Shortcut Trick

Total observations = 11 (odd number)

Median position = (11 + 1) ÷ 2 = 6th term

Arrange numbers mentally and pick middle value

6th value = 60

∴ Answer = 60

Alternate Method

Given: 45, 62, 58, 71, 66, 54, 60, 49, 68, 57, 63

Formula used: Median = (n + 1) ÷ 2 th term (for odd n)

Calculations:

⇒ Arrange in ascending order: 45, 49, 54, 57, 58, 60, 62, 63, 66, 68, 71

⇒ n = 11

⇒ Median position = (11 + 1) ÷ 2 = 6

⇒ 6th term = 60

∴ The correct answer is 60.

Additional Information

Median for Even Number of Observations

Median = average of (n ÷ 2)th and (n ÷ 2 + 1)th terms

Mean vs Median

Mean = sum of observations ÷ total observations, while median is the middle value

Mode

Mode is the value that occurs most frequently in the dataset

Effect of Extreme Values

Median is not affected by very large or small values, unlike mean

Shortcut Trick

For doubling in Simple Interest, Interest = Principal

So, SI = P ⇒ (P × R × T) ÷ 100 = P

Cancel P ⇒ (R × 20) ÷ 100 = 1

R = 100 ÷ 20 = 5%

∴ Answer = 5%

Alternate Method

Given: Time = 20 years, Amount = 2P

Formula used: SI = (P × R × T) ÷ 100

Calculations:

⇒ Since amount doubles ⇒ SI = Amount − Principal = P

⇒ So, P = (P × R × 20) ÷ 100

⇒ Cancel P from both sides

⇒ 1 = (R × 20) ÷ 100

⇒ R = 100 ÷ 20 = 5

∴ The correct answer is 5%.

Additional Information

Simple Interest Formula

SI = (P × R × T) ÷ 100

Amount Formula

Amount = Principal + Simple Interest

Doubling Time (SI)

Time required to double = 100 ÷ Rate

Rule of 72 (CI concept)

Doubling time ≈ 72 ÷ Rate (used in Compound Interest)

Shortcut Trick

Multiply both sides by x ⇒ x² − 1 = 17x

Rearrange ⇒ x² − 17x − 1 = 0

Check discriminant sign: b² − 4ac = (−17)² − 4(1)(−1)

= 289 + 4 = 293 > 0 and not a perfect square

∴ Roots are real, distinct and irrational

Alternate Method

Given:

x − 1/x = 17

Formula used:

Discriminant D = b² − 4ac

Calculations:

⇒ Multiply both sides by x ⇒ x² − 1 = 17x

⇒ Rearranging ⇒ x² − 17x − 1 = 0

⇒ Here, a = 1, b = −17, c = −1

⇒ D = (−17)² − 4 × 1 × (−1)

⇒ D = 289 + 4 = 293

⇒ Since D > 0 and not a perfect square

∴ The correct answer is real, distinct and irrational roots.

Additional Information

Nature of Roots (Discriminant)

If D > 0 → real and distinct, D = 0 → real and equal, D < 0 → complex roots

Perfect Square Condition

If D is a perfect square, roots are rational; otherwise irrational

Forming Quadratic from Fraction

Equations like x − 1/x = k can be converted to x² − kx − 1 = 0

Sum and Product of Roots

Sum = −b/a and Product = c/a for ax² + bx + c = 0

The correct answer is 2008.

Key Points

• The Government of India officially declared Telugu and Kannada as Classical Languages in the year 2008.
• The announcement was made by the Ministry of Culture on October 31, 2008, following the recommendations of a committee of experts.
• Kannada, predominantly spoken in Karnataka, and Telugu, predominantly spoken in Andhra Pradesh and Telangana, were recognized for their rich literary heritage and antiquity.
• This designation followed the precedent set by Tamil (2004) and Sanskrit (2005), which were the first two languages to receive this status.
• The status is granted to languages that have a high antiquity of their early texts/recorded history over a period of 1500–2000 years.

Additional Information

• Criteria for Classical Status:
• High antiquity of its early texts/recorded history over a period of 1500–2000 years.
• A body of ancient literature/texts, which is considered a valuable heritage by generations of speakers.
• The literary tradition must be original and not borrowed from another speech community.
• The classical language and literature being distinct from modern, there may also be a discontinuity between the classical language and its later forms or its offshoots.
• List of Classical Languages in India (Chronological):
• Tamil: Declared in 2004. It was the first language to be accorded this status.
• Sanskrit: Declared in 2005.
• Kannada: Declared in 2008.
• Telugu: Declared in 2008.
• Malayalam: Declared in 2013.
• Odia: Declared in 2014.
• Benefits of Recognition:
• Two major international awards for scholars of eminence in the language are awarded annually.
• A Centre of Excellence for Studies in Classical Languages is set up.
• The University Grants Commission (UGC) is requested to create, to start with at least in the Central Universities, a certain number of Professional Chairs for Classical Languages for scholars of eminence.

Important Points

• Recent Developments (2024): In October 2024, the Union Cabinet, chaired by Prime Minister Narendra Modi, approved the conferment of Classical Language status to five more languages: Marathi, Pali, Prakrit, Assamese, and Bengali.
• As of late 2024, the total number of languages with Classical Status in India has reached 11.
• The inclusion of Pali and Prakrit is significant as they are the root languages for many Buddhist and Jain scriptures, respectively.
• The Central Institute of Indian Languages (CIIL) in Mysuru plays a key role in the promotion and research of these designated languages.
• The recognition helps in the digitization and preservation of ancient manuscripts and supports academic research globally.

The correct answer is Amend Fundamental Rights.

Key Points

• The 24th Constitutional Amendment Act was enacted in the year 1971 during the tenure of Prime Minister Indira Gandhi. This amendment was primarily brought to nullify the effect of the Supreme Court judgment in the Golaknath case (1967).
• It amended Article 13 and Article 368 of the Constitution of India to affirm that Parliament has the absolute power to amend any part of the Constitution, including Fundamental Rights listed in Part III. Hence, option A is correct.
• The amendment clarified that Article 13, which states that any law inconsistent with Fundamental Rights shall be void, would not apply to any constitutional amendment made under Article 368.
• Prior to this, the Supreme Court in the Golaknath case had ruled that Parliament could not abridge or take away any of the Fundamental Rights through a constitutional amendment.
• The power to suspend High Court judgments or bypass judicial proceedings is not a feature of the 24th Amendment; such issues were more relevant to the 42nd Amendment or specific emergency provisions. Hence, option B is incorrect.
• While the amendment sought to limit the scope of Judicial Review over constitutional changes, it did not entirely "override" the concept of judicial review, which was later protected as a part of the Basic Structure. Hence, option C is incorrect.
• The 24th Amendment does not deal with the suspension of elections, which is governed by the Representation of the People Act and Emergency provisions of the Constitution. Hence, option D is incorrect.

Additional Information

• Article 368: This article provides the Parliament with the constituent power to amend the Constitution by way of addition, variation, or repeal of any provision according to the procedure laid down therein.
• President's Assent: The 24th Amendment made it mandatory for the President of India to give his assent to a Constitution Amendment Bill. Before this, the President had the discretion to withhold assent or return the bill.
• Golaknath v. State of Punjab (1967): In this landmark 6:5 majority judgment, the Supreme Court held that Fundamental Rights are "transcendental" and "immutable," meaning Parliament has no power to amend them. This created a legal deadlock that the 24th Amendment resolved.
• Article 13: It originally acted as a shield for Fundamental Rights, declaring that any "law" made by the state that takes away these rights is void. The 24th Amendment added a clause stating that "nothing in this article shall apply to any amendment of this Constitution made under Article 368."
• Legislative Supremacy: This amendment represented a period of intense conflict between the Judiciary and the Legislature in India, where the government sought to establish the supremacy of Parliament in matters of social and economic reform.

Important Points

• Kesavananda Bharati Case (1973): The validity of the 24th Amendment was challenged in this famous case. The Supreme Court upheld the amendment but introduced the Basic Structure Doctrine, stating that while Parliament can amend any part of the Constitution, it cannot alter its "basic structure" or "essential features."
• Fundamental Rights vs. DPSP: The 24th Amendment was a precursor to the 25th Amendment, which sought to give Directive Principles of State Policy (DPSP) precedence over Fundamental Rights in certain cases (specifically Articles 39(b) and 39(c)).
• Constitutional Balance: Today, the power of Parliament to amend the Constitution is widely accepted, provided it respects the core values like Secularism, Democracy, Federalism, and Judicial Review as established by the 13-judge bench in 1973.
• The amendment effectively changed the status of Fundamental Rights from being unalterable to being amendable, ensuring that the Constitution remains a living document capable of adapting to the changing needs of the Indian people.

Shortcut Trick

Supplementary angles sum = 180°

Let smaller = x ⇒ larger = x + 32

So, x + (x + 32) = 180

2x = 148 ⇒ x = 74

∴ Answer = 74°

Alternate Method

Given:

Sum of two supplementary angles = 180°, difference = 32°

Formula used:

Sum = 180°, Let angles be a and b such that a + b = 180

Calculations:

⇒ Let smaller angle = x

⇒ Larger angle = x + 32

⇒ x + (x + 32) = 180

⇒ 2x + 32 = 180

⇒ 2x = 148

⇒ x = 74

∴ The correct answer is 74°.

Additional Information

Supplementary Angles

Two angles whose sum is 180° are called supplementary angles

Complementary Angles

Two angles whose sum is 90° are called complementary angles

Linear Pair

A linear pair of angles always adds up to 180°

General Formula

If difference is d, smaller angle = (180 − d) ÷ 2

Shortcut Trick

Downstream speed = 8 + 2 = 10 km/hr, Upstream speed = 8 − 2 = 6 km/hr

Total time = 3 hr 12 min = 3.2 hr

Round trip time formula: Time = 2D × (1/10 + 1/6)

⇒ 3.2 = 2D × (16/60) = 2D × (4/15)

D = 6 km

∴ Answer = 6 km

Alternate Method

Given:

Speed in still water = 8 km/hr

Stream speed = 2 km/hr

Total time = 3 hr 12 min = 3.2 hr

Formula used:

Downstream speed = u + v

Upstream speed = u − v

Time = Distance ÷ Speed

Calculations:

⇒ Downstream speed = 8 + 2 = 10 km/hr

⇒ Upstream speed = 8 − 2 = 6 km/hr

⇒ Let distance = D km

⇒ Time downstream = D ÷ 10

⇒ Time upstream = D ÷ 6

⇒ Total time = D/10 + D/6 = 3.2

⇒ Taking LCM 30 ⇒ (3D + 5D) ÷ 30 = 3.2

⇒ 8D ÷ 30 = 3.2

⇒ 4D ÷ 15 = 3.2

⇒ D = (3.2 × 15) ÷ 4 = 48 ÷ 4 = 12

∴ The correct answer is 12 km.

Additional Information

Downstream and Upstream Speed

Downstream = u + v, Upstream = u − v where u = still water speed and v = stream speed

Round Trip Time

Total time = Distance/Downstream + Distance/Upstream

LCM Method

Use LCM of denominators to simplify fractional equations quickly

Unit Conversion

Always convert minutes into hours: minutes ÷ 60

The correct answer is Fermentation.

Key Points

• Fermentation is a metabolic process that produces chemical changes in organic substrates through the action of enzymes. In the context of bread making, it refers specifically to the process where yeast (primarily Saccharomyces cerevisiae) converts sugars (glucose, fructose, and sucrose) into ethanol and carbon dioxide (CO2).
• The carbon dioxide gas produced during this reaction is trapped within the dough by the gluten network. As the gas expands, it causes the dough to rise, a process known as leavening. This creates the light, airy texture characteristic of bread.
• The chemical equation for this anaerobic process can be represented as: C6H12O6 (glucose) → 2C2H5OH (ethanol) + 2CO2 (carbon dioxide). While ethanol is also produced, it mostly evaporates during the baking process at high temperatures.
• Fermentation is highly sensitive to temperature and moisture. Most bread yeasts work optimally between 25°C to 35°C. Temperatures above 50°C typically kill the yeast cells, stopping the fermentation process.
• Apart from leavening, fermentation contributes significantly to the flavor and aroma of the bread due to the production of organic acids and other by-products during the breakdown of sugars.

Additional Information

• Oxidation-Reduction Reaction: While redox reactions occur during dough mixing (impacting the disulfide bonds in gluten proteins), they are not the primary mechanism for leavening. Oxidation helps in strengthening the dough, but does not produce the gas required for rising.
• Enzymatic Reaction: In bread making, amylase enzymes are crucial as they break down starch into maltose and glucose. This provides the substrate (food) for the yeast to perform fermentation. However, the production of CO2 itself is the result of the fermentation pathway rather than a simple enzymatic hydrolysis.
• Acid-Base Reaction: This is the mechanism used in chemical leavening rather than biological leavening. It involves the reaction between an acid (like buttermilk or cream of tartar) and a base (like sodium bicarbonate/baking soda) to release carbon dioxide quickly. This is common in cakes and biscuits but not traditional yeast bread.
• Role of Gluten: Gluten is a protein complex formed from gliadin and glutenin when flour is mixed with water. It provides the elasticity and extensibility necessary to hold the gas bubbles produced during fermentation. Without gluten, the CO2 would escape, and the bread would remain flat.

Important Points

• Maillard Reaction: This is a chemical reaction between amino acids and reducing sugars that gives browned food its distinctive flavor. It occurs on the crust of the bread during baking at temperatures above 140°C, which is separate from the fermentation process occurring in the crumb.
• Proofing: This is the final rise of the dough after it has been shaped but before it is baked. During this stage, fermentation continues at a steady rate to ensure the final volume of the loaf.
• Historical Context: The use of yeast for fermentation dates back to Ancient Egypt (around 3000 BCE), where bakers discovered that leaving dough in the open air allowed wild yeast to settle and ferment the sugars.
• Biological vs. Chemical: Yeast fermentation is a biological process involving living organisms, whereas using baking powder is a chemical process. Traditional breads like sourdough rely on a symbiotic culture of yeast and lactic acid bacteria.

Family Chart:

Given:

S is married to R.

S is the father of Q.

Q has a sister named K and a brother named M.

 

So, K is the daughter of R

Hence, the correct answer is "Option 4".

Given: (Left) # F * G W # C # Y R & @ W Z @ L & L N % # W (Right)

Now,

Letters, which are immediately preceded by a symbol and also immediately followed by a symbol.

So, Needed pattern is: Symbol - Letter - Symbol

(Left) **# F *** G W # C # Y R & @ W Z @ L & L N % # W (Right)

So, total valid letters = 3

Hence, the correct answer is Option 3.

The correct answer is World Artificial Intelligence Cooperation Organization (WAICO).

Key Points

• During the Asia-Pacific Economic Cooperation (APEC) proceedings in late 2024 and leading into the 2025 agenda, Chinese President Xi Jinping proposed the establishment of the World Artificial Intelligence Cooperation Organization (WAICO) to foster global collaboration.
• The proposal aims to create a centralized body that facilitates international cooperation on AI technology, ensuring that the benefits of Artificial Intelligence are shared globally, particularly with developing nations in the Global South.
• President Xi Jinping emphasized that the WAICO should serve as a platform for policy coordination, technical exchange, and the development of international standards for AI ethics and safety.
• This initiative follows China’s Global AI Governance Initiative, which was first introduced in October 2023 at the Third Belt and Road Forum, highlighting sovereignty and mutual respect in digital governance.
• The proposal at APEC reflects China’s strategic move to take a leadership role in shaping the global governance framework for emerging technologies and addressing the digital divide.

Additional Information

• Global AI Governance Initiative:
• Launched by China in 2023, this initiative outlines eleven core principles for AI development, including equal rights for all countries to develop and use AI regardless of their political system.
• It opposes the creation of exclusive groups or technological blockades that hinder the development of AI in other nations.
• APEC (Asia-Pacific Economic Cooperation):
• Established in 1989, APEC is an inter-governmental forum for 21 member economies in the Pacific Rim that promotes free trade throughout the Asia-Pacific region.
• The 2024 APEC Summit was held in Lima, Peru, where leaders discussed sustainable growth, digital transformation, and inclusive trade.
• United Nations and AI:
• In March 2024, the UN General Assembly adopted its first global resolution on Artificial Intelligence, encouraged by the United States and co-sponsored by China and over 120 other nations.
• The resolution emphasizes the need for safe, secure, and trustworthy AI systems that respect human rights and international law.
• Technological Rivalry:
• The proposal for WAICO comes amidst a backdrop of technological competition between the United States and China, particularly concerning semiconductors and AI infrastructure.
• While China promotes multilateral governance through organizations like WAICO, the USA often focuses on alliances with G7 partners and democratic nations to set AI norms.

Important Points

• Date of Proposal: The concept gained significant traction during the APEC meetings in November 2024 and is a key foreign policy objective for China for the year 2025.
• Core Objective: To prevent the monopolization of AI technologies by a few countries and to ensure that Global AI Governance is handled under a multilateral framework, potentially through the United Nations.
• Features of WAICO: It is intended to be an open and inclusive organization that welcomes participation from governments, international organizations, research institutions, and private enterprises.
• Administrative Focus: The organization would likely focus on data security, algorithmic transparency, and preventing AI from being used for interference in the internal affairs of other countries.

The correct answer is Integrated circuits (ICs).

Key Points

• A CPU (Central Processing Unit) is the primary component of any computer system that performs arithmetic, logic, and input/output operations. Physically, it is manufactured on a small piece of semiconductor material, typically silicon, which is known as an Integrated circuit (IC).
• An Integrated Circuit acts as a single unit containing thousands to billions of miniature electronic components like transistors, resistors, and capacitors. These are etched onto the silicon wafer through a process called photolithography.
• When an entire CPU is contained on a single Integrated Circuit, it is specifically referred to as a microprocessor. In modern computing, almost all CPUs are microprocessors, but the physical hardware category they belong to is ICs.
• The Integrated Circuit technology allowed for the miniaturization of computers. Before ICs, computers like the ENIAC used thousands of vacuum tubes and occupied entire rooms. The shift to silicon-based ICs significantly increased processing speed while reducing power consumption. Hence, the statement regarding Integrated circuits being the physical microchip for a CPU is correct.

Additional Information

• Evolution of ICs: The concept of the Integrated Circuit was first developed in 1958 by Jack Kilby of Texas Instruments and independently by Robert Noyce of Fairchild Semiconductor in 1959. This invention led to the third generation of computers.
• Microprocessors: The first commercially available microprocessor was the Intel 4004, released in 1971. It combined all the functions of a CPU onto a single chip, revolutionizing the personal computer industry.
• Scale of Integration: Modern ICs utilize Very Large Scale Integration (VLSI) or Ultra Large Scale Integration (ULSI), allowing developers to pack billions of MOSFET (Metal-Oxide-Semiconductor Field-Effect Transistor) devices into a space smaller than a fingernail.
• Moore's Law: Coined by Gordon Moore in 1965, this observation states that the number of transistors on a microchip doubles approximately every two years, though the cost of computers is halved. This trend has driven the rapid growth of computing power for decades.

Important Points

• Transistors: These are the fundamental building blocks of an IC. They act as switches or amplifiers. While a CPU is made of transistors, it is not "placed on" them; rather, the transistors are fabricated within the Integrated Circuit.
• Compact Disks (CDs): These are optical storage devices used to store data in a digital format. They have no role in the physical construction of a CPU and are used for secondary storage only.
• Semiconductor Material: Silicon is the most common element used for ICs due to its abundance and its unique ability to have its electrical conductivity modified by adding impurities (a process called doping).
• Form Factor: The CPU chip is usually protected by a ceramic or plastic housing and connected to the motherboard via a socket (such as LGA or PGA). This housing helps in heat dissipation and provides structural integrity to the delicate silicon die.

Given Statements:

All chairs are tables.

Some tables are boards.

No chair is a desk.

The least possible Venn diagram shows:

Conclusions:

(I) Some boards are tables

Since “Some tables are boards”, it directly means there is an intersection between tables and boards.

So, this conclusion follows.

(II) No table is a desk

We only know that no chair is a desk, but tables (outside chairs) may or may not be desks.

So this conclusion does not necessarily follow.

Hence, only conclusion (I) follows.

Hence, the correct answer is "Option 1".

The correct answer is RK Shanmukham Chetty.

Key Points

• RK Shanmukham Chetty served as the first Finance Minister of independent India following the end of British rule in 1947.
• He held this prestigious designation from August 15, 1947, to August 1948, under the leadership of Prime Minister Jawaharlal Nehru.
• He has the distinction of presenting the first-ever Union Budget of independent India on November 26, 1947.
• The first budget presented by him was an interim budget that covered a period of 7.5 months, specifically from August 15, 1947, to March 31, 1948.
• RK Shanmukham Chetty was a distinguished lawyer, economist, and politician who had earlier served as the President of the Central Legislative Assembly between 1933 and 1935.
• Before Independence, he served as the Dewan of Cochin State from 1935 to 1941 and represented India at the Bretton Woods Conference in 1944.

Additional Information

• Rajkumari Amrit Kaur:
• She was the first Health Minister of independent India and served for 10 years in the cabinet.
• She was the first woman to hold a cabinet rank in India and played a fundamental role in the establishment of the All India Institute of Medical Sciences (AIIMS) in New Delhi in 1956.
• Dr. CH Bhabha:
• Cooverji Hormusji Bhabha served as the first Commerce Minister of independent India.
• In the Interim Government formed in 1946, he was initially assigned the portfolio of Works, Mines, and Power.
• Sardar Baldev Singh:
• He was the first Defence Minister of India and played a key role in the partition negotiations.
• He managed the Indian Army during the Indo-Pakistani War of 1947 and oversaw the integration of the armed forces.
• John Mathai:
• He succeeded RK Shanmukham Chetty as the Finance Minister and presented the first budget of the Republic of India in 1950.
• He was also instrumental in the nationalization of the State Bank of India in 1955.

Important Points

• Article 112: According to the Constitution of India, the Union Budget is officially referred to as the Annual Financial Statement.
• It represents the estimated receipts and expenditure of the Government for a financial year, which runs from April 1 to March 31.
• The Budget is presented in the Lok Sabha by the Union Finance Minister, usually after the President has recommended its introduction.
• Historically, the Railway Budget and the General Budget were presented separately following the Acworth Committee report of 1921, but they were merged back into a single budget in 2017.

Shortcut Trick

Successive increase formula: Final = Initial × (1 + a/100) × (1 + b/100)

Population = 2,90,000 × 1.15 × 1.20

= 2,90,000 × 1.38

= 4,00,200

∴ Answer = 4,00,200

Alternate Method

Given:

Initial population = 2,90,000

Increase in first year = 15%

Increase in second year = 20%

Formula used:

New Value = Old Value × (1 + Rate/100)

Calculation:

⇒ After 1st year = 2,90,000 × (1 + 15/100)

⇒ = 2,90,000 × 1.15 = 3,33,500

⇒ After 2nd year = 3,33,500 × (1 + 20/100)

⇒ = 3,33,500 × 1.20 = 4,00,200

∴ The correct answer is 4,00,200.

Additional Information

Successive Percentage Change

Net change = a + b + (ab/100). Used when two percentage changes are applied.

Population Growth Formula

Population after n years = P × (1 + r/100)ⁿ

Compound Growth Concept

Each year's increase is applied to the updated population, not the original.

Shortcut Net Increase

15% and 20% successive increase ⇒ Net = 15 + 20 + (15×20/100) = 38%

The correct answer is Rank or position of an official.

Key Points

• The term Mansab is derived from the Arabic language, which literally translates to rank, position, or status. In the context of the Mughal administration, it defined the grade of an officer in the imperial hierarchy.
• The Mansabdari system was a unique administrative framework introduced by the Mughal Emperor Akbar in the 19th year of his reign, approximately 1571-72. It was designed to organize the nobility and the military of the empire.
• A Mansabdar was an individual who held a Mansab. This system determined three specific things for the official: their rank in the administrative hierarchy, their fixed salary, and the military responsibility (number of cavalrymen they had to maintain).
• The rank of a Mansabdar was divided into two numerical representations: Zat and Sawar. Zat indicated the personal status and the salary of the officer, while Sawar indicated the number of cavalrymen (soldiers and horses) the official was required to bring for service.
• By standardizing the ranks, Akbar was able to create a centralized bureaucracy where every officer, whether civil or military, was part of a single service under the Emperor's direct control.

Additional Information

• Hierarchy and Ranks: The Mansabs were classified into various grades, ranging from a minimum of 10 to a maximum of 10,000. Ranks above 5,000 were usually reserved for the Princes of the Royal Blood. For instance, Raja Man Singh was one of the few non-royal officials to hold a high rank of 7,000.
• Appointment and Promotion: The Emperor held the absolute power to appoint, promote, or dismiss any Mansabdar. The Mir Bakshi was the head of the military department who presented candidates for appointment and maintained the records of the Mansabdars.
• Non-Hereditary Nature: The Mansabdari system was not hereditary. A Mansab was granted for the lifetime of the officer. Upon the death of a Mansabdar, their rank was abolished, and their property was often confiscated by the state under the Law of Escheat.
• Mode of Payment: Mansabdars were paid either in cash (Naqdi) or through land revenue assignments known as Jagirs. However, even if they held a Jagir, they did not have ownership of the land; they only had the right to collect the revenue equivalent to their salary.
• Evolution of the System: During the reign of Jahangir, the system was modified with the introduction of Du-aspa Sih-aspa, which allowed a Mansabdar to maintain a higher number of Sawar without increasing their Zat rank.

Important Points

• Military Obligations: Every Mansabdar had to bring their cavalrymen for review. To prevent corruption and cheating, the Mughals used the Dagh system (branding of horses) and the Chehra system (descriptive rolls of soldiers).
• Classification of Officers: Officials holding a rank below 500 were called Mansabdars. Those holding ranks between 500 and 2,500 were known as Amirs, and those above 2,500 were called Amir-i-Umda or Amir-al-Azam.
• Linguistic Basis: While the system was implemented in India, it had roots in Central Asian traditions and the Mongol military organization (the decimal system), which Akbar adapted to suit the Indian socio-political landscape.
• Administrative Impact: This system helped Akbar integrate the diverse Rajput, Turani, Irani, and Indian Muslim nobility into a unified administrative structure, ensuring the stability of the Mughal Empire for centuries.

Shortcut Trick

Take total work = LCM(27,18) = 54 units

P = 2 units/hr, Q = 2 units/hr ⇒ Together = 4 units/hr

In 3 hours ⇒ work done = 12 units

R empties 12 units in 4 hrs ⇒ R = −3 units/hr

Net = 4 − 3 = 1 unit/hr

∴ Answer = 54 hours

Alternate Method

Given:

Pipe P fills 5/9 in 15 hours

Pipe Q fills 7/9 in 21 hours

P and Q run for 3 hours

Pipe R empties water in 4 hours

Formula used:

Efficiency = Total Work ÷ Time

Calculation:

⇒ Efficiency of P = 2 units/hr

⇒ Efficiency of Q = 2 units/hr

⇒ Combined (P + Q) = 4 units/hr

⇒ Work done in 3 hours = 3 × 4 = 12 units

⇒ R empties 12 units in 4 hrs ⇒ Efficiency of R = −3 units/hr

⇒ Net efficiency (P + Q + R) = 4 − 3 = 1 unit/hr

⇒ Time = Total Work ÷ Net Efficiency = 54 ÷ 1 = 54 hours

∴ The correct answer is 54 hours.

Additional Information

LCM Method Advantage

Converts fractions into whole numbers, making calculations faster and simpler.

Efficiency Concept

Efficiency = Work done per unit time. Higher efficiency means faster completion.

Negative Work

Emptying pipes have negative efficiency and reduce total work.

Combined Work

Net efficiency = Sum of all individual efficiencies (taking sign into account).

Shortcut Trick

Empirical relation: Mode = 3Median − 2Mean

⇒ Mode − Mean = 3(Median − Mean)

Given Mode − Mean = 33.6

⇒ Median − Mean = 33.6 ÷ 3 = 11.2

⇒ Mode − Median = 33.6 − 11.2 = 22.4

∴ Answer = 22.4

Alternate Method

Given:

Mode − Mean = 33.6

Formula used:

Mode = 3Median − 2Mean

Calculation:

⇒ Mode − Mean = (3Median − 2Mean) − Mean

⇒ Mode − Mean = 3Median − 3Mean

⇒ Mode − Mean = 3(Median − Mean)

⇒ 33.6 = 3(Median − Mean)

⇒ Median − Mean = 11.2

⇒ Mode − Median = (Mode − Mean) − (Median − Mean)

⇒ = 33.6 − 11.2 = 22.4

∴ The correct answer is 22.4.

Additional Information

Empirical Formula

Mode = 3Median − 2Mean. Used for moderately skewed distributions.

Relation Derived

Mode − Mean = 3(Median − Mean)

Difference Relation

Mode − Median = (Mode − Mean) − (Median − Mean)

Use Case

Applicable when exact data is not given but mean, median, and mode are related.

Given:

REST → 5729

SEAT → 7625

Thus, A = 6

Hence, the correct answer is Option 4.

The logic followed here is based on the alphabetical position pattern:

Option 1: YCX

Option 2: GKF

Option 3: NRM

Option 4: TYS

Thus, YCX does not follow the pattern.

Hence, the odd one out is Option 1.

Given: (Left) = N * R ^ S V L ^ W O P Y $ @ H A F ? E R (Right)

Now,

Letters, which are immediately preceded by a symbol and also immediately followed by a symbol.

So, Needed pattern is: Symbol - Letter - Symbol

(1): (Left) [**= N ]* R ^ S V L ^ W O P Y $ @ H A F ? E R (Right)

(2): (Left) = N [*** R ^**] S V L ^ W O P Y $ @ H A F ? E R (Right)

So, total valid letters = 2

Hence, the correct answer is Option 4.

The correct answer is Article 43B.

Key Points

• Article 43B was inserted into the Constitution of India by the 97th Constitutional Amendment Act, 2011. It specifically mandates the State to promote voluntary formation, autonomous functioning, democratic control, and professional management of cooperative societies. Hence, Option A is the correct answer.
• The inclusion of this article reflects the Directive Principles of State Policy (DPSP) under Part IV, which aims to establish a social and economic democracy.
• The 97th Amendment aimed to address the various problems faced by cooperative sectors, such as lack of professionalism, delayed elections, and excessive government interference.
• By making it a constitutional directive, the State is encouraged to create a favorable legal and administrative environment for cooperatives to thrive as effective economic units.
• This amendment also introduced Part IXB to the Constitution, which contains detailed provisions regarding the incorporation, terms of members, and audit of cooperative societies.

Additional Information

• Article 43A:
• This article was added by the 42nd Constitutional Amendment Act, 1976.
• It directs the State to take steps to secure the participation of workers in the management of undertakings, establishments, or other organizations engaged in any industry. Hence, Option B is incorrect.
• Article 48A:
• This article was also introduced by the 42nd Constitutional Amendment Act, 1976.
• It focuses on the protection and improvement of the environment and the safeguarding of forests and wildlife of the country. Hence, Option C is incorrect.
• Article 38:
• This is an original article of the Constitution that directs the State to secure a social order for the promotion of the welfare of the people.
• It was further bolstered by the 44th Amendment Act, 1978, which added a provision to minimize inequalities in income, status, facilities, and opportunities. Hence, Option D is incorrect.
• Part IXB of the Constitution:
• Introduced by the same 97th Amendment, it covers Articles 243ZH to 243ZT.
• It provides for the maximum number of directors (21), reservation of seats for SC/STs and women on boards, and the duration of the term (5 years) for elected members of cooperative societies.

Important Points

• Fundamental Right: The 97th Amendment also modified Article 19(1)(c) of the Constitution. It made the right to form cooperative societies a Fundamental Right for all citizens of India.
• Supreme Court Ruling: In 2021, in the case of Union of India v. Rajendra N. Shah, the Supreme Court of India struck down a portion of the 97th Amendment (specifically Part IXB) insofar as it applied to State Cooperative Societies because it was not ratified by the State Legislatures as required by Article 368(2). However, the court upheld the validity of the amendment regarding Multi-State Cooperative Societies and the insertion of Article 43B.
• Linguistic and Cultural Context: Cooperatives in India are vital for rural development and agricultural credit, with famous examples like AMUL (Gujarat Co-operative Milk Marketing Federation Ltd) showcasing the success of the cooperative model.

Given: # : MNI :: UVQ : %

Option 1) # = RJH , % = IQL

For # (RJH) to MNI

For % (IQL) to UVQ

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

Option 2) # = OPN , % = PBW

For # (OPN) to MNI

For % (PBW) to UVQ

Since, the patterns do not match, Option 2 is incorrect.

Option 3) # = RSN , % = PQL

For # (RSN) to MNI

For % (PQL) to UVQ

Since, both transformations follow a consistent shift pattern, Option 3 is correct.

Option 4) # = RUN , % = IOL

For # (RUN) to MNI

For % (IOL) to UVQ

Since, the patterns do not match, Option 4 is incorrect.

Hence, the correct answer is "Option 3".

Shortcut Trick

Girish is 60 less than 92% ⇒ 768 + 60 = 828 = 92%

⇒ 1% = 828 ÷ 92 = 9

⇒ Total marks = 9 × 100 = 900

Friend % = (738 ÷ 900) × 100 = 82%

∴ Answer = 82%

Alternate Method

Given:

Girish's marks = 768

He is 60 marks less than 92% of maximum marks

Friend's marks = 738

Formula used:

Percentage = (Obtained Marks ÷ Maximum Marks) × 100

Calculation:

⇒ Let maximum marks = M

⇒ 92% of M = 0.92M

⇒ Given: 0.92M − 60 = 768

⇒ 0.92M = 768 + 60 = 828

⇒ M = 828 ÷ 0.92 = 900

⇒ Friend's percentage = (738 ÷ 900) × 100

⇒ = 82%

∴ The correct answer is 82%.

Additional Information

Percentage Concept

x% of a number = (x/100) × number

Reverse Percentage

If a value represents x%, divide by x and multiply by 100 to get total.

Marks Formula

Percentage = (Marks Obtained ÷ Total Marks) × 100

Shortcut Tip

When value is close to a percentage, adjust first (add/subtract) then find base.

The correct answer is Alt+Space.

Key Points

• The keyboard shortcut Alt+Space is used to open the System Menu (also known as the window menu) for the currently active window. This menu provides options such as Restore, Move, Size, Minimize, Maximize, and Close. Hence, option D is correct.
• Alt+F4 is a widely used shortcut in Windows OS to close the active item or exit the active application. If no program is open, it triggers the Shut Down Windows dialog box. Hence, option A is incorrect.
• Alt+Enter is primarily used in File Explorer to display the Properties dialog box for the selected file or folder. In some older applications or command prompts, it is used to toggle between windowed mode and full-screen mode. Hence, option B is incorrect.
• Alt+Tab is the standard shortcut for Task Switching. It allows the user to switch between open applications or windows by holding the Alt key and pressing Tab to cycle through the list. Hence, option C is incorrect.
• Using Alt+Space is particularly helpful for accessibility purposes or when a mouse is unavailable, allowing users to manage window placement and sizing entirely through the keyboard.

Additional Information

• Windows Operating System (OS): Developed by Microsoft, it relies heavily on Graphical User Interface (GUI) elements and Keyboard Shortcuts to enhance productivity and user experience.
• System Menu Functions:
• Move: Allows the user to reposition the window using arrow keys.
• Size: Enables resizing of the window borders via the keyboard.
• Minimize/Maximize: Controls the visibility and scaling of the window on the Desktop.
• Alternative Shortcuts for Navigation:
• Ctrl+Shift+Esc: Directly opens the Task Manager to monitor system performance and background processes.
• Windows Key + D: Instantly minimizes all open windows to show the Desktop.
• Windows Key + L: Used to lock the computer or switch users securely.
• Alt + Esc: Cycles through windows in the order in which they were originally opened.
• History and Evolution: Most of these shortcuts, including Alt+Space and Alt+Tab, have been consistent features since the early versions of Windows 3.1 and Windows 95, maintaining legacy compatibility for professional users.

Important Points

• Keyboard Accessibility: Shortcuts like Alt+Space are essential for users with motor impairments, as they provide a way to interact with the Operating System without requiring precise mouse movements.
• Troubleshooting: If a window is "lost" off-screen (due to changing monitor resolutions), a user can press Alt+Space, select Move, and use the arrow keys to bring the window back into the visible area.
• Cross-Platform Compatibility: While these shortcuts are specific to Microsoft Windows, similar functionalities exist in macOS (using the Command key) and Linux distributions (like Ubuntu or Fedora).

Shortcut Trick

CP per article = 102 ÷ 12 = 8.5

SP per article = 68

Profit per article = 68 − 8.5 = 59.5

Profit % = (59.5 ÷ 8.5) × 100 = 700%

∴ Answer = 700% profit

Alternate Method

Given:

Number of dozens = 32

CP per dozen = ₹102

SP per article = ₹68

Formula used:

Profit % = (Profit ÷ Cost Price) × 100

Calculation:

⇒ Total articles = 32 × 12 = 384

⇒ Total CP = 32 × 102 = ₹3264

⇒ Total SP = 384 × 68 = ₹26112

⇒ Profit = 26112 − 3264 = ₹22848

⇒ Profit % = (22848 ÷ 3264) × 100

⇒ = 700%

∴ The correct answer is 700% profit.

Additional Information

Dozen Concept

1 dozen = 12 articles. Convert to per article for easy comparison.

Profit Formula

Profit % = (SP − CP) ÷ CP × 100

Unit Method

Always reduce to per unit to avoid large calculations.

Quick Check

If SP is many times CP, expect very high profit percentage.

The logic followed here is:

Logic: Each step is obtained by dividing by 2, and then alternately adding 10 or multiplying by 2 in a fixed repeating pattern.

For, 100 – 50 – 60 – 30

⇒ 100 ÷ 2 = 50

⇒ 50 + 10 = 60

⇒ 60 ÷ 2 = 30

For, 300 – 150 – 160 – 80

⇒ 300 ÷ 2 = 150

⇒ 150 + 10 = 160

⇒ 160 ÷ 2 = 80

Now, checking the options using the same pattern:

Option 1) 100 – 50 – 40 – 20

⇒ 100 ÷ 2 = 50

⇒ 50 − 10 = 40

⇒ 40 ÷ 2 = 20

Option 2) 160 – 80 – 90 – 180

⇒ 160 ÷ 2 = 80

⇒ 80 + 10 = 90

⇒ 90 × 2 = 180

Option 3) 80 – 40 – 50 – 25

⇒ 80 ÷ 2 = 40

⇒ 40 + 10 = 50

⇒ 50 ÷ 2 = 25

Option 4) 220 – 110 – 120 – 30

⇒ 220 ÷ 2 = 110

⇒ 110 + 10 = 120

⇒ 120 ÷ 2 = 60 ≠ 30

Thus,  80 – 40 – 50 – 25 matches the given pattern.

Hence, the correct answer is Option 3.

The logic followed here is:

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

Hence, the correct option is "Option 3".

The correct answer is Lakhpati Didis.

Key Points

• The term Lakhpati Didis refers to women members of Self-Help Groups (SHGs) who have achieved a sustainable annual income of ₹1 lakh (one lakh rupees) or more through various livelihood interventions.
• This initiative was prominently announced by Prime Minister Narendra Modi during his 77th Independence Day speech on August 15, 2023, with the aim of empowering rural women economically.
• The program is a strategic part of the Deendayal Antyodaya Yojana - National Rural Livelihoods Mission (DAY-NRLM), which focuses on mobilizing rural poor households into SHGs and providing them with diversified livelihood opportunities.
• During the Interim Budget 2024-25, the Union Finance Minister Nirmala Sitharaman announced an increase in the target for Lakhpati Didis from 2 crore to 3 crore women.
• The initiative focuses on providing skills training in areas such as plumbing, LED bulb making, drone operation, and tailoring to help women establish micro-enterprises. Hence, the statement regarding the term used for SHG women earning ₹1 lakh or more is correct.

Additional Information

• Deendayal Antyodaya Yojana - National Rural Livelihoods Mission (DAY-NRLM):
• Launched in June 2011 by the Ministry of Rural Development, it is one of the world's largest initiatives to improve the livelihoods of the rural poor.
• As of 2024, the mission has mobilized more than 9 crore women into nearly 83 lakh Self-Help Groups.
• The mission provides Revolving Funds (RF) and Community Investment Funds (CIF) to these groups to facilitate internal lending and business startups.
• Livelihood Diversification:
• The Lakhpati Didi model encourages women to adopt at least two to three distinct livelihood activities to ensure a stable income throughout the year.
• Activities include organic farming, livestock rearing, handicrafts, and non-farm sectors like operating Common Service Centres (CSCs).
• Financial Inclusion:
• Under this initiative, the government facilitates bank linkages for SHGs to provide credit at affordable interest rates.
• Women are also encouraged to become Bank Sakhis (Business Correspondents) to provide banking services in remote rural areas.

Important Points

• Namo Drone Didi Scheme:
• A major sub-component of the empowerment plan is the Namo Drone Didi scheme, launched in November 2023.
• The government aims to provide 15,000 selected women SHGs with drones to offer rental services to farmers for agricultural purposes like spraying pesticides and fertilizers.
• This scheme provides an additional income stream of approximately ₹60,000 to ₹1,00,000 per year for the drone pilots.
• Monitoring and Support:
• The progress of the Lakhpati Didi initiative is tracked through a dedicated MIS portal to monitor the household-level income of SHG members across different States and Union Territories.
• Technical support is provided through Cluster Level Federations (CLFs) and State Rural Livelihood Missions (SRLMs) to ensure market access for products made by these women.

Given:

Vishu starts from A and drives 31 km East.

He turns left → 19 km North.

He turns left → 34 km West.

He turns left → 32 km South.

He turns left → 3 km East and reaches P.

 

To reach A from P → move 13 km North.

Hence, the correct answer is Option 3.

The correct answer is Hayli Gubbi.

Key Points

• Hayli Gubbi is a shield volcano located in the Afar Region of Ethiopia. It is the southernmost volcano of the Erta Ale volcanic range.
• The volcano is notably recognized for its eruption in November 2008. While the question mentions 2025, this is likely a typographical error in the source material referring to the 2008 event, which is a common subject in geographical examinations. Hence, Option D is the correct answer.
• During the 2008 eruption, significant seismic activity and lava flows were reported in the Danakil Depression, specifically within the Afar Triangle.
• The summit of Hayli Gubbi reaches an elevation of approximately 521 meters (1,709 feet) and contains a small caldera. Its volcanic activity is primarily basaltic, typical of volcanoes situated along tectonic rift zones.
• The Afar Depression, where Hayli Gubbi is situated, is a triple junction where three tectonic plates—the Arabian, Nubian, and Somali plates—are diverging, leading to high levels of volcanic and seismic activity.

Additional Information

• Erta Ale:
• Commonly known as the "Smoking Mountain" in the local Afar language, Erta Ale is one of the most active volcanoes in Ethiopia.
• It is famous for harboring a persistent lava lake, one of only a few in the world, which has been active since 1967. Hence, statement regarding Erta Ale being the answer for a specific Nov 2008 eruption is incorrect.
• Mount Nyiragongo:
• This is a large stratovolcano located in the Democratic Republic of the Congo (DRC), not Ethiopia.
• It is situated within the Virunga National Park and is notorious for its extremely fluid lava and its most recent major eruptions in 2002 and May 2021. Hence, statement regarding Nyiragongo being an Ethiopian volcano is incorrect.
• Volcanism in Ethiopia:
• Ethiopia is home to more than 60 volcanoes that have been active in the last 10,000 years. This is due to its position on the East African Rift System.
• Important volcanic peaks include Dabbahu (which had a major eruption in 2005), Dama Ali, and Alayta.
• Afar Triangle Significance:
• This region is not only geologically active but also archaeologically vital. It is the site where the famous 3.2 million-year-old hominin fossil "Lucy" was discovered in 1974.
• The Danakil Depression within this region is one of the lowest points on Earth and is known for its extreme heat and hydrothermal fields like Dallol.

Important Points

• Shield Volcano Characteristics: Hayli Gubbi is classified as a shield volcano, which means it is built almost entirely of fluid lava flows. These volcanoes have broad, gently sloping sides, resembling a warrior's shield.
• Rift Valley Tectonics: The East African Rift is a developing divergent plate boundary. As the plates move apart, the lithosphere thins, allowing magma to rise to the surface, creating the volcanic chains seen in Ethiopia, Kenya, and Tanzania.
• Monitoring: Most volcanoes in the Afar region are monitored via satellite remote sensing (such as InSAR and MODIS) due to the remote and harsh environment of the Danakil Desert, which makes ground-based monitoring difficult.

The correct answer is Radiation therapy administered after bladder cancer surgery.

Key Points

• In 2025, researchers from the Tata Memorial Centre (TMC) in Mumbai, India, published the results of a landmark Phase III trial regarding bladder cancer treatment. The study focused on patients with Muscle-Invasive Bladder Cancer (MIBC) who are at high risk of recurrence after undergoing a Radical Cystectomy (surgical removal of the bladder).
• The intervention demonstrated to be highly effective is Adjuvant Radiation Therapy (Radiation therapy administered after bladder cancer surgery). The study showed that this intervention significantly reduces the rate of pelvic recurrence, which is a common site for the cancer to return. Hence, option C is correct.
• Immunotherapy used as a standalone post-surgical treatment (Option A) has been explored in various global trials (like CheckMate 274), but the specific 2025 breakthrough by Indian researchers highlighted in this context specifically validated the role of radiation. Hence, option A is incorrect.
• Targeted drug therapy replacing surgery (Option B) is currently not the standard of care for high-risk muscle-invasive bladder cancer, as Radical Cystectomy remains the primary curative surgical intervention. Hence, option B is incorrect.
• Chemotherapy administered before bladder cancer surgery (Option D), known as Neoadjuvant Chemotherapy (NAC), is a well-established standard treatment used to shrink tumors before surgery, but it was not the specific post-surgical intervention highlighted in the 2025 Indian study for reducing pelvic recurrence. Hence, option D is incorrect.

Additional Information

• Muscle-Invasive Bladder Cancer (MIBC): This is an aggressive form of cancer where the malignancy has spread into the detrusor muscle of the bladder wall. Patients with MIBC often require aggressive treatment including surgery, chemotherapy, and now, as per the latest findings, post-operative radiation.
• Radical Cystectomy: This is the gold standard surgical procedure for MIBC. It involves the removal of the entire urinary bladder, nearby lymph nodes, and part of the urethra. In men, it may include the removal of the prostate, and in women, the uterus and ovaries.
• Pelvic Recurrence: Despite successful surgery, nearly 25% to 45% of high-risk patients experience cancer returning in the pelvic region. The Indian study showed that Adjuvant Radiation can reduce this risk by approximately 50%.
• Intensity-Modulated Radiation Therapy (IMRT): The researchers used advanced IMRT technology, which allows for precise targeting of the pelvic nodes while minimizing damage to the surrounding intestines and bowels, thereby reducing side effects.
• Global Impact: This research is particularly significant for India and other Low and Middle-Income Countries (LMICs) because Radiation therapy is more cost-effective and accessible compared to expensive Immunotherapy drugs like Nivolumab.

Important Points

• The POBC Trial: The study, known as the Post-Operative Bladder Cancer (POBC) trial, enrolled over 200 patients at Tata Memorial Hospital. The lead researcher, Dr. Vedang Murthy, emphasized that this trial provides Level 1 evidence for a treatment that was previously controversial.
• Disease-Free Survival (DFS): The study reported a significant improvement in 3-year Disease-Free Survival for patients receiving radiation compared to those who only underwent surgery and observation.
• Year of Significance: While the trial recruitment happened over several years, the 2024-2025 period marks the global dissemination of these results, influencing international clinical guidelines.
• Standard of Care: This finding is expected to change the Standard of Care globally, shifting Adjuvant Radiation from an "optional" or "investigational" status to a recommended treatment for high-risk bladder cancer patients post-surgery.

Shortcut Trick

In continued proportion: x² = 8 × 18

⇒ x² = 144

⇒ x = √144 = 12

∴ Answer = 12

Alternate Method

Given:

8, x, 18 are in continued proportion

Formula used:

In continued proportion: a : b = b : c ⇒ b² = a × c

Calculation:

⇒ x² = 8 × 18

⇒ x² = 144

⇒ x = √144

⇒ x = 12

∴ The correct answer is 12.

Additional Information

Continued Proportion

Three numbers a, b, c are in continued proportion if a : b = b : c.

Key Formula

b² = a × c

Geometric Mean

The middle term in continued proportion is called the geometric mean.

Shortcut Tip

Directly multiply first and third term, then take square root.

The correct answer is A sharp reversal led to severe rainfall deficits in many regions..

Key Points

• Monsoon variability: Despite earlier heavy rains, a sharp reversal in monsoon patterns occurred due to sudden changes in atmospheric circulation, leading to rainfall deficits in many regions. This phenomenon is often influenced by factors like the El Niño effect.
• Nearly 19% of India faced drought or drought-like conditions by August 2025. The rainfall deficit created challenges for agriculture, water availability, and overall economic stability in affected areas.
• Delayed monsoon retreat: The abrupt cessation of rains during critical periods, coupled with dry spells, exacerbated water stress and reduced soil moisture levels.
• Climate change: The reversal can also be linked to broader climate change effects, such as rising temperatures that disrupt normal monsoon patterns and intensify rainfall variability.
• Regional disparities: Some regions experienced above-normal rainfall initially, but others faced prolonged dry periods, leading to uneven impacts across the country.

Additional Information

• El Niño and La Niña:
• El Niño is characterized by warming of the Pacific Ocean waters, which typically leads to weaker monsoons and reduced rainfall in India.
• La Niña, on the other hand, often results in increased rainfall in India but can also lead to regional imbalances.
• Indian Monsoon Mechanism:
• The monsoon is driven by the temperature contrast between land and ocean, creating pressure gradients that drive moisture-laden winds inland.
• Disruptions in this mechanism, such as delayed onset or abrupt retreat, can create rainfall deficits in critical agricultural areas.
• Impact on agriculture:
• A sharp reversal in rainfall patterns directly affects crop yields, particularly for water-intensive crops like rice and sugarcane.
• Reduced soil moisture and drying reservoirs further stress irrigation systems, impacting food security.
• Water resource management:
• India's dependence on monsoon rainfall makes effective water conservation strategies crucial during drought-like conditions.
• Excessive river damming or mismanagement of water resources can compound the effects of rainfall deficits.
• Climate change adaptation:
• Long-term solutions to address monsoon variability include afforestation, sustainable agriculture practices, and improved weather forecasting systems.
• India's National Action Plan on Climate Change (NAPCC) aims to mitigate climate change impacts through focused missions like the National Water Mission and Green India Mission.

Important Points

• Rainfall deficit statistics:
• By August 2025, rainfall deficits reached 19% across the country, severely impacting agricultural productivity.
• Regions like Maharashtra, Karnataka, and Rajasthan were most affected by drought-like conditions.
• Government initiatives:
• Programs like the Pradhan Mantri Krishi Sinchai Yojana aim to improve irrigation infrastructure and reduce dependency on monsoon rains.
• The National Adaptation Fund for Climate Change (NAFCC) provides financial support to mitigate climate change impacts on vulnerable sectors.
• Economic implications:
• Rainfall deficits lead to reduced agricultural output, impacting GDP and causing spikes in food prices.
• Increased reliance on water-intensive industries exacerbates the water crisis during such periods.

Given Statements:

I. Tanya scored more than Ritu and Seema but less than Usha.

II. Varsha scored more than Tanya but less than Usha.

Question: Who scored the highest marks?

Analysis:

From Statement I:

Usha > Tanya > Ritu, Seema

But Varsha’s position is unknown, so highest cannot be confirmed.

So Statement I alone is not sufficient.

From Statement II:

Usha > Varsha > Tanya

But Ritu and Seema’s positions are unknown, so highest cannot be confirmed.

So Statement II alone is not sufficient.

Combining I and II:

Usha > Varsha > Tanya > Ritu, Seema

Now it is clear that Usha scored the highest marks.

Hence, both statements I and II together are sufficient, but neither statement alone is sufficient.

Hence, the correct answer is "Option 4".

The logic followed here is:

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

Only two people sit between R and P when counted from the left of P.

Only three people sit between C and O when counted from the left of C.

P sits to the immediate right of O.

B sits to the immediate right of Q.

Now, fourth to the left of D = Q

Hence, the correct answer is "Option 4".

Shortcut Trick

Let MP = 100 ⇒ SP₁ = 3/10 × 100 = 30

Loss 25% ⇒ SP₁ = 75% of CP ⇒ CP = 30 ÷ 0.75 = 40

Now SP₂ = 69% of MP = 69

Profit = 69 − 40 = 29

Profit% = (29 ÷ 40) × 100 = 72.5%

∴ Answer = 72.5%

Alternate Method

Given:

First SP = (3/10) of MP

Loss = 25%

Second SP = 69% of MP

Formula used:

Loss% = (Loss ÷ CP) × 100

Profit% = (Profit ÷ CP) × 100

Calculation:

⇒ Let Marked Price (MP) = 100

⇒ First SP = 3/10 × 100 = 30

⇒ Loss 25% ⇒ SP = 75% of CP

⇒ 30 = 0.75 × CP

⇒ CP = 30 ÷ 0.75 = 40

⇒ Second SP = 69% of MP = 69

⇒ Profit = 69 − 40 = 29

⇒ Profit% = (29 ÷ 40) × 100

⇒ = 72.5%

∴ The correct answer is 72.5%.

Additional Information

Assumption Method

Taking MP = 100 simplifies percentage calculations directly.

Loss Concept

If loss = x%, then SP = (100 − x)% of CP.

Profit Concept

Profit% = (SP − CP) ÷ CP × 100

Marked Price Relation

SP is often given as a percentage of MP in discount problems.

The correct answer is Indian Councils Act, 1861.

Key Points

• The Indian Councils Act of 1861 is a significant landmark in the constitutional and political history of India as it initiated the process of representative institutions by associating Indians with the law-making process.
• It provided that the Viceroy should nominate some Indians as non-official members of his expanded council. In 1862, Lord Canning, the then Viceroy, nominated three Indians to his legislative council: the Raja of Benares, the Maharaja of Patiala, and Sir Dinkar Rao.
• This Act initiated the process of decentralization by restoring the legislative powers to the Bombay and Madras Presidencies, reversing the centralizing tendency that had started with the Regulating Act of 1773.
• It also provided for the establishment of new legislative councils for Bengal, North-Western Frontier Province (NWFP), and Punjab, which were established in the years 1862, 1866, and 1897, respectively.
• The Act empowered the Viceroy to make rules and orders for the more convenient transaction of business in the council, effectively laying the foundation for the Cabinet system in India.

Additional Information

• Pitt’s India Act, 1784:
• This Act distinguished between the commercial and political functions of the East India Company.
• It established a system of double government by creating a Board of Control to manage political affairs while allowing the Court of Directors to manage commercial affairs.
• The Board of Control was empowered to supervise and direct all operations of the civil and military government or revenues of the British possessions in India.
• Charter Act, 1853:
• It was the last of the series of Charter Acts passed by the British Parliament between 1793 and 1853.
• It separated, for the first time, the legislative and executive functions of the Governor-General’s council.
• It introduced an open competition system for the selection and recruitment of civil servants. The Macaulay Committee (the Committee on the Indian Civil Service) was appointed in 1854 for this purpose.
• Government of India Act, 1858:
• This Act was enacted in the wake of the Revolt of 1857 (the First War of Independence) and is known as the Act for the Good Government of India.
• It abolished the East India Company and transferred the powers of government, territories, and revenues to the British Crown.
• It changed the designation of the Governor-General of India to that of Viceroy of India. Lord Canning became the first Viceroy of India.
• It ended the system of double government by abolishing the Board of Control and Court of Directors, creating a new office, Secretary of State for India.

Important Points

• Portfolio System: The Indian Councils Act of 1861 gave statutory recognition to the portfolio system introduced by Lord Canning in 1859. Under this, a member of the Viceroy’s council was made in-charge of one or more departments.
• Ordinance Power: The Act also empowered the Viceroy to issue ordinances without the concurrence of the legislative council during an emergency. The life of such an ordinance was limited to 6 months.
• Nature of Representation: While the Act of 1861 introduced Indian representation, the members were nominated and not elected, and their role was limited primarily to a consultative capacity in the legislative process.

The logic followed here is:

Logic: The second number = (first number × 5) + 1

For, 8 → 41

⇒ 8 × 5 = 40

⇒ 40 + 1 = 41

For, 81 → 406

⇒ 81 × 5 = 405

⇒ 405 + 1 = 406

Now, applying the same logic:

13 → 13 × 5

⇒ 13 × 5 = 65

⇒ 65 + 1 = 66

Hence, the correct answer is Option 4.

Shortcut Trick

Rationalize first term: cosθ/(1 + sinθ)

⇒ Multiply by (1 − sinθ)/(1 − sinθ)

⇒ cosθ(1 − sinθ)/(1 − sin²θ) = (1 − sinθ)/cosθ

Now add: (1 − sinθ)/cosθ + (1 + sinθ)/cosθ = 2/cosθ

∴ Answer = 2 secθ

Alternate Method

Given:

(cosθ / (1 + sinθ)) + ((1 + sinθ) / cosθ)

Concept Used:

Trigonometric identities and rationalization

Calculation:

⇒ (cosθ / (1 + sinθ)) × ((1 − sinθ)/(1 − sinθ))

⇒ cosθ(1 − sinθ)/(1 − sin²θ)

⇒ cosθ(1 − sinθ)/cos²θ

⇒ (1 − sinθ)/cosθ

⇒ Expression = (1 − sinθ)/cosθ + (1 + sinθ)/cosθ

⇒ (2)/cosθ

∴ The correct answer is 2 secθ.

Additional Information

Pythagorean Identity

sin²θ + cos²θ = 1 ⇒ 1 − sin²θ = cos²θ

Rationalization

Multiply numerator and denominator by conjugate to simplify expressions.

Reciprocal Identity

secθ = 1/cosθ

Shortcut Tip

Convert complex fractions into same denominator to combine quickly.

The correct answer is Konkan Coast.

Key Points

• The Konkan Coast is the rugged section of the western coastline of India that extends from the Gulf of Khambhat (specifically from Daman) in the north to Goa in the south. It spans across the coastal districts of Maharashtra and Goa.
• This sector is characterized by its submerged nature and indented topography, which provides excellent natural conditions for the development of ports. Major ports such as the Mumbai Port and the Jawaharlal Nehru Port Trust (JNPT) are located along this stretch.
• Geographically, it lies between the Western Ghats (Sahyadri Range) to the east and the Arabian Sea to the west. The width of the plain varies but is generally narrow, ranging from 50 to 80 kilometers.
• The region is famous for its production of Alphonso mangoes, cashews, and rice. The Konkan Railway, an engineering marvel completed in 1998, runs through this coastal strip, connecting Mumbai to Mangalore.
• Since the question asks for the sector between Mumbai and Goa, the Konkan Coast is the most accurate geographical designation. Hence, the correct answer is Konkan Coast.

Additional Information

• Malabar Coast:
• This refers to the southern part of the Western Coastal Plain, primarily located in the state of Kerala. It extends from Mangalore in the north to Kanyakumari in the south.
• The Malabar Coast is famous for its backwaters, locally known as Kayals, such as the Vembanad Lake. It receives very heavy rainfall during the South-West Monsoon.
• Karnataka Coast (Kanara Coast):
• This sector lies between the Konkan Coast to the north and the Malabar Coast to the south. It covers the coastal areas of Karnataka, specifically between Goa and Mangalore.
• The region features a narrow plain and is known for its beautiful beaches and the Netravati River.
• Coromandel Coast:
• Unlike the other options, this is part of the Eastern Coastal Plain. It extends from the False Divi Point (near the Krishna River Delta) in Andhra Pradesh to Kanyakumari in Tamil Nadu.
• It remains dry during the South-West Monsoon but receives significant rainfall from the North-East Monsoon during the Winter months of October to December.
• Gujarat Coast:
• The northernmost part of the western coast consists of the Kachchh and Kathiawar peninsulas. The Kachchh region is largely a desert and marshy land known as the Rann of Kachchh, while Kathiawar lies south of it.

Important Points

• The Western Coastal Plain is narrower compared to the Eastern Coastal Plain. While the western rivers like the Narmada and Tapi form Estuaries, the eastern rivers like the Ganga, Godavari, and Krishna form extensive Deltas.
• The total length of the Indian coastline is approximately 7,516.6 kilometers, including the mainland and the islands of Andaman & Nicobar and Lakshadweep.
• The Konkan Coast is specifically noted for its laterite soil, which is conducive to horticulture but poses challenges for intensive cereal farming.

The correct answer is Heavy industries.

Key Points

• The Second Five Year Plan, spanning from 1956 to 1961, was based on the Mahalanobis Model, named after the famous statistician Prasanta Chandra Mahalanobis. It shifted the focus from agriculture to rapid industrialization.
• The government decided to develop and manage Heavy industries directly to build a strong industrial base for the Indian economy. This included sectors like iron and steel, chemicals, and heavy engineering. Hence, Option D is correct.
• The Agricultural sector was the primary focus of the First Five Year Plan (1951-1956). While agriculture remained important, the Second Plan intentionally allocated more resources to the industrial sector to achieve self-reliance. Hence, Option C is incorrect.
• Small businesses and cottage industries were encouraged to provide employment and produce consumer goods, but they were not the primary sectors intended for direct State management and development compared to heavy industries. Hence, Option B is incorrect.
• The Service sector (such as banking, insurance, and transport) began to expand, but the core objective of the 1956 policy was the creation of capital goods through the public sector. Hence, Option A is incorrect.
• The plan aimed for a 25% increase in national income through rapid industrialization, although the actual growth achieved was approximately 4.27%.

Additional Information

• Industrial Policy Resolution of 1956: This resolution formed the legal basis for the Second Five Year Plan. It classified industries into three schedules: Schedule A (exclusive state responsibility), Schedule B (state-led with private participation), and Schedule C (remaining private sector).
• Strategic Steel Plants: Under the Second Plan, three major steel plants were established with foreign collaboration: Bhilai (with USSR), Durgapur (with United Kingdom), and Rourkela (with West Germany).
• Focus on Capital Goods: The plan emphasized the production of capital goods (machines that make other machines) rather than consumer goods, a strategy intended to ensure long-term economic independence.
• Socialistic Pattern of Society: The 1956 Resolution and the Second Plan officially adopted the goal of a socialistic pattern of society, where the public sector would occupy the strategic heights of the economy.
• Infrastructure Development: Significant investments were made in railways and hydroelectric power projects during this period to support the burgeoning heavy industries.

Important Points

• Institutional Growth: During the Second Plan period, the Atomic Energy Commission was established in 1958 with Homi J. Bhabha as the first chairman, highlighting the focus on scientific research and high-technology industries.
• Financial Challenges: The plan faced a foreign exchange crisis due to the massive import of machinery and equipment required for industrialization, leading to a scaling back of some targets in the year 1958.
• Tata Institute of Fundamental Research (TIFR) and the Indian Institutes of Technology (IITs) received significant support to create the technical manpower needed for managing heavy industries.
• The target growth rate was set at 4.5%, but the actual growth rate recorded was 4.27%, which was considered a success despite the inflationary pressures and food shortages experienced toward the end of the 1950s.

Family Chart:

Decoding the Symbols:

Given: K + L − M × N + O

It means: K is the sister of L, L is the husband of M, M is the mother of N, N is the sister of O.

Here, K is Father’s sister of O.

Hence, the correct answer is "Option 2".

Given: A, B, C, Q, R and S live on six different floors of the same building. Floor numbers are 1 (lowest) to 6 (highest).

Q lives on floor 5.

B lives on a floor above Q.

Only R lives below C.

A lives on an even-numbered floor.

Now, people below S→ 2 people

Hence, the correct answer is "Option 2".

Given: P, Q, R, S, T and U live on six different floors numbered 1 to 6.

Q lives on a prime-numbered floor.

The product of floors of Q and R is 3.

Only 2 people live above P.

T lives immediately below S.

Now, people below U (floor 2) = 1 person

Hence, the correct answer is "Option 3".

Given number: 749216358

Logic: Arrange the digits in descending order (left to right)

Original digits: 7 4 9 2 1 6 3 5 8

After arranging in descending order: 9 8 7 6 5 4 3 2 1

Now, Second from the left = 8

Third from the right = 3

Product = 8 × 3 = 24

Hence, the correct answer is Option 3.

Shortcut Trick

Customer pays for 14 but gets 16 ⇒ effective SP = 14 × 95% = 13.3 parts of MP

Profit 33% ⇒ SP = 133% of CP

⇒ 13.3 MP = 133% of 16 CP ⇒ 13.3 MP = 21.28 CP

⇒ MP/CP = 21.28 ÷ 13.3 = 1.6

∴ Answer = 60%

Alternate Method

Given:

Discount = 5%

Articles paid = 14

Articles received = 16

Gain = 33%

Formula used:

Selling price = Marked price × (100 − Discount) ÷ 100

Selling price = Cost price × (100 + Gain) ÷ 100

Calculation:

⇒ Let CP per article = C and MP per article = M

⇒ SP per article = 0.95M

⇒ Total SP = 14 × 0.95M = 13.3M

⇒ Total CP = 16C

⇒ Profit 33% ⇒ SP = 133% of CP

⇒ 13.3M = 16C × 133 ÷ 100

⇒ 13.3M = 21.28C

⇒ M = 21.28C ÷ 13.3

⇒ M = 1.6C

⇒ Increase % = (1.6C − C) ÷ C × 100

⇒ = 0.6 × 100 = 60%

∴ The correct answer is 60%.

Additional Information

Effective Selling Price

Free items reduce effective SP per unit since more items are given for same payment.

Profit Relation

33% gain ⇒ SP = 133% of CP = (133/100) × CP

Ratio Method

Convert full equation into MP : CP ratio to directly find percentage increase.

Shortcut Tip

Combine discount and free offers into one effective SP before applying profit.

Shortcut Trick

Use options: try u = 3, v = −18, w = 17

Check (1): 3 − 18 + 17 = 2 ✔

Check (2): 6×3 + 4(−18) + 5×17 = 18 − 72 + 85 = 31 ✔

Check (3): 5×3 + 2(−18) + 2×17 = 15 − 36 + 34 = 13 ✔

∴ Answer: u = 3, v = −18, w = 17

Alternate Method

Given:

u + v + w = 2

6u + 4v + 5w = 31

5u + 2v + 2w = 13

Concept Used:

Substitution and elimination method

Calculation:

⇒ From (1): u = 2 − v − w

⇒ Substitute in (3): 5(2 − v − w) + 2v + 2w = 13

⇒ 10 − 5v − 5w + 2v + 2w = 13

⇒ 10 − 3v − 3w = 13

⇒ −3v − 3w = 3

⇒ v + w = −1 ...(4)

⇒ Substitute u in (2): 6(2 − v − w) + 4v + 5w = 31

⇒ 12 − 6v − 6w + 4v + 5w = 31

⇒ 12 − 2v − w = 31

⇒ −2v − w = 19 ...(5)

⇒ From (4): w = −1 − v

⇒ Substitute in (5): −2v − (−1 − v) = 19

⇒ −2v + 1 + v = 19

⇒ −v = 18 ⇒ v = −18

⇒ w = −1 − (−18) = 17

⇒ u = 2 − v − w = 2 + 18 − 17 = 3

∴ The correct answer is u = 3, v = −18, w = 17.

Additional Information

Option Substitution Method

Try given options directly in equations to quickly identify correct solution.

Elimination Method

Reduce equations step-by-step to eliminate variables.

Verification Tip

Always verify all equations to avoid partial correctness.

Quick Strategy

Use substitution when one equation is simple and easy to rearrange.

Shortcut Trick

Simplify first: x^2.5/y^0.5 × √(xy) = x³

Simplify second: y^1.5/√x × √(xy) = y²

LCM = take highest powers ⇒ x³y² = x(xy)2

HCF = take lowest common ⇒ 1

∴ The correct answer is x(xy)2 and 1.

Alternate Method

Given:

(x^2.5/y^0.5) × √(xy)

(y^1.5/√x) × √(xy)

Concept Used:

Laws of exponents and LCM-HCF rules

Calculation:

⇒ First expression:

⇒ x^2.5/y^0.5 × (xy)^0.5

⇒ x^2.5 × x^0.5 / y^0.5 × y^0.5

⇒ x³

⇒ Second expression:

⇒ y^1.5/x^0.5 × (xy)^0.5

⇒ y^1.5 × y^0.5 / x^0.5 × x^0.5

⇒ y²

⇒ Now numbers are x³ and y²

⇒ Since x and y are co-prime:

⇒ LCM = x³y² = x(xy)2

⇒ HCF = 1

∴ The correct answer is x(xy)2 and 1.

Additional Information

Exponent Rules

a^m × aⁿ = a^m+n, a^m/aⁿ = a^m−n

Radical Form

√x = x^1/2

LCM of Variables

Take highest powers of each variable.

HCF of Variables

Take lowest common powers; if none common ⇒ 1.

The correct answer is Nagda.

Key Points

• The Banas culture, also known as the Ahar-Banas culture, is a Chalcolithic archaeological culture that flourished in the Banas River valley of southeastern Rajasthan between approximately 3000 BCE and 1500 BCE.
• Gilund: This is a major archaeological site located in the Rajsamand district of Rajasthan. It was a large regional center of the Banas culture and was excavated by B.B. Lal in 1959-60 and later by a joint team from the University of Pennsylvania. Hence, Gilund is an excavated site of the Banas culture.
• Ahar: Located on the banks of the Ahar River near Udaipur, it is the type-site for this culture. Excavations conducted by R.C. Agrawal and H.D. Sankalia revealed a culture rich in copper metallurgy, leading to its ancient name Tambavati. Hence, Ahar is an excavated site of the Banas culture.
• Bagor: Situated on the Kothari River in the Bhilwara district of Rajasthan, Bagor is primarily known as the largest Mesolithic site in India. However, its Phase II (dating to the 2nd millennium BCE) shows significant evidence of Chalcolithic Ahar culture influence and contact. Hence, Bagor is considered an associated excavated site of the Banas culture complex.
• Nagda: Located in the Ujjain district of Madhya Pradesh, Nagda is an important archaeological site belonging to the Malwa culture (specifically the Kayatha-Malwa sequence) in the Chambal valley. It is not part of the Banas culture of Rajasthan. Hence, Nagda is the correct answer as it was not a site of the Banas culture.

Additional Information

• Characteristics of Banas Culture: The culture is distinguished by its unique Black-and-Red Ware (BRW) pottery, often painted with white geometric designs. It co-existed with the Indus Valley Civilization but remained a distinct rural, agropastoral culture.
• Copper Metallurgy: Unlike the Harappans who used bronze extensively, the Ahar-Banas people focused on copper. Excavations at Ahar revealed copper slag and smelting furnaces, indicating that they were pioneers in copper technology in Western India.
• Geographical Spread: The culture was centered in the Mewar region of Rajasthan. Other significant excavated sites include Balathal, Ojiyana, and Marmi. Balathal is particularly famous for having one of the earliest fortified enclosures in the Chalcolithic period.
• Economic Life: The inhabitants practiced agriculture, cultivating crops like wheat, barley, and rice. They also domesticated cattle, sheep, and goats. The presence of terracotta bull figurines suggests that cattle held religious or symbolic importance.
• Malwa Culture (Nagda): The Malwa culture (c. 1700–1200 BCE) followed the Ahar and Kayatha cultures in Central India. Sites like Nagda, Navdatoli, and Eran are known for their beautiful Malwa Ware, which is characterized by a buff or orange slip with black painted designs.

Important Points

• Architecture: Unlike the Harappan burnt bricks, the Ahar-Banas people built their houses using mud-bricks, stone, and wattle-and-daub. Multi-room structures have been discovered at Gilund and Ahar.
• Trade Links: The discovery of lapis lazuli beads and certain ceramic styles suggests that the Banas culture had exchange networks with Harappan settlements in Gujarat and other Chalcolithic groups in Central India.
• Chronological Significance: The Ahar-Banas culture represents an important transition in the Proto-history of India, bridging the gap between the Neolithic/Mesolithic past and the later Iron Age cultures.

The correct answer is Separation of chromatids and reformation of the nuclear envelope.

Key Points

• Anaphase is the third stage of mitosis, characterized by the splitting of the centromeres that hold sister chromatids together. The spindle fibers shorten, pulling the daughter chromosomes toward opposite poles of the cell. This ensures each new cell receives an identical set of genetic material. Hence, the separation of chromatids is a core function of this stage and is correct.
• Telophase is the final stage of mitosis where the chromosomes reach their respective poles and begin to decondense back into chromatin. During this phase, the nuclear envelope reforms around each set of chromosomes using fragments of the parent cell's nuclear membrane. Hence, the reformation of the nuclear envelope is a core function of this stage and is correct.
• The anaphase-telophase transition effectively completes the karyokinesis (nuclear division) process. It moves from the physical movement of DNA to the structural re-establishment of the nucleus.
• Condensation of chromosomes primarily occurs during Prophase to make them manageable for movement. Hence, this statement is incorrect in the context of the anaphase-telophase transition.
• Synthesis of new DNA strands and initiation of DNA replication occur during the S-phase (Synthesis phase) of Interphase, long before mitosis begins. Hence, these statements are incorrect.

Additional Information

• Mitosis was first observed in detail by Walther Flemming in 1882. It is also known as equational division because the number of chromosomes in the daughter cells remains the same as in the parent cell (2n to 2n).
• Prophase: This is the first stage where chromatin fibers coil into chromosomes, the nucleolus disappears, and the mitotic spindle begins to form in the cytoplasm.
• Metaphase: The chromosomes align along the metaphase plate (equatorial plane). This is the best stage to study the morphology and number of chromosomes under a microscope.
• Cytokinesis: Usually following telophase, this is the division of the cytoplasm. In animal cells, it occurs via a cleavage furrow, while in plant cells, it involves the formation of a cell plate.
• Significance: Mitosis is essential for growth, tissue repair, and asexual reproduction in multicellular organisms, maintaining genetic stability across generations.

Important Points

• Regulation: The transition from metaphase to anaphase is regulated by the Anaphase-Promoting Complex (APC/C), which triggers the degradation of securin, allowing separase to break down the cohesin proteins holding chromatids together.
• Microtubule Role: Kinetochore microtubules provide the mechanical force required for chromatid separation, while non-kinetochore microtubules help elongate the cell during the anaphase-telophase transition.
• Organelle Reformation: Besides the nuclear envelope, other organelles like the Endoplasmic Reticulum (ER) and Golgi complex, which disappear during prophase, start to reorganize and reappear during Telophase.
• Ploidy: While the cell briefly contains double the number of chromosomes during anaphase, the subsequent division ensures that each daughter nucleus restores the diploid (2n) or haploid (n) state of the parent cell.

The correct answer is Sharat Chandra Chatterjee – Devdas.

Key Points

• Sharat Chandra Chatterjee was a prominent Bengali novelist and short story writer of the 20th century. He wrote the classic novel Devdas in 1901, although it was published much later in 1917. The story revolves around themes of tragic love, social barriers, and self-destruction. Hence, statement A is correct.
• Anandamath is a celebrated Bengali political novel written by Bankim Chandra Chatterjee, not Rabindranath Tagore. Published in 1882, it is set against the backdrop of the Sannyasi Rebellion and the Famine of Bengal in the late 18th century. Hence, statement B is incorrect.
• Kamayani is an epic poem in Hindi authored by Jaishankar Prasad, published in 1936. It is considered one of the greatest literary works of the Chhayavaadi school of Hindi literature and explores human emotions and the evolution of consciousness through the story of Manu. Hence, statement C is incorrect.
• Madhushala (The House of Wine) is a book of 135 quatrains written by the renowned Hindi poet Harivansh Rai Bachchan, not Munshi Premchand. Published in 1935, it is famous for its lyrical quality and metaphorical use of wine to represent the complexities of life. Hence, statement D is incorrect.

Additional Information

• Rabindranath Tagore:
• He was the first Indian and Asian to win the Nobel Prize in Literature in 1913 for his collection of poems titled Gitanjali.
• His notable works include Gora, The Home and the World (Ghare-Baire), and Chokher Bali. He also composed the national anthems of India and Bangladesh.
• Bankim Chandra Chatterjee:
• Often referred to as the Sahitya Samrat (Emperor of Literature), he is the author of the national song of India, Vande Mataram, which first appeared in his novel Anandamath.
• His other significant works include Durgeshnandini (1865) and Kapalkundala (1866).
• Munshi Premchand:
• Known as the Upanyas Samrat, he was a prolific writer in Hindi and Urdu. His works are characterized by social realism, focusing on the lives of common people and peasants.
• His masterpieces include Godan (1936), Gaban, Karmabhoomi, and the famous short story Idgah.
• Sharat Chandra Chatterjee's Influence:
• His works have been adapted into numerous films across different Indian languages. Devdas alone has been made into movies more than 15 times in languages like Hindi, Bengali, and Telugu.
• Other famous works by him include Parineeta, Pather Dabi, and Srikanta.

Important Points

• Vande Mataram: This song, featured in Anandamath, became a rallying cry for Indian revolutionaries during the Swadeshi Movement and the overall Freedom Struggle against British rule.
• Chhayavaad: This was a romantic movement in Hindi literature (roughly 1918–1938). Jaishankar Prasad, Suryakant Tripathi 'Nirala', Sumitranandan Pant, and Mahadevi Varma are considered the four pillars of this movement.
• Literary Contributions: These authors and their works played a vital role in shaping the cultural and nationalist identity of India during the 19th and 20th centuries.

Given: Seven people K, L, M, N, P, Q and R are sitting around a circular table facing the centre.

Only two people sit between R and N when counted from the left of N.

L sits third to the left of Q.

P sits to the immediate right of Q.

P sits second to the left of R.

M is not an immediate neighbour of L.

Now, third to the right of K = P

Hence, the correct answer is "Option 2".

Shortcut Trick

Total of 3 numbers = 20 × 3 = 60

Sum of given numbers = 13 + 22 = 35

Third number = 60 − 35 = 25

∴ Answer = 25

Alternate Method

Given:

Average of 3 numbers = 20

Two numbers = 13 and 22

Formula used:

Average = Total Sum ÷ Number of terms

Calculation:

⇒ Total sum = Average × Number of terms

⇒ Total sum = 20 × 3 = 60

⇒ Sum of two numbers = 13 + 22 = 35

⇒ Third number = 60 − 35 = 25

∴ The correct answer is 25.

Additional Information

Average Formula

Average = Sum of observations ÷ Number of observations

Total from Average

Total = Average × Number of observations

Missing Value

Unknown value = Total − Sum of known values

Quick Tip

Always convert average into total first for faster solving.

The logic followed here is:

For, UND → SSB

For, QXZ → OCX

Now checking the options using the same pattern:

Option 1) WRK → SWG

Option 2) ZQV → VTR

Option 3) MHV → KMT

Option 4) TBE → QFB

Thus, only MHV → KMT follows the same pattern.

Hence, the correct answer is Option 3.

Shortcut Trick

Ratio = 9 : 5 : 2, Z = 2 parts = 83,000 ⇒ 1 part = 41,500

X = 9 parts = 3,73,500, Y = 5 parts = 2,07,500

X works 6 months full + 6 months half ⇒ effective = 9 months

Y works full 12 months

Ratio = 9×9 : 5×12 : 2×12 = 81 : 60 : 24

Difference (X − Y) = 21 parts ⇒ (21/165) × 88,000 = 11,200

∴ Answer = ₹11,200

Alternate Method

Given:

Ratio of investment = 9 : 5 : 2

Z invests = ₹83,000

Total profit = ₹88,000

Formula used:

Profit ∝ Capital × Time

Calculation:

⇒ Profit ratio = 81 : 60 : 24

⇒ Total ratio = 165

⇒ Difference (X − Y) = 21 parts

⇒ Required difference = (21/165) × 88,000

⇒ = ₹11,200

∴ The correct answer is ₹11,200.

Additional Information

Partnership Formula

Profit share ∝ Capital × Time invested.

Changing Capital

If capital changes, calculate separately for each time period.

Ratio Simplification

Convert into simplest ratio before dividing profit.

Quick Tip

Multiply capital ratio directly with effective time to get profit ratio.

Shortcut Trick

Use identity: a³ + b³ + c³ = 3abc when a + b + c = 0

Here a = (5x − 1), b = (x + 3), c = 2(3x − 4)

Given RHS = 6(5x − 1)(x + 3)(3x − 4) = 3abc

⇒ So a + b + c = 0

⇒ (5x − 1) + (x + 3) + 2(3x − 4) = 0 ⇒ 12x − 6 = 0 ⇒ x = 1/2

∴ Answer = 1/2

Alternate Method

Given:

(5x − 1)³ + (x + 3)³ + 8(3x − 4)³ = 6(5x − 1)(x + 3)(3x − 4)

Concept Used:

Identity: a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca)

Calculation:

⇒ Let a = (5x − 1), b = (x + 3), c = 2(3x − 4)

⇒ Then equation becomes: a³ + b³ + c³ = 3abc

⇒ Using identity ⇒ a + b + c = 0

⇒ (5x − 1) + (x + 3) + 2(3x − 4) = 0

⇒ 5x − 1 + x + 3 + 6x − 8 = 0

⇒ 12x − 6 = 0

⇒ x = 1/2

∴ The correct answer is 1/2.

Additional Information

Cubic Identity

a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca)

Special Case

If a³ + b³ + c³ = 3abc ⇒ a + b + c = 0

Coefficient Adjustment

Match terms like 8(3x − 4)³ = [2(3x − 4)]³

Shortcut Tip

Always try to convert expressions into identity form before expanding.

Given Statements:

All cars are tram.

All cars are rickshaw.

All cars are bus.

The least possible Venn diagram shows:

Conclusions:

(I) All trams are bus

We only know that all cars are inside both trams and buses, but trams may exist outside cars and may not be inside buses.

So this conclusion does not follow.

(II) Some buses are rickshaws

All cars are rickshaws and also all cars are buses.

So the common “cars” part lies inside both buses and rickshaws.

Therefore, some buses are definitely rickshaws.

So, this conclusion follows.

Hence, only conclusion (II) follows.

Hence, the correct answer is "Option 4".

The correct answer is Chennai.

Key Points

• In 2025, the Global AI Conclave, which focused on reinforcing India’s role in safe and trusted artificial intelligence, was hosted in Chennai.
• Hosting Institution: The conclave was led by IIT Madras (specifically the Centre for Responsible AI - CeRAI) in collaboration with the IndiaAI Mission under the Ministry of Electronics and Information Technology (MeitY).
• Key Focus: The event was a strategic "Pre-Summit Event" held on December 10–11, 2025, aimed at translating responsible AI principles into practical governance frameworks.
• Significance: It was described as a preparatory milestone for the India-AI Impact Summit 2026, which is scheduled to take place in New Delhi.
• Notable Proposal: During the conclave, participants explored the establishment of an "AI Safety Commons" for the Global South, emphasizing shared datasets and interoperable governance resources.

Additional Information

• IndiaAI Mission: This is a flagship initiative by the Government of India with a dedicated budget of Rs. 10,372 crore. It focuses on building AI supercomputing infrastructure and providing GPU-based compute power to startups and researchers.
• Global Partnership on Artificial Intelligence (GPAI): India has played a pivotal role as the Lead Chair of GPAI, an international initiative to guide the responsible development of AI. Major summits related to this partnership are frequently held in New Delhi.
• NITI Aayog’s National Strategy for AI: Released in 2018, this strategy outlines India's vision to be a "Garage for AI," focusing on how AI can solve challenges in emerging economies.
• Bletchley Declaration: India is a signatory to this international treaty, which emphasizes AI safety and risk management, particularly concerning frontier AI models that could pose existential risks.
• Digital Personal Data Protection (DPDP) Act, 2023: This Act provides the legal framework for data privacy in India, which is a critical pillar for training AI models ethically and legally.

Important Points

• Airavat: India's dedicated AI supercomputer, which is ranked among the top 100 most powerful systems in the world, is housed at C-DAC, Pune, and supports the IndiaAI Mission.
• Sovereign AI: The conclave highlighted the importance of Sovereign AI, which refers to a country’s ability to build its own AI infrastructure and large language models (LLMs) to ensure data sovereignty and strategic independence.
• Startup Ecosystem: India currently boasts the third-largest startup ecosystem in the world, with a significant number of unicorns specializing in Generative AI and Machine Learning.
• Linguistic Diversity: A unique feature of AI development in India is the focus on multilingual models, such as Bhashini, which aims to bridge the language barrier using voice-to-voice translation in 22 scheduled Indian languages.
• Ethical Guidelines: The 2025 Conclave emphasized the UNESCO recommendations on the Ethics of AI, advocating for transparency, fairness, and accountability in automated decision-making systems.

The correct answer is He/She ceases to be an Indian citizen.

Key Points

• According to Article 9 of the Constitution of India, no person shall be a citizen of India if he or she has voluntarily acquired the citizenship of any foreign state. This provision applies to the acquisition of citizenship before or at the commencement of the Constitution on 26 January 1950.
• For cases occurring after the commencement of the Constitution, Section 9 of the Citizenship Act, 1955 provides the legal framework. It stipulates that any citizen of India who, by naturalization, registration, or otherwise, voluntarily acquires the citizenship of another country shall cease to be a citizen of India. Hence, the statement that he/she ceases to be an Indian citizen is correct.
• India maintains a strict policy of single citizenship. Unlike some Western nations, the Indian legal framework does not permit dual citizenship. If an individual acquires a foreign passport or citizenship, their Indian citizenship is terminated automatically by operation of law.
• The power to regulate the right of citizenship and its termination is vested in the Parliament of India under Article 11 of the Constitution. This ensures that the Union Government has the exclusive authority to determine the status of individuals regarding their national identity.

Additional Information

• Modes of Losing Citizenship:
• Renunciation: A voluntary act where an Indian citizen of full age and capacity makes a declaration renouncing their citizenship. Upon registration of such declaration, the person ceases to be an Indian citizen.
• Termination: This occurs automatically when an Indian citizen voluntarily acquires the citizenship of another country. It is the most common way citizenship is lost in the modern context of migration.
• Deprivation: A compulsory termination of citizenship by the Central Government. This can happen if citizenship was obtained by fraud, if the citizen has shown disloyalty to the Constitution, or if the citizen has been ordinarily resident out of India for seven years continuously.
• Overseas Citizenship of India (OCI):
• Since India does not allow dual citizenship, the government introduced the OCI scheme via the Citizenship (Amendment) Act, 2005.
• An OCI cardholder is a foreign citizen of Indian origin who enjoys certain privileges like a multi-purpose, multiple-entry, lifelong visa for visiting India. However, they do not have the right to vote, hold constitutional posts, or buy agricultural land.

Important Points

• Constitutional Articles (5-11):
• Article 5: Citizenship at the commencement of the Constitution for persons domiciled in India.
• Article 6: Rights of citizenship of certain persons who have migrated to India from Pakistan.
• Article 8: Rights of citizenship of certain persons of Indian origin residing outside India.
• Article 10: Every person who is or is deemed to be a citizen of India shall continue to be such citizen, subject to the provisions of any law made by Parliament.
• Citizenship Act, 1955: This Act is the comprehensive legislation dealing with the acquisition and termination of citizenship after 1950. It has been amended several times, most notably in 1986, 1992, 2003, 2005, 2015, and 2019 to address changing geopolitical and social needs.

The correct answer is Seed Coat.

Key Points

• The edible portion of a pomegranate (Punica granatum) is the Seed Coat, specifically the juicy, fleshy outer layer known as the Sarcotesta.
• While the entire seed is often consumed, it is the succulent aril (the red, juice-filled part) surrounding the hard seed that provides the primary nutritional and flavor value.
• Botanically, the pomegranate fruit is classified as a Balausta, which is a many-celled, many-seeded berry characterized by a leathery exocarp (rind) and an inner structure divided by membranous walls.
• The Seed Coat in pomegranates is unique because it evolves into a fluid-filled tissue designed to attract animals for seed dispersal, unlike many other fruits where the Mesocarp or Endocarp is the edible part.
• The fruit develops from a multicarpellary, inferior ovary, and the edible arils are attached to the Placenta inside the various chambers of the fruit.

Additional Information

• Geographical Context: Pomegranates are widely cultivated in India, Iran, and the Mediterranean region. In India, the state of Maharashtra is the leading producer, contributing significantly to the global supply, followed by Gujarat and Karnataka.
• Common Edible Parts of Other Fruits:
• Mango: The edible part is the Mesocarp.
• Apple/Pear: The edible part is the Fleshy Thalamus (making them "false fruits").
• Coconut: The edible part is the Endosperm (both liquid and solid).
• Litchi: The edible part is the Fleshy Aril.
• Citrus Fruits (Lemon/Orange): The edible parts are the Unicellular Glandular Hairs on the endocarp.
• Nutritional Value: Pomegranates are high in Antioxidants, specifically Punicalagins and Punicic Acid. They are also rich sources of Vitamin C, Vitamin K, and Dietary Fiber.
• Applications: Beyond direct consumption, the Seed Coat juice is used for making Grenadine syrup, wines, and various traditional medicines due to its Anti-inflammatory properties.

Important Points

• Fruit Structure: The pomegranate fruit consists of three main layers: the Exocarp (the tough, red outer skin), the Mesocarp (the white, spongy inner rind), and the Endocarp (the thin membranes that separate the seed clusters). None of these three layers are typically consumed.
• Clarification on Terminology: While the term Aril is commonly used in general literature to describe the red edible part, strictly botanical texts often distinguish it as a Sarcotesta because it originates directly from the integuments of the seed rather than an independent growth from the funiculus.
• Economic Significance: The cultivation of pomegranate has seen a rise in India since the 1990s due to the development of high-yield varieties like Bhagwa and Mridula.
• Health Benefits: Regular consumption is linked to improved Heart Health and the regulation of Blood Pressure, as noted in various Medical Indices and nutritional surveys.

The correct answer is Twelve.

Key Points

• Article 80 of the Constitution of India provides for the composition of the Council of States, commonly known as the Rajya Sabha.
• As per Article 80(1)(a), the President of India is authorized to nominate Twelve members to the Council of States. Hence, the statement regarding the nomination of twelve members is correct.
• These nominated members must be individuals having special knowledge or practical experience in respect of matters such as Literature, Science, Art, and Social Service as mentioned in Article 80(3). Hence, the criteria for nomination are strictly defined by the Constitution.
• The primary purpose of this provision is to allow eminent persons who have excelled in their respective fields to contribute to the legislative process without undergoing the process of a formal Election.
• Apart from these 12 nominated members, the Rajya Sabha consists of not more than 238 representatives of the States and of the Union Territories, making the total maximum strength 250.

Additional Information

• Qualifications and Tenure:
• To become a member of the Rajya Sabha, a person must be a citizen of India and must not be less than 30 years of Age.
• The Rajya Sabha is a Permanent House and is not subject to dissolution; however, one-third of its members retire every Second Year.
• The Term of an individual member of the Rajya Sabha is 6 years.
• Election Process:
• The representatives of the States are elected by the elected members of the Legislative Assemblies of the respective states.
• The election is held in accordance with the system of Proportional Representation by means of the Single Transferable Vote.
• The Fourth Schedule of the Constitution deals with the allocation of seats in the Rajya Sabha to the States and Union Territories.
• Presiding Officers:
• The Vice-President of India serves as the Ex-officio Chairman of the Rajya Sabha.
• The House also elects a Deputy Chairman from among its members to perform duties in the absence of the Chairman.

Important Points

• Nominated Members' Rights: While nominated members enjoy almost all the powers and privileges of elected members, they cannot vote in the Election of the President of India as per Article 54. However, they have the right to vote in the election of the Vice-President.
• Historical Context: The provision for nomination was inspired by the Irish Constitution, aiming to bring specialized talent into the Parliament.
• Special Powers: The Rajya Sabha holds unique powers, such as the authority to pass a resolution under Article 249 allowing Parliament to legislate on matters in the State List, and under Article 312 for the creation of All India Services.
• Current Strength: Currently, the Rajya Sabha has 245 members, which includes 233 elected members and 12 nominated members.

Shortcut Trick

Distance from center to chord = radius of smaller circle = 15

Half chord = √(17² − 15²)

= √(289 − 225) = √64 = 8

Chord length = 2 × 8 = 16

∴ Answer = 16 cm

Alternate Method

Given:

Radius of larger circle = 17 cm

Radius of smaller circle = 15 cm

Formula used:

Length of chord = 2 × √(R² − d²)

Calculation:

⇒ Length of chord = 2 × √(17² − 15²)

⇒ = 2 × √(289 − 225)

⇒ = 2 × √64

⇒ = 2 × 8 = 16 cm

∴ The correct answer is 16 cm.

Additional Information

Chord Formula

Length of chord = 2√(R² − d²)

Tangent Concept

If chord is tangent to inner circle, distance from center = inner radius.

Right Triangle

Radius, distance, and half chord form a right triangle.

Quick Tip

Always use Pythagoras to find half chord first.

The logic followed here is:

So, 'TIV 22' will replace the question mark in the given series.

Hence, the correct answer is "Option 3".

The logic followed here is:

So, 'UFP 40' will replace the question mark in the given series.

Hence, the correct answer is "Option 4".

Given number: 6134527

Logic: Add 1 to each odd digit and add 2 to each even digit

Original number: 6 1 3 4 5 2 7

New number: 8 2 4 6 6 4 8

Now, First digit = 8

Last digit = 8

Sum = 8 + 8 = 16

Hence, the correct answer is Option 4.