencement. However, the Parliament has the authority to extend this period by enacting further laws if deemed necessary.
• Rotation of Seats: The Act provides that the seats reserved for women shall be rotated to different constituencies in the State or Union Territory after every subsequent exercise of delimitation.
• Scope of the Act: It is important to note that this reservation does not apply to the Rajya Sabha (Council of States) or the State Legislative Councils (Upper Houses of State Legislatures), where members are not directly elected by the people.
• Historical Context: The quest for women's reservation in the Indian Parliament dates back several decades, with earlier versions of the bill being introduced in 1996, 1998, 1999, and 2008, but failing to pass both houses until the 2023 amendment.

Important Points

• Delimitation Condition: Article 334A specifies that the reservation will come into effect only after an exercise of delimitation is undertaken following the publication of the relevant figures of the first Census conducted after the Constitution (One Hundred and Sixth Amendment) Act, 2023 comes into force.
• Voting Statistics: The bill was passed almost unanimously in the Lok Sabha with 454 votes in favor and only 2 against. In the Rajya Sabha, it was passed unanimously with 214 votes on September 21, 2023.
• Union Law Minister: The bill was moved in the Parliament by the Union Minister of Law and Justice, Shri Arjun Ram Meghwal.
• Impact on Total Seats: In the current Lok Sabha with 543 seats, once implemented, the number of women members will rise to at least 181, significantly increasing from the 82 women members elected in the 2019 general elections.

The correct answer is Photosynthesis.

Key Points

• Photosynthesis is the fundamental biological process by which autotrophic organisms, such as green plants, algae, and certain cyanobacteria, synthesize their own food. This process effectively converts solar energy into chemical energy stored in the bonds of carbohydrates.
• The process primarily takes place in the leaves of the plant, specifically within specialized organelles called chloroplasts. These organelles contain the pigment chlorophyll, which is responsible for capturing light energy from the sun.
• For Photosynthesis to occur, the plant requires three essential raw materials: Carbon dioxide (CO2) absorbed from the atmosphere through the stomata, Water (H2O) absorbed from the soil via the roots, and Sunlight.
• The primary product of this reaction is Glucose (C6H12O6), a simple sugar that serves as the main source of energy for the plant's growth and metabolism. A vital byproduct of this process is Oxygen (O2), which is released back into the air.
• The generalized chemical equation for the process is: 6CO2 + 6H2O + Light Energy -> C6H12O6 + 6O2. Hence, Photosynthesis is the correct process described in the question.

Additional Information

• Respiration:
• Unlike photosynthesis, respiration is a catabolic process that occurs in all living cells, including plants. It involves the breakdown of glucose in the presence of oxygen to release energy in the form of ATP (Adenosine Triphosphate).
• This process takes place in the mitochondria and produces carbon dioxide and water as waste products. While photosynthesis "builds" food, respiration "burns" it for energy. Hence, statement regarding respiration is incorrect in the context of food making.
• Transpiration:
• Transpiration is the evaporation of water from the aerial parts of a plant, mainly through the stomata on the leaves.
• This process creates a suction force (transpiration pull) that helps in the upward movement of water and minerals from the roots to the rest of the plant. It also helps in cooling the plant during hot weather. Hence, statement regarding transpiration is incorrect.
• Fermentation:
• Fermentation is an anaerobic (occurring without oxygen) metabolic process. It is used by microorganisms like yeast and bacteria to convert sugars into ethanol, lactic acid, or gases.
• In humans, it occurs in muscle cells during intense exercise when oxygen supply is low, leading to the production of lactic acid. It is not a method for plants to manufacture food using sunlight. Hence, statement regarding fermentation is incorrect.

Important Points

• Two Stages of Photosynthesis: The process is divided into the Light-dependent reactions, which occur in the thylakoid membranes of the chloroplasts, and the Light-independent reactions (also known as the Calvin Cycle), which take place in the stroma.
• Factors Affecting the Rate: The efficiency of food production in plants is influenced by several external factors:
• Light Intensity: Increasing light generally increases the rate up to a certain point.
• Temperature: Enzymes required for the process work best within a specific temperature range (usually 25°C to 35°C).
• CO2 Concentration: Since carbon dioxide is a raw material, its availability directly affects the speed of the reaction.
• Global Significance: Photosynthesis is the primary source of all organic matter on Earth. It is responsible for maintaining the Oxygen levels in the atmosphere (approximately 21%), which is essential for the survival of aerobic organisms.
• Vascular Tissues: The Xylem tissue is responsible for transporting water from the roots to the leaves for photosynthesis, while the Phloem tissue transports the manufactured glucose (food) to other parts of the plant.

The correct answer is Malayalam.

Key Points

• Malayalam is a Dravidian language primarily spoken in the Indian state of Kerala and the union territories of Lakshadweep and Puducherry. It underwent a complex scriptural evolution involving Vatteluttu, Grantha, and Kolezhuthu. Hence, the statement regarding the scriptural evolution refers to Malayalam and is correct.
• The earliest script used for Malayalam was Vatteluttu (meaning "round writing"), which was also used for Tamil. By the 9^th century AD, as seen in the Vazhappally Inscription (dated 830 AD), Vatteluttu was the dominant script for the region.
• The Grantha script was later introduced to represent Sanskrit phonemes that were not present in the Vatteluttu alphabet. This led to a hybrid script known as Arya Ezhuthu, which eventually evolved into the modern Malayalam script.
• Kolezhuthu (meaning "rod-writing") was a derivative of Vatteluttu used primarily for maintaining land records and administrative documents in the Malabar and Cochin regions until the 18^th century.
• Malayalam was officially designated as a Classical Language of India in May 2013, becoming the fifth language to receive this status. This recognition was based on its high antiquity, a body of ancient literature, and an original literary tradition.

Additional Information

• Tamil: It was the first language to be declared a Classical Language in 2004. Its script evolved from Tamil Brahmi to Vatteluttu and finally to the modern Tamil script. It is primarily spoken in Tamil Nadu and Sri Lanka.
• Sanskrit: Declared a Classical Language in 2005. It is the liturgical language of Hinduism and has a vast body of literature including the Vedas and Upanishads. Its modern script is Devanagari.
• Kannada and Telugu: Both were granted Classical Language status in 2008. Kannada script evolved from the Kadamba script, while Telugu shares a common scriptural ancestor (Old Kannada-Telugu script) with Kannada.
• Odia: It was declared a Classical Language in 2014. The Odia script is a descendant of the Brahmi script and is used in the state of Odisha. It is known for its unique curved appearance due to the historical practice of writing on palm leaves.
• The Ministry of Culture sets the criteria for Classical Languages, which includes a recorded history of over 1500-2000 years and a literary heritage that is considered valuable by generations of speakers.

Important Points

• Thunchaththu Ezhuthachan, a 16^th-century poet, is revered as the Father of modern Malayalam literature. He is credited with popularizing the Arya Ezhuthu script through his translation of the Ramayana (Adhyathmaramayanam Kilippattu).
• The Vazhappally Inscription is the oldest available lithic record of Malayalam, written in the Vatteluttu script during the reign of Chera Perumal King Rajashekhara Varman.
• The linguistic identity of Malayalam is distinct from Tamil despite their shared Dravidian roots, with Malayalam exhibiting unique features such as the loss of personal endings in verbs and a heavy influence of Sanskrit vocabulary.
• The 8^th Schedule of the Indian Constitution currently lists 22 languages, including all the Classical Languages, which provides them with official institutional support and promotion.

Shortcut Trick

⇒ Mean = (7×12 + 8×13 + 9×12 + 10×11) ÷ 48

⇒ = (84 + 104 + 108 + 110) ÷ 48 = 406/48 ≈ 8.458 ≈ 8.485

⇒ Variance ≈ 1.207, SD = √1.207 ≈ 1.099

⇒ Match: Mean → 8.485, SD → 1.099, Variance → 1.207

∴ Answer: i-1, ii-3, iii-2

Alternate Method

Given:

Marks: 7, 8, 9, 10

Frequency: 12, 13, 12, 11 (Total = 48)

Concept Used:

Mean = Σ(fx)/Σf, Variance = Σf(x − mean)²/N

Calculation:

⇒ Mean = (7×12 + 8×13 + 9×12 + 10×11) ÷ 48

⇒ = 406/48 = 8.458 ≈ 8.485

⇒ Using mean ≈ 8.485

⇒ Variance = [Σf(x − mean)²] ÷ 48 ≈ 1.207

⇒ Standard Deviation = √1.207 ≈ 1.099

∴ Matching:

i → 8.485 (1)

ii → 1.099 (3)

iii → 1.207 (2)

∴ Final Answer: i-1, ii-3, iii-2

Additional Information

Mean Formula: Mean = Σ(fx)/Σf

Variance: Measures spread = Σf(x − mean)²/N

Standard Deviation: SD = √(Variance)

Exam Tip: Always calculate mean first, then variance and SD.

The correct answer is Article 43B - Promotion of co-operative societies.

Key Points

• The Constitution (Ninety-seventh Amendment) Act of 2011 was enacted to provide constitutional status and protection to co-operative societies. It inserted Article 43B into the Directive Principles of State Policy (DPSP). Hence, statement 1 is correct.
• Article 43B mandates that the State shall endeavour to promote voluntary formation, autonomous functioning, democratic control, and professional management of co-operative societies.
• Article 43A, which deals with the participation of workers in the management of industries, was inserted by the 42^nd Constitutional Amendment Act of 1976, not the 97^th. Hence, statement 2 is incorrect.
• Article 48A, focusing on the protection and improvement of the environment and safeguarding of forests and wildlife, was added to the Constitution by the 42^nd Amendment Act in 1976. Hence, statement 3 is incorrect.
• Article 39A provides for equal justice and free legal aid to ensure that opportunities for securing justice are not denied to any citizen by reason of economic or other disabilities. This was also inserted by the 42^nd Amendment Act of 1976. Hence, statement 4 is incorrect.

Additional Information

• The Directive Principles of State Policy (DPSP) are enumerated in Part IV of the Indian Constitution from Article 36 to 51. They are borrowed from the Irish Constitution of 1937.
• The 97^th Constitutional Amendment Act of 2011 brought three significant changes to the Constitution:
• It made the right to form co-operative societies a Fundamental Right under Article 19(1)(c).
• It included a new Directive Principle of State Policy on the promotion of co-operative societies as Article 43B.
• It added a new Part IXB in the Constitution, titled "The Co-operative Societies" (consisting of Articles 243ZH to 243ZT).
• In July 2021, the Supreme Court of India upheld a Gujarat High Court verdict that struck down certain provisions of the 97^th Amendment (specifically Part IXB) as they were passed without the required ratification by at least half of the State Legislatures, though it remains valid for Multi-State Co-operative Societies.

Important Points

• The 42^nd Amendment Act, 1976, often called the "Mini-Constitution", added four new Directive Principles: Article 39 (opportunities for healthy development of children), Article 39A (equal justice and free legal aid), Article 43A (participation of workers), and Article 48A (environment protection).
• The 44^th Amendment Act, 1978 added one more Directive Principle, Article 38(2), which requires the State to minimize inequalities in income, status, facilities, and opportunities.
• The 86^th Amendment Act, 2002 changed the subject matter of Article 45 and made elementary education a fundamental right under Article 21A. The revised Article 45 directs the State to provide early childhood care and education for all children until they complete the age of six years.
• The DPSP are non-justiciable in nature, meaning they are not legally enforceable by the courts for their violation, yet they are fundamental in the governance of the country.

The correct answer is Introduction of Fundamental Duties under Article 51A.

Key Points

• The 42^nd Constitutional Amendment Act, 1976 was enacted during the Internal Emergency (1975-1977) by the Indira Gandhi government and is often described as the "Mini-Constitution" due to the vast changes it brought to the Constitution of India.
• It introduced a new Part IV-A to the Constitution, which consisted of Article 51A. This article enumerated 10 Fundamental Duties for the citizens, based on the recommendations of the Swaran Singh Committee. Hence, statement 2 is correct.
• The 31^st Constitutional Amendment Act, 1973 increased the Lok Sabha seats from 525 to 545 to account for the population growth revealed in the 1971 Census. Hence, statement 1 is incorrect.
• While the 42^nd Amendment did add several laws to the 9^th Schedule to protect them from judicial review, the comprehensive Nationalization of Land Ceiling Laws was not a singular defining feature of this amendment; such reforms were initiated through the 1^st, 4^th, and 17^th Amendments. Hence, statement 3 is incorrect.
• The Right to Privacy was declared a Fundamental Right under Article 21 of the Constitution by the Supreme Court in the landmark Justice K.S. Puttaswamy (Retd.) v. Union of India case in 2017, not by the 42^nd Amendment. Hence, statement 4 is incorrect.

Additional Information

• Changes to the Preamble:
• The 42^nd Amendment is the only amendment to have modified the Preamble of India. It added three new words: Socialist, Secular, and Integrity.
• It changed the description of India from a "Sovereign Democratic Republic" to a "Sovereign Socialist Secular Democratic Republic."
• Fundamental Duties (Part IV-A):
• Initially, there were 10 Fundamental Duties. The 11^th Fundamental Duty (providing education opportunities to children aged 6 to 14 years) was added later by the 86^th Constitutional Amendment Act, 2002.
• These duties are non-justiciable, meaning they cannot be enforced directly by the courts, though they serve as a guide for citizens.
• Transfer of Subjects:
• This amendment transferred 5 subjects from the State List to the Concurrent List: Education, Forests, Weights and Measures, Protection of Wild Animals and Birds, and Administration of Justice.
• Duration of Legislatures:
• The 42^nd Amendment extended the tenure of the Lok Sabha and the State Legislative Assemblies from 5 years to 6 years. However, this change was later reversed by the 44^th Amendment Act, 1978.

Important Points

• Directive Principles of State Policy (DPSP):
• The amendment added four new Directive Principles: Article 39 (opportunities for healthy development of children), Article 39A (Equal justice and free legal aid), Article 43A (participation of workers in management of industries), and Article 48A (protection of environment and forests).
• Judicial Powers:
• It sought to curtail the power of the Supreme Court and High Courts regarding judicial review and writ jurisdiction. Many of these restrictive provisions were subsequently struck down or repealed by the 43^rd and 44^th Amendments to restore democracy and judicial independence.
• Presidential Obligations:
• It made the President bound by the advice of the Council of Ministers headed by the Prime Minister.

Shortcut Trick

⇒ Profit ∝ Investment × Time

⇒ Trisha = 8 × 12 = 96

⇒ Riya = 5 × 12 = 60

⇒ Poorva = 5 × 6 = 30

⇒ Ratio = 96 : 60 : 30 = 16 : 10 : 5

∴ Answer = 16 : 10 : 5

Alternate Method

Given:

Investment ratio (Trisha : Riya) = 8 : 5

Poorva joins after 6 months with same investment as Riya

Total time = 12 months

Concept Used:

Profit ratio = Investment × Time

Calculation:

⇒ Trisha: 8 × 12 = 96

⇒ Riya: 5 × 12 = 60

⇒ Poorva: 5 × 6 = 30

⇒ Ratio = 96 : 60 : 30

⇒ Divide by 6

⇒ 16 : 10 : 5

∴ The correct answer is 16 : 10 : 5.

Additional Information

Partnership Rule: Profit ∝ Capital × Time

Joining Late: Time reduces, so share reduces proportionally.

Equal Investment: Same capital means only time affects ratio.

Exam Tip: Multiply directly instead of forming equations.

The correct answer is Seismograph.

Key Points

• A seismograph, also known as a seismometer, is an instrument designed to detect and record seismic waves produced by earthquakes, volcanic eruptions, or explosions.
• The primary function of the device is to record the ground motion over a period of time. It works on the principle of inertia, where a heavy mass remains stationary while the frame moves with the vibrating earth.
• The output produced by this instrument is a graph called a seismogram, which geologists and seismologists use to determine the magnitude, depth, and location of the earthquake's epicenter.
• Modern seismographs are highly sensitive electronic devices that can detect vibrations so small they are imperceptible to humans, even from thousands of kilometers away.
• These instruments are critical for disaster management, early warning systems, and scientific research into the internal structure of the Earth.

Additional Information

• Tiltmeter:
• It is an extremely sensitive inclinometer used to measure very small changes in the vertical level or slope of the ground or a structure.
• Uses: It is primarily used in volcanology to monitor the "breathing" or swelling of volcanoes caused by magma movement, as well as in civil engineering to monitor the stability of dams and tunnels.
• Anemometer:
• An anemometer is a device used for measuring wind speed and wind direction.
• The cup anemometer, a common type, was invented by John Thomas Romney Robinson in 1846.
• Applications: It is an essential tool in meteorology, aviation, and for navigation at sea.
• Barometer:
• A barometer is a scientific instrument used to measure atmospheric pressure.
• The first mercury barometer was invented by Evangelista Torricelli in the year 1643.
• Features: Since atmospheric pressure changes with altitude and weather patterns, it is used for weather forecasting and as an altimeter in aircraft.

Important Points

• The magnitude of an earthquake is often expressed using the Richter Scale, developed by Charles F. Richter in 1935. It is a logarithmic scale where each whole number increase represents a ten-fold increase in measured amplitude.
• The intensity or the actual damage caused by an earthquake is measured using the Modified Mercalli Intensity (MMI) Scale, which uses Roman numerals from I to XII.
• The point inside the Earth where the earthquake starts is called the focus or hypocenter, while the point directly above it on the surface is called the epicenter.
• In India, the Bureau of Indian Standards (BIS) has classified the country into four seismic zones (Zone II, III, IV, and V) based on the seismic hazard and geological data.

The logic followed here is:

Given: A, B, C, D, E, F and G are sitting around a circular table facing the centre.

A sits to the immediate right of E.

A sits second to the left of F.

Only two people sit between F and B when counted from the left of B.

G sits third to the left of E.

D is an immediate neighbor of G.

So, There are 3 people between A and G.

Hence, the correct answer is "Option 3".

Shortcut Trick

⇒ Height = Length × sin60°

⇒ sin60° = √3/2 = 1.74/2 = 0.87

⇒ Height = 28 × 0.87

⇒ = 24.36 m

∴ Answer = 24.36 m

Alternate Method

Given:

Length of ladder = 28 m

Angle with ground = 60°

Formula:

sinθ = Perpendicular / Hypotenuse

      60°  28 m Height Ground Wall

Calculation:

⇒ sin60° = Height / 28

⇒ (√3)/2 = Height / 28

⇒ Height = 28 × (√3/2)

⇒ = 28 × (1.74/2)

⇒ = 28 × 0.87

⇒ = 24.36 m

∴ The correct answer is 24.36 m.

Additional Information

Trigonometry: sinθ = Perpendicular / Hypotenuse

Important Value: sin60° = √3/2

Right Triangle: Ladder-wall-ground forms a right triangle.

Exam Tip: Use sin for height when angle with ground is given.

Shortcut Trick

Multiples: 7, 14, 21, ... , 350×7

Average of AP = (First + Last) ÷ 2

⇒ = (7 + 2450) ÷ 2

⇒ = 2457 ÷ 2 = 1228.5

∴ Answer = 1228.5

Alternate Method

Given:

First 350 multiples of 7

Formula Used:

Average of AP = (First Term + Last Term) ÷ 2

Calculation:

⇒ First term (a) = 7

⇒ Last term (l) = 350 × 7 = 2450

⇒ Average = (7 + 2450) ÷ 2

⇒ = 2457 ÷ 2 = 1228.5

∴ Final Answer = 1228.5

Additional Information

AP Average: (First + Last) ÷ 2

n^th Term: a_n = n × d (for multiples)

Exam Insight: No need for full sum, just use first and last term

The correct answer is Pune.

Key Points

• Satyashodhak Samaj, which translates to the Truth Seekers' Society, was founded by Jyotirao Govindrao Phule, popularly known as Jyotiba Phule, in the year 1873.
• The location of the foundation of this organisation was Pune (then known as Poona) in the state of Maharashtra, India.
• The society was established on September 24, 1873, with the primary objective of liberating the Shudra and Ati-Shudra communities from exploitation by upper castes and priests.
• It focused on social rights and political access for underprivileged groups, emphasizing the importance of education as a tool for social change.
• The Satyashodhak Samaj rejected the need for middlemen or priests in religious ceremonies, advocating for a direct connection between the individual and the divine.

Additional Information

• Jyotiba Phule was a prolific writer; his most famous book is Gulamgiri (Slavery), published in 1873, which he dedicated to the African American movement to end slavery in the USA.
• He also authored other significant works like Shetkarayacha Aasud (The Cultivator's Whipcord) in 1881 and Sarvajanik Satya Dharma, which was published posthumously.
• In 1888, the designation of Mahatma (Great Soul) was conferred upon him by Vithalrao Krishnaji Vandekar at a public meeting in Mumbai (then Bombay).
• Phule's wife, Savitribai Phule, was a pioneer in women's education and worked alongside him to establish the first school for girls in India at Bhide Wada, Pune, in 1848.
• They also founded the Infanticide Prohibition Home (Balhatya Pratibandhak Griha) to prevent the killing of children born to widows and provide them with a safe environment.

Important Points

• The Satyashodhak Samaj movement was unique because it allowed people of all castes and religions to become members, provided they agreed with its core principles of equality.
• Jyotiba Phule served as a member of the Poona Municipality for a period of 7 years, from 1876 to 1883, where he worked on urban administrative issues.
• He is often regarded as the Father of Indian Social Revolution due to his radical challenge to the existing caste hierarchy and his advocacy for universal human rights.
• The impact of his work was deeply felt by later reformers; Dr. B.R. Ambedkar, the architect of the Indian Constitution, considered Jyotiba Phule as one of his three primary gurus (teachers).
• The Satyashodhak Samaj continued its work after Phule's death in 1890, eventually influencing the Non-Brahmin Movement in Maharashtra during the early 20^th century.

The correct answer is Vinayak Damodar Savarkar.

Key Points

• Vinayak Damodar Savarkar, popularly known as Veer Savarkar, authored the influential book 'The Indian War of Independence 1857'.
• He wrote this book in 1909 while he was staying at India House in London, United Kingdom.
• In this work, Savarkar was the first to challenge the British narrative that the uprising was merely a "Sepoy Mutiny". Instead, he termed it the "First War of Independence" of India against British rule.
• The book was originally written in Marathi under the title '1857 che Swatantrya Samar'. Because of its revolutionary content, the British Government banned the book even before its official publication.
• Despite the ban, the book was printed in Holland in 1909 and smuggled into India, serving as a significant source of inspiration for Indian revolutionaries.

Additional Information

• Vinayak Damodar Savarkar:
• He was born on May 28, 1883, in Bhagur, Nasik, Maharashtra.
• He founded the Abhinav Bharat Society in 1904 and the Free India Society in London.
• He was sentenced to 50 years of imprisonment and sent to the Cellular Jail in the Andaman and Nicobar Islands in 1911.
• Jawaharlal Nehru:
• He was the first Prime Minister of India, serving from 1947 to 1964.
• His famous literary works include 'The Discovery of India' and 'Glimpses of World History'.
• He played a pivotal role in the Non-Alignment Movement and the Five-Year Plans.
• Bal Gangadhar Tilak:
• Known as 'Lokmanya', he was a prominent leader in the Indian Independence Movement.
• He authored books such as 'Gita Rahasya' (written during his imprisonment in Mandalay) and 'The Arctic Home in the Vedas'.
• He started the newspapers Kesari (in Marathi) and Mahratta (in English).
• Mahatma Gandhi:
• Born on October 2, 1869, he is known as the 'Father of the Nation'.
• His major literary contributions include his autobiography, 'The Story of My Experiments with Truth', and 'Hind Swaraj', which was published in 1909.
• He led massive movements like the Salt March (1930) and the Quit India Movement (1942) using the principles of Ahimsa and Satyagraha.

Important Points

• The Revolt of 1857 began on May 10, 1857, in Meerut and spread across Northern and Central India.
• Prominent leaders of the revolt included Rani Laxmibai of Jhansi, Nana Saheb of Kanpur, and Begum Hazrat Mahal of Lucknow.
• Savarkar's book acted as a catalyst for later revolutionaries like Bhagat Singh, who published an edition of the book to motivate his fellow freedom fighters.
• The British reaction to the revolt led to the Government of India Act 1858, which transferred the administration of India from the East India Company to the British Crown.

The logic followed here is based on the positional shift between the two letter clusters:

Option 1: BX − VU

Option 2: CY − XT

Option 3: UQ − PL

Option 4: VR − QM

Thus,  BX − VU is different.

Hence, the odd one out is Option 1.

Given:

Rahul walks 6 km North.

He turns left → 3 km West.

He turns left → 6 km South.

He turns left → 6 km East.

 

So, Rahul is 3 km away from starting point.

Hence, the correct answer is Option 1.

The logic followed here is:

Logic: Second number = (First number - Third number) × 2

(19, 24, 7)

⇒ (19 - 7) × 2 = 12 × 2 = 24 (2^nd number)

(12, 14, 5)

⇒ (12 - 5) × 2 = 7 × 2 = 14 (2^nd number)

Similarly,

Option (1): (3, 4, 1)

⇒ (3 - 1) × 2 = 2 × 2 = 4 ⇒ 2^nd number (True)

Hence, the correct answer is Option 1.

Shortcut Trick

Use weighted average

⇒ Total = (69×468) + (65×120) + (88×276)

⇒ = 32292 + 7800 + 24288 = 64380

Total members = 69 + 65 + 88 = 222

⇒ Average = 64380 ÷ 222 = 290

∴ Answer = 290

Alternate Method

Given:

Group A: 69 members, avg = 468

Group B: 65 members, avg = 120

Group C: 88 members, avg = 276

Formula Used:

Overall Average = (Σ f x) ÷ (Σ f)

Calculation:

⇒ Total amount A = 69 × 468 = 32292

⇒ Total amount B = 65 × 120 = 7800

⇒ Total amount C = 88 × 276 = 24288

⇒ Total amount = 32292 + 7800 + 24288 = 64380

⇒ Total members = 69 + 65 + 88 = 222

⇒ Overall average = 64380 ÷ 222 = 290

∴ Final Answer = 290

Additional Information

Weighted Average: (Σ f x) ÷ (Σ f)

Shortcut Insight: Multiply group size with average to get total directly

Exam Tip: Avoid decimals by keeping values in integer form

Shortcut Trick

Mean proportional = √(x × 36) = 18

⇒ Square both sides

⇒ x × 36 = 324

⇒ x = 324 ÷ 36 = 9

∴ Answer = 9

Alternate Method

Given:

Mean proportional between x and 36 = 18

Formula Used:

Mean proportional = √(a × b)

Calculation:

⇒ √(x × 36) = 18

⇒ Squaring both sides:

⇒ x × 36 = 18² = 324

⇒ x = 324 ÷ 36 = 9

∴ Final Answer = 9

Additional Information

Mean Proportional: √(a × b)

Alternative Form: If a : x = x : b, then x = √(ab)

Exam Insight: Always square directly to eliminate root

Shortcut Trick

Use identity: (a + b)² + (a − b)² = 2(a² + b²)

Here a = 555, b = 444

⇒ Numerator = 2(555² + 444²)

⇒ Denominator = 555² + 444²

⇒ Value = 2

∴ Answer = 2

Alternate Method

Given: ((555 + 444)² + (555 − 444)²) ÷ (555 × 555 + 444 × 444)

Formula: (a + b)² = a² + b² + 2ab, (a − b)² = a² + b² − 2ab

⇒ (555 + 444)² = 555² + 444² + 2 × 555 × 444

⇒ (555 − 444)² = 555² + 444² − 2 × 555 × 444

⇒ Adding both:

⇒ = 2(555² + 444²)

⇒ Denominator = 555² + 444²

⇒ Required value = 2(555² + 444²) ÷ (555² + 444²)

⇒ = 2

∴ Final Answer = 2

Additional Information

Identity 1: (a + b)² + (a − b)² = 2(a² + b²) — very useful in simplification.

Identity 2: (a + b)² − (a − b)² = 4ab — helps in quick elimination.

Shortcut Trick

In Simple Interest, Total Amount = Principal + Interest.

If the final amount is 5 times the principal, then Simple Interest (SI) = 5P − P = 4P.

Using SI formula: SI = PRT ÷ 100, we get 4P = P × R × 4 ÷ 100.

Solve for R: R = (4P × 100) ÷ (P × 4) = 100%.

∴ Answer = 100% (Option 3)

Alternate Method

Given:

Principal = P, Final Amount = 5P, Time = 4 years.

Formula used:

Simple Interest (SI) = PRT ÷ 100

Principal (P) Interest (4P) Final Amount (5P)

Calculations:

From the formula, SI = A − P = 5P − P = 4P.

⇒ SI = PRT ÷ 100 ⇒ 4P = P × R × 4 ÷ 100.

⇒ R = (4P × 100) ÷ (P × 4) = 100%.

∴ The correct answer is 100% (Option 3).

Additional Information

Difference Between SI and CI

In SI, interest remains constant every year, while in CI, interest compounds over time. CI formula: A = P(1 + r/100)^t.

Rule of 72

To estimate doubling time under SI, use T ≈ 72 ÷ R, where R is the annual interest rate.

Effective Rate in Compound Interest

For compound interest, the effective annual rate can be calculated using (1 + r/100)ⁿ − 1, where n is the compounding frequency.

The correct answer is Netumbo Nandi-Ndaitwah.

Key Points

• Netumbo Nandi-Ndaitwah made history by being elected as the first female President of Namibia following the general elections held in November 2024.
• She was officially inaugurated in March 2025, succeeding Nangolo Mbumba, who had served as the interim president after the passing of President Hage Geingob in February 2024.
• She represented the South West Africa People's Organisation (SWAPO), the ruling political party that has governed Namibia since it gained independence from South Africa in 1990.
• Netumbo Nandi-Ndaitwah secured approximately 57.31% of the total votes, ensuring a first-round victory and maintaining the political dominance of the SWAPO party.
• Before becoming President, she held several high-ranking positions, including Vice President of Namibia (appointed in 2024) and Deputy Prime Minister, as well as the Minister of International Relations and Cooperation.

Additional Information

• Saara Kuugongelwa:
• She is a prominent Namibian politician who became the country's fourth Prime Minister in 2015.
• She was the first woman to hold the office of Prime Minister in Namibia, serving under President Hage Geingob.
• Ellen Johnson Sirleaf:
• She served as the 24^th President of Liberia from 2006 to 2018.
• She is internationally recognized as Africa's first elected female head of state and was awarded the Nobel Peace Prize in 2011 for her efforts in women's safety and rights.
• Joyce Banda:
• She was the President of Malawi from April 2012 to May 2014.
• She took office following the death of President Bingu wa Mutharika, becoming Malawi's first female president and the second woman to lead a nation in the African continent.
• Namibia:
• Located in Southern Africa, it is known for its vast Namib Desert and diverse wildlife.
• The capital city is Windhoek, and the country uses the Namibian Dollar (NAD) as its primary currency, which is pegged to the South African Rand.

Important Points

• Political Career: Netumbo Nandi-Ndaitwah joined SWAPO in 1966 and was actively involved in the struggle for independence. She spent many years in exile in Zambia and the United Kingdom, where she gained significant diplomatic experience.
• The 2024 Election: This election was considered a critical test for SWAPO due to rising unemployment among the youth and economic challenges. Her victory signifies a continuation of the party's legacy while breaking the gender barrier at the highest level of governance.
• International Relations: During her tenure as Foreign Minister, she was a strong advocate for South-South cooperation and played a vital role in SADC (Southern African Development Community) deliberations.
• Age and Background: Born in 1952, she has spent over five decades in public service, making her one of the most experienced stateswomen in Africa as of 2025.

Shortcut Trick

Cost price per article = 300 ÷ 12 = 25

Selling price per article = 90

⇒ Profit per article = 90 − 25 = 65

⇒ Profit % = (65 ÷ 25) × 100 = 260%

∴ Answer = 260%

Alternate Method

Given: 48 dozens, CP = 300 per dozen, SP = 90 per article

⇒ Total articles = 48 × 12 = 576

⇒ Total CP = 48 × 300 = 14400

⇒ Total SP = 576 × 90 = 51840

⇒ Profit = 51840 − 14400 = 37440

⇒ Profit % = (37440 ÷ 14400) × 100

⇒ = 2.6 × 100 = 260%

∴ Final Answer = 260%

Additional Information

Unit Method: Always convert dozen to single unit to simplify profit/loss quickly.

Profit % Formula: Profit % = (Profit ÷ Cost Price) × 100

Shortcut Insight: When SP per unit is given, avoid total calculation — compare per unit directly.

Shortcut Trick

Take assumed mean A = 35

Mid values: 15, 25, 35, 45, 55

Deviations: −20, −10, 0, +10, +20

⇒ (15×−20) + (21×−10) + (41×10) + (20X) = 0

⇒ −300 −210 + 410 + 20X = 0 ⇒ 20X = 100

⇒ X = 5

∴ Answer = 5

Alternate Method

Given:

Mean = 35

Formula Used:

Mean = (Σ f x) ÷ (Σ f)

Calculation:

⇒ Mid values (x) = 15, 25, 35, 45, 55

⇒ Σf = 15 + 21 + 43 + 41 + X = 120 + X

⇒ Σfx = (15×15) + (21×25) + (43×35) + (41×45) + (55X)

⇒ = 225 + 525 + 1505 + 1845 + 55X

⇒ = 4100 + 55X

⇒ (4100 + 55X) ÷ (120 + X) = 35

⇒ 4100 + 55X = 35(120 + X)

⇒ 4100 + 55X = 4200 + 35X

⇒ 20X = 100

⇒ X = 5

∴ Final Answer = 5

Additional Information

Mean Formula: Mean = (Σ f x) ÷ (Σ f)

Assumed Mean Method: Reduces calculation using deviations from a central value.

Exam Insight: If mean equals a class midpoint, deviation sum becomes zero.

The correct answer is Paris Agreement.

Key Points

• The United Nations Climate Change Conference, also known as COP30, is scheduled to be held in November 2025. The primary focus of this conference is the review and enhancement of commitments under the Paris Agreement, which was originally adopted in December 2015.
• The 2025 conference is set to take place in Belém, Brazil, marking a significant moment as it is hosted in the Amazon region to emphasize the importance of tropical forests in climate mitigation.
• A central requirement of the Paris Agreement discussed during this period is the submission of new Nationally Determined Contributions (NDCs). These are climate action plans to cut emissions and adapt to climate impacts, which every party is required to update every five years.
• The Paris Agreement aims to keep the increase in the global average temperature to well below 2°C above pre-industrial levels and to pursue efforts to limit the temperature increase to 1.5°C. The 2025 talks are crucial for evaluating if current pledges align with these targets.
• The conference serves as a follow-up to the first Global Stocktake concluded in 2023, providing a roadmap for countries to ramp up their ambition in 2025 to ensure global emissions peak before the end of the decade.

Additional Information

• Glasgow Pact:
• The Glasgow Climate Pact was the main outcome of COP26, held in November 2021 in Scotland.
• It was the first climate agreement to explicitly plan for the "phase down" of unabated coal power and the phasing out of inefficient fossil fuel subsidies.
• It stressed the urgency of the "Critical Decade" and requested countries to revisit and strengthen their 2030 targets by the end of 2022.
• Montreal Accord (Protocol):
• Signed in 1987, the Montreal Protocol is a global agreement to protect the stratospheric ozone layer by phasing out the production and consumption of ozone-depleting substances (ODS).
• It targets substances like chlorofluorocarbons (CFCs) and halons. The Kigali Amendment in 2016 added hydrofluorocarbons (HFCs) to the list to help reduce global warming.
• It is considered one of the most successful environmental treaties, having achieved near-universal ratification by 198 Parties.
• Kyoto Protocol:
• Adopted in 1997 and entered into force in 2005, the Kyoto Protocol operationalized the UNFCCC by committing industrialized countries to limit and reduce greenhouse gas emissions.
• It established legally binding targets for 37 industrialized nations and the European Community during its first commitment period (2008–2012).
• It introduced flexible market mechanisms such as International Emissions Trading, the Clean Development Mechanism (CDM), and Joint Implementation.

Important Points

• Climate Finance: A major point of discussion in 2025 involves the New Collective Quantified Goal (NCQG), which aims to set a new financial target to support developing countries in their climate actions post-2025, replacing the previous $100 billion annual goal.
• Loss and Damage: Following the establishment of a Loss and Damage Fund at COP27, the 2025 discussions focus on the operationalization and funding levels to assist vulnerable nations facing the brunt of climate disasters.
• UNFCCC Role: The United Nations Framework Convention on Climate Change, established in 1992 at the Rio Earth Summit, remains the parent treaty for all subsequent agreements, including Kyoto and Paris, focusing on stabilizing greenhouse gas concentrations in the atmosphere.
• Data and Targets: Science indicates that to limit warming to 1.5°C, global greenhouse gas emissions must be reduced by 43% by 2030 and reach net zero by 2050. The COP30 in Brazil is viewed as the "last chance" to lock in these pathways through the 2035 NDCs$.

Shortcut Trick

The sum of all interior angles of any polygon is given by the formula: (n − 2) × 180°, where n is the number of sides.

A trapezium has 4 sides (n = 4).

∴ Sum of all interior angles = (4 − 2) × 180° = 360°.

∴ Answer = 360° (Option 2)

Alternate Method

Given:

A trapezium has 4 sides.

Formula used:

Sum of all interior angles = (n − 2) × 180°, where n is the number of sides.

A B C D 360°

Calculations:

(n − 2) × 180°, where n = 4.

⇒ (4 − 2) × 180° = 2 × 180° = 360°.

∴ The correct answer is 360° (Option 2).

Additional Information

Polygon Interior Angle Sum Formula

The sum of all interior angles of an n-sided polygon is (n − 2) × 180°.

Trapezium Properties

A trapezium is a quadrilateral with one pair of parallel sides. The sum of all interior angles is always 360°.

Exterior Angle Sum

The sum of all exterior angles of any polygon is always 360°, irrespective of the number of sides.

Quadrilateral Angle Sum

For all quadrilaterals (4-sided polygons), the interior angle sum is always 360°.

Given Statements:

All horses are donkeys.

Some cats are monkeys.

All monkeys are donkeys.

The least possible Venn diagram shows:

Conclusions:

(I) All cats are donkeys

This does not follow because only some cats are monkeys, and only monkeys are confirmed to be inside donkeys. Cats may exist outside this relation.

(II) Some horses are monkeys

This does not follow because there is no direct or indirect relationship between horses and monkeys given in the statements.

Therefore, neither conclusion (I) nor (II) follows.

Hence, the correct answer is "Option 3".

The correct answer is Northeastern India.

Key Points 

• Northeastern India contributes comparatively less to the formal tertiary sector despite having important urban centers such as Guwahati, Shillong, Agartala, and Imphal.
• The tertiary sector includes activities such as:
• Banking and insurance
• Information technology services
• Tourism and hospitality
• Transport and communication
• Trade and business services
• Education and healthcare
• The region has a relatively smaller share in organized service-sector activities because:
• Industrial development remains limited.
• Connectivity challenges due to mountainous terrain reduce business expansion.
• Private investment and corporate presence are comparatively low.
• IT and financial service hubs are underdeveloped compared to metropolitan regions.
• A large proportion of employment remains in the informal sector and agriculture.
• Although cities like Guwahati act as regional commercial centers, the overall contribution of the Northeast to India’s national service economy remains limited due to lower urban-industrial integration.
• The region also experiences:
• Lower infrastructure density
• Limited large-scale corporate employment
• Smaller market size
• Dependence on government services rather than diversified private tertiary activities
• Therefore, among the given regions, Northeastern India shows the least contribution to the formal tertiary sector.

Additional Information 

• Northern India
• Includes major urban and economic centers such as Delhi, Chandigarh, Jaipur, and Lucknow.
• Has strong growth in:
• Banking
• Education services
• Government administration
• Retail and logistics
• Delhi NCR is one of India’s largest service-sector hubs.
• Western India
• Contains highly developed states such as Maharashtra and Gujarat.
• Mumbai is India’s leading center for:
• Finance
• Stock markets
• Corporate headquarters
• Media and entertainment
• Western India has one of the highest contributions to India’s GDP from services.
• Southern India
• Known for advanced service-sector growth in cities like Bengaluru, Hyderabad, Chennai, and Kochi.
• Major strengths include:
• Information Technology
• Software exports
• Healthcare services
• Educational institutions
• Bengaluru is called the “Silicon Valley of India” due to its dominance in the IT industry.
• Formal Tertiary Sector
• Refers to officially registered service-sector activities regulated by the government.
• Workers generally receive:
• Fixed salaries
• Legal protection
• Social security benefits
• Examples include:
• Banks
• IT companies
• Airlines
• Hospitals
• Educational institutions

The logic followed here is:

Given:

SEMI → 3615

TIME → 1523

Hence, the code for T is 2

Hence, the correct answer is "Option 1".

Given numbers: 351, 417, 211, 159, 294

Here, identify highest and lowest numbers:

Highest number = 417

Lowest number = 159

Now, taking required digits:

417 → second digit = 1

159 → third digit = 9

Add ⇒ 1 + 9 = 10

Hence, the correct answer is "Option 2".

The correct answer is The Banking Laws (Amendment) Act, 2025.

Key Points

• The Banking Laws (Amendment) Act, 2025 (introduced as a Bill in August 2024) was designed to update and modernize the regulatory environment for the banking sector in India.
• One of the most significant features of this Act is the introduction of uniform reporting standards for all scheduled commercial banks. Historically, banks reported their demand and time liabilities to the Reserve Bank of India (RBI) based on "reporting Fridays."
• Under the new provisions, the reporting frequency has been shifted to specific dates, namely the 15^th and the last day of every month. This ensures that the data provided by banks is consistent and easier to reconcile with other financial indices and surveys. Hence, the statement regarding the introduction of uniform reporting standards via this Act is correct.
• This Act amends several existing laws, including the Reserve Bank of India Act, 1934 and the Banking Regulation Act, 1949, to give the RBI greater functions in supervising the liquidity and statutory reserves of banks.
• The move to uniform reporting aims to reduce data discrepancies that occurred due to the variations in the number of Fridays in different months or years.

Additional Information

• Reserve Bank of India Act, 1934:
• This Act provided the legal framework for the establishment of the Reserve Bank of India on April 1, 1935.
• It defines the functions of the RBI as the country’s central bank, including the issuance of currency notes and the regulation of the monetary system to maintain stability in India.
• It also contains provisions for the Cash Reserve Ratio (CRR) that banks must maintain with the RBI.
• Banking Regulation Act, 1949:
• Originally passed as the Banking Companies Act, 1949, it was later renamed in 1966.
• This Act gives the RBI the power to license banks, regulate their shareholding, and supervise the appointment of boards and management.
• It applies to both commercial and cooperative banks across the country, ensuring a safe banking environment for depositors.
• State Bank of India Act, 1955:
• This Act led to the formation of the State Bank of India (SBI) on July 1, 1955, by taking over the Imperial Bank of India.
• Its primary application was to expand banking facilities in rural areas and serve the government's financial needs.

Important Points

• Nomination Updates: The Banking Laws (Amendment) Act, 2025 increased the number of permitted nominees per account from one to four, allowing for simultaneous or successive nominations.
• Substantial Interest: The Act revised the numerical value defining "substantial interest" for directors, increasing it from Rs. 5 lakhs to Rs. 2 crores, which reflects current economic data and market valuations.
• Director Tenures: In the context of Cooperative Banks, the Act extends the tenure of directors to align with other government guidelines and laws, specifically moving the limit from eight years to ten years in certain organizations.
• Regulatory Reporting: By shifting to a fixed-date reporting system (the 15^th and 30^th/31^st), the RBI can better calculate the Statutory Liquidity Ratio (SLR) and Cash Reserve Ratio (CRR) for the entire banking sector simultaneously.

The correct answer is Taj Mahal.

Key Points

• The Taj Mahal is an ivory-white marble mausoleum located on the southern bank of the Yamuna River in Agra, Uttar Pradesh, India. It was commissioned in 1632 by the Mughal Emperor Shah Jahan to house the tomb of his beloved wife, Mumtaz Mahal. Hence, this is the correct option.
• The monument was designated as a UNESCO World Heritage Site in 1983 for being "the jewel of Muslim art in India and one of the universally admired masterpieces of the world's heritage." It is also considered one of the New Seven Wonders of the World.
• Jama Masjid (Agra) was built by Shah Jahan in 1648 and dedicated to his daughter, Jahanara Begum. While it is a significant 17^th-century structure in Agra, it is not individually listed as a UNESCO World Heritage Site in the same capacity as the Taj Mahal. Hence, this statement is incorrect.
• Safdarjung Tomb is located in New Delhi and was built in 1754 for Nawab Safdarjung during the late Mughal Empire era. Since it was built in the 18^th century and is not located in Agra, it does not fit the criteria. Hence, this statement is incorrect.
• Sikandra Tomb is the final resting place of the Mughal Emperor Akbar. It is located in Agra, but its construction was completed by his son, Emperor Jahangir, in 1613. It was not built by Shah Jahan. Hence, this statement is incorrect.

Additional Information

• Architectural Style: The Taj Mahal is the pinnacle of Mughal Architecture, which is a unique blend of Indian, Persian, and Islamic styles. The construction project involved approximately 20,000 artisans under the guidance of a board of architects led by Ustad Ahmad Lahauri.
• Materials and Decoration: The main structure is constructed of white marble sourced from the quarries of Makrana in Rajasthan. It is famous for its Pietra Dura work, which involves inlaying precious and semi-precious stones like lapis lazuli, jade, crystal, and turquoise into the marble to create floral and geometric patterns.
• Timeline: The construction of the mausoleum was essentially completed in 1643, but work continued on other phases of the project for another 10 years. The entire complex is believed to have been completed in its entirety in 1653 at a cost estimated at the time to be around 32 million rupees.
• The Garden (Charbagh): The complex is set around a large 300-metre square Charbagh (Mughal garden). The garden uses raised pathways that divide each of the four quarters of the garden into 16 sunken parterres or flowerbeds.

Important Points

• Shah Jahan's Reign: Known as the Golden Age of Mughal Architecture, Shah Jahan (the fifth Mughal Emperor) commissioned several famous monuments including the Red Fort (Lal Qila) in Delhi, the Jama Masjid in Delhi, and the city of Shahjahanabad.
• UNESCO Sites in Agra: There are three UNESCO World Heritage Sites located in or near Agra: the Taj Mahal (1983), the Agra Fort (1983), and Fatehpur Sikri (1986).
• Conservation: To protect the monument from environmental pollution and the yellowing of marble caused by industrial emissions, the Government of India established the Taj Trapezium Zone (TTZ). This is a defined area of 10,400 sq km around the Taj Mahal where strict pollution control standards are enforced.
• Mumtaz Mahal: She was the second wife of Shah Jahan. She died in 1631 in Burhanpur while giving birth to their 14^th child, Gauhara Begum. Her body was eventually moved to the Taj Mahal complex once it was ready.