The Correct answer is Prime Minister, Lok Sabha Speaker, Leader of the Opposition, Chief Justice of India, and an eminent jurist nominated by the President.

Key Points

• The Lokpal is an anti-corruption authority or ombudsman in India that addresses complaints against public officials, including the Prime Minister, Ministers, and Members of Parliament.
• The selection committee for the Lokpal is composed of the following members:
• Prime Minister - Chairperson of the selection committee.
• Lok Sabha Speaker - Represents the Parliament in the selection process.
• Leader of the Opposition - Ensures bipartisan participation in the selection process.
• Chief Justice of India - Represents the judiciary in the committee.
• An eminent jurist - Nominated by the President of India based on the recommendations of the other members of the committee.
• This composition ensures a diverse and balanced representation from the executive, legislative, and judicial branches of the government.
• The inclusion of an eminent jurist ensures that the committee benefits from legal expertise during the decision-making process.
• The Lokpal Act, 2013, which governs the establishment of the Lokpal, mandates this composition to ensure transparency and accountability.

Additional Information

• Prime Minister, Chief Justice of India, Leader of the Opposition, Vice-President, and a Cabinet Minister
• This option is incorrect because the Vice-President and a Cabinet Minister are not part of the Lokpal selection committee.
• The committee's composition is specifically defined in the Lokpal and Lokayuktas Act, 2013, and does not include these positions.
• Prime Minister, Home Minister, Chief Justice of India, Attorney General, and Leader of the Opposition
• The Attorney General and the Home Minister are not members of the Lokpal selection committee.
• This option wrongly includes these officials, which is not aligned with the provisions of the Lokpal Act.
• President, Prime Minister, Chief Election Commissioner, Lok Sabha Speaker, and a Jurist
• The President and the Chief Election Commissioner are not part of the Lokpal selection committee.
• While the President is responsible for appointing the Lokpal members, the selection process is carried out by the committee defined under the Lokpal Act.

The Correct answer is Absolute poverty uses a fixed threshold; relative poverty compares individuals within a society.

Key Points

• Absolute poverty refers to a condition where individuals lack the basic necessities of life such as food, clothing, and shelter. It is measured using a fixed threshold, such as the international poverty line defined by the World Bank, which is currently set at $2.15 per person per day (as of 2022).
• This threshold is globally standardized, making it applicable across different countries and regions, irrespective of societal variations.
• Relative poverty, on the other hand, considers an individual’s economic status in comparison to others within a specific society or community. It is not defined by a fixed amount but instead evaluates the income distribution within a population.
• Relative poverty highlights income inequality and is often used to assess disparities in wealth and living standards within a particular country or region.
• While absolute poverty focuses on universal needs and survival, relative poverty sheds light on social equity and economic gaps between individuals.
• For example, in developed countries, relative poverty is often measured as a percentage of median income (e.g., 50% or 60% of median household income).

Additional Information

• Absolute poverty is based on income inequality; relative poverty is not.
• This option is incorrect because absolute poverty is not directly related to income inequality. It focuses on whether individuals meet basic needs irrespective of societal income disparities.
• Relative poverty, however, is closely linked to income inequality as it evaluates individuals' economic status relative to others in their society.
• Absolute poverty is subjective; relative poverty is objective.
• This option is incorrect because the measurement of absolute poverty is objective, relying on fixed global standards like the poverty line.
• Relative poverty involves subjective societal comparisons but often uses objective data, such as median income, for calculation.
• There is no difference between the two.
• This option is incorrect as there are clear differences between absolute poverty and relative poverty. Absolute poverty relies on universal thresholds, while relative poverty focuses on societal comparisons.

Given series: (Left) 7 & 9 ^ # 1 * 5 ≺ 2 6 = 4 Δ 3 $ @ 8 (Right)

According to the question,

Required condition: Odd Number - Symbol - Not Even Number (i.e., it can be an odd number or another symbol).

(Left) 7 & 9 ^ # 1 * 5 ≺ 2 6 = 4 Δ 3 $ @ 8 (Right)

Symbols that satisfy the condition: & , ^ , * , $ (7 & 9 ,9 ^ # , 1 * 5 and 3 $ @ )

Thus, there are more than three such symbols that are immediately preceded by a number but NOT immediately followed by an even number.

Hence, "Option 3" is the correct answer.

The Correct answer is Ctrl + V

Key Points

• Ctrl + V is the standard keyboard shortcut used to paste copied content in most operating systems and applications.
• The shortcut is universally recognized and works in Windows, macOS (using Command + V), Linux, and other platforms.
• When content is copied to the clipboard using Ctrl + C (copy) or Ctrl + X (cut), the Ctrl + V command allows you to paste it into the desired location, such as a text editor, document, or web browser.
• This shortcut improves efficiency and saves time by eliminating the need for navigating menus to paste content.
• It is widely used in applications such as Microsoft Office, Google Docs, Notepad, and web-based tools.
• Keyboard shortcuts like Ctrl + V are essential for enhancing productivity in tasks involving repetitive actions.
• The key combination is part of a group of universal shortcuts, including Ctrl + C (Copy), Ctrl + X (Cut), Ctrl + Z (Undo), and Ctrl + Y (Redo).

Additional Information

• Ctrl + B
• Ctrl + B is a shortcut used to bold text in text editors and word processing applications.
• This combination is commonly used in programs like Microsoft Word, Google Docs, and email platforms.
• It does not perform paste operations and is specifically for text formatting.
• Ctrl + K
• Ctrl + K is used to insert or edit hyperlinks in documents and web-based applications.
• This shortcut is widely utilized in programs like Microsoft Word, Excel, Google Docs, and email clients for creating links.
• Ctrl + P
• Ctrl + P is the shortcut used to open the print dialog in most applications.
• This shortcut is helpful for initiating printing tasks in programs such as Adobe Acrobat, Microsoft Word, and web browsers.

The Correct answer is Article 165.

Key Points

• Article 165 of the Indian Constitution provides for the appointment of the Advocate General for the State.
• The Advocate General is the highest law officer in a state and is responsible for giving advice to the state government on legal matters.
• He/she is appointed by the Governor of the State and holds office during the pleasure of the Governor.
• The Advocate General must be a person qualified to be appointed as a Judge of a High Court, which means he/she should have been an advocate of a High Court for at least 10 years or should have held a judicial office for a similar period.
• The duties of the Advocate General include:
• Giving advice on legal matters to the state government.
• Performing legal duties assigned by the Governor.
• Representing the state government in the High Court or the Supreme Court in cases where the state is a party.
• The Advocate General has the right to speak and take part in the proceedings of the state legislature, but he/she does not have the right to vote.

Additional Information

• Article 164
• Article 164 of the Constitution pertains to the appointment of Chief Ministers and other Ministers for the state by the Governor.
• It also mentions the collective responsibility of the Council of Ministers to the state legislature.
• Article 162
• Article 162 defines the extent of executive power of the state government.
• It states that the executive power of the state extends to matters on which the state legislature has the power to make laws.
• Article 163
• Article 163 deals with the Council of Ministers to aid and advise the Governor of a state.
• The Governor is required to act according to the advice of the Council of Ministers, except in cases where the Constitution requires him to act at his discretion.

The Correct answer is Restrictions on freedom of expression.

Key Points

• The Rowlatt Act, officially known as the Anarchical and Revolutionary Crimes Act of 1919, was enacted by the British government in India to suppress political dissent and revolutionary activities.
• It allowed the government to arrest individuals suspected of revolutionary activities without providing a warrant and detain them without trial for an indefinite period, which was a direct violation of basic human rights.
• One of the provisions included the censorship of the press, aimed at curbing the dissemination of anti-government information and revolutionary ideas.
• The act gave authorities the power to arrest political leaders and activists without requiring a warrant, which undermined legal safeguards for individuals.
• The provision of "arrest without trial" was one of the most controversial aspects, as it denied individuals the right to a fair trial, violating the principles of justice.
• However, the act did not explicitly include any clause that imposed "restrictions on freedom of expression". Although censorship of the press indirectly affected freedom of expression, the act did not target this right specifically as a provision.
• This act faced widespread protests across India, including the famous Jallianwala Bagh massacre, which occurred as a result of public agitation against the act.

Additional Information

• Censorship of press
• The Rowlatt Act imposed censorship on the press to suppress revolutionary ideas and anti-government sentiments.
• Under this provision, newspapers and publications were monitored, and any content deemed inflammatory or against British rule was censored.
• This restriction was aimed at controlling public opinion and preventing the spread of nationalist ideas.
• Arrest of political leaders without warrants
• One of the most criticized provisions of the Rowlatt Act was the authority given to the police to arrest political leaders and activists without requiring a warrant.
• This provision enabled arbitrary arrests, targeting prominent leaders involved in the freedom struggle.
• Arrest without trial
• The act allowed detention without trial, meaning individuals could be imprisoned indefinitely without being formally charged or given a chance to defend themselves in court.
• This provision violated fundamental judicial principles and sparked widespread outrage among Indians.

The least possible Venn diagram for the given statements is as shown below :

Conclusions:

(I) No letter is a post → Does not follow (As all letters are message, some messages are emails and no email is a post. As no direct relation is given between letters and post, therefore is false.)

(II) Some emails are letters → Does not follow (As all letters are message and some messages are emails. So it is possible but not definite.)

∴ Here, Neither conclusion (I) nor (II) follows.​

Hence, the correct answer is "Option 3".

The Correct answer is Article 237.

Key Points

• Article 237 of the Indian Constitution empowers the Governor to extend the provisions relating to the conditions of service of judicial officers to certain magistrates.
• This article allows the Governor to declare that the provisions of Part VI, Chapter VI of the Constitution (dealing with subordinate courts) shall apply to any magistrate or judicial officer.
• The provisions are intended to ensure that judicial services are uniform and consistent across the country.
• This enables administrative and procedural improvements in the functioning of magistrates, ensuring they conform to judicial standards.
• The decision under Article 237 allows for better integration of judicial services into the wider legal framework of the Constitution.
• It is significant for maintaining judicial independence and ensuring fair administration of justice.
• Article 237 is part of the broader constitutional framework aimed at enhancing the efficiency and accountability of judicial officers.

Additional Information

• Article 233
• Article 233 deals with the appointment of District Judges.
• It specifies that appointments, posting, and promotions of District Judges are made by the Governor of the state in consultation with the High Court.
• This article ensures judicial independence by involving the judiciary in the appointment process.
• Article 142
• Article 142 empowers the Supreme Court of India to pass any decree or order necessary for doing complete justice in any matter.
• This article is used as a tool for judicial activism, enabling the Supreme Court to deliver justice in extraordinary circumstances.
• It is often invoked for enforcing orders that go beyond the limits of statutory law.
• Article 234
• Article 234 deals with the recruitment of persons to the judicial service other than District Judges.
• It specifies that such appointments are made by the Governor of the state in consultation with the State Public Service Commission and the High Court.
• This ensures proper procedures in the recruitment process for subordinate judicial officers.

Given: A, B, L, M, S, T and Z are sitting around a circular table facing the centre.

1) S sits third to the right of Z.

2) S sits to the immediate right of M. 

3) M sits third to the left of T. 

4 ) Only one person sits between B and L when counted from the left of L.

5) A is not an immediate neighbour of M.

Thus, three people sit between A and L when counted from the right of A.

Hence, "Option 4" is the correct answer.

The Correct answer is Intense solar heating.

Key Points

• During summer, the Thar Desert experiences extreme heat due to its geographical location and climatic conditions.
• The intense solar heating causes the temperature to rise significantly, leading to the formation of a low-pressure zone over the region.
• Low-pressure zones occur because the heated air becomes lighter and rises, creating a pressure difference.
• This phenomenon is common in arid and semi-arid regions such as the Thar Desert, which is part of the larger tropical desert climate.
• The low-pressure zone over the Thar Desert plays a critical role in influencing the Indian monsoon winds, as it attracts moisture-laden winds from surrounding regions.
• The intense solar heating during summer also contributes to the harsh and dry conditions that define the desert's climate.

Additional Information

• Western Disturbances
• Western disturbances are extra-tropical storms that originate in the Mediterranean region.
• They primarily affect the northern regions of India during the winter months, bringing rainfall and sometimes snow.
• These systems are not responsible for the low-pressure zones in the Thar Desert during summer.
• Frontal Cyclones
• Frontal cyclones are associated with the meeting of cold and warm air masses, forming fronts.
• They are more common in temperate regions and are not a characteristic feature of the Thar Desert's climatic conditions.
• Coastal Humidity
• Coastal humidity is associated with regions near large water bodies where high moisture content is present in the air.
• The Thar Desert is a landlocked area and does not experience coastal humidity.

The logic followed here is:

KORJ is related to DHKC

And,

IMPH is related to BFIA

​Similarly,

NRUM is related to

Hence, "Option 3" is the correct answer.

The Correct answer is Gravitational Force.

Key Points

• Gravitational Force is a fundamental force that acts without physical contact.
• It governs the motion of celestial bodies such as planets, stars, and moons.
• This force is responsible for holding objects in their orbits, such as the Earth revolving around the Sun or the Moon orbiting the Earth.
• The force is described by Newton's Law of Universal Gravitation, which states that every particle in the universe attracts every other particle with a force proportional to their masses and inversely proportional to the square of the distance between them.
• Gravitational force is always attractive and acts along the line connecting the centers of two masses.
• It plays a critical role in the formation and structure of galaxies, solar systems, and the universe itself.
• Gravitational force also governs phenomena such as tides, which are caused by the gravitational pull of the Moon and the Sun on Earth's oceans.
• It is one of the weakest forces in nature but has an infinite range, making it significant on a cosmic scale.

Additional Information

• Spring Force
• Spring Force is a contact force that occurs in objects like springs when they are stretched or compressed.
• The force exerted by a spring is governed by Hooke's Law, which states that the force is proportional to the displacement.
• This force is used in various applications, such as shock absorbers, mechanical clocks, and measuring devices like spring balances.
• Friction
• Friction is a contact force that opposes the relative motion between two surfaces in contact.
• It is critical in everyday activities like walking, driving, and holding objects.
• However, friction cannot act at a distance and is not responsible for celestial body motion.
• Tension
• Tension is a force that arises in strings, ropes, or cables when they are pulled taut.
• This is a contact force and is commonly seen in structures like bridges or when lifting objects using ropes.
• It does not act at a distance and is not involved in the motion of celestial bodies.

The correct answer is 0.176.

Key Points

• The decadal growth rate refers to the percentage increase in the population of a country over a decade (10 years).
• According to the Census of India 2011, the decadal growth rate of India's population during the period 2001-2011 was approximately 17.6%, which is equivalent to 0.176 in decimal form.
• This growth rate was a decrease compared to the previous decade (1991-2001), which had a growth rate of 21.54%.
• The decline in the growth rate indicates progress in population control measures, literacy rates, and awareness campaigns.
• The Census of India is conducted every 10 years and provides detailed data on the demographics, socio-economic factors, and population trends.
• India's population during the 2011 Census was recorded at 1.21 billion, making it the second-most populous country in the world after China.
• The decadal growth rate is a significant indicator for understanding population dynamics and planning for resources, infrastructure, and development.

Additional Information

• Census of India: The Census of India is conducted under the guidance of the Registrar General and Census Commissioner of India, appointed by the Government of India under the Census Act, 1948.
• Population Control Measures: The reduction in the growth rate is attributed to measures such as increased family planning programs, better access to healthcare, and a rise in education levels.
• Socio-economic Impact: A slower growth rate provides an opportunity for better resource allocation, economic development, and improved living standards.

Given number: 6597423

According to the question, 

The sum of all the even digits in the new number thus formed → 8 + 6 + 4 = 18

Hence, the correct answer is "Option 1".

The Correct answer is Manipuri.

Key Points

• Manipuri is one of the eight classical dance forms of India.
• It originates from the state of Manipur in northeastern India.
• The dance is deeply rooted in Vaishnavism and has a strong devotional aspect, often focusing on the love story of Radha and Krishna.
• Jagoi refers to the soft and graceful movement aspect of the dance, which emphasizes the lyrical quality.
• Cholom is the vigorous and rhythmic drum dance performed by male dancers, showcasing a more dynamic style.
• The costumes in Manipuri dance are unique and elaborate, often featuring bright colors, flowing skirts, and intricate designs.
• Manipuri dance is known for its subtle expressions, fluid movements, and spiritual themes, making it distinct from other Indian classical dances.
• The dance is performed in various styles, including Raas Leela (dramatic representation of Krishna's life) and Thang-Ta (martial art dance).

Additional Information

• Kuchipudi
• Kuchipudi is a classical dance form from Andhra Pradesh.
• It is known for its blend of dance, music, and drama.
• Performances often involve dialogues and narratives, making it distinct from purely rhythmic dance forms.
• The dance is performed on themes from Hindu mythology, particularly stories of Lord Krishna.
• Kathak
• Kathak is a classical dance form originating in North India.
• It is characterized by intricate footwork, spins, and storytelling, often using ghungroos (ankle bells).
• The themes typically revolve around epics like the Mahabharata and Ramayana or devotional stories of Lord Krishna.
• Odissi
• Odissi is a classical dance form from the state of Odisha.
• It is known for its graceful movements, sculpturesque poses, and deep spiritual essence.
• Odissi primarily depicts stories of Lord Jagannath and themes from Hindu mythology.

The correct answer is A team from Norway.

Key Points

• The ISSF World Cup is a prestigious international shooting competition organized by the International Shooting Sport Federation (ISSF).
• The 10 m Air Rifle Mixed Team event is a discipline where pairs of shooters (one male and one female) compete together for combined scores.
• In the 2025 ISSF World Cup, a team from Norway emerged victorious in the gold medal match against the Indian duo Rudrankksh Patil and Arya Borse.
• Norwegian shooters are known for their precision and consistency, having a strong tradition in shooting sports.
• The victory demonstrates the team's excellent preparation and competitive edge in international competitions.
• The ISSF World Cup serves as a platform for shooters to gain recognition and improve their world rankings.
• Such events also contribute to the development of shooting sports by promoting global talent and competition.

Additional Information

• A team from Germany
• Germany has a rich history in shooting sports and frequently performs well in international competitions.
• German shooters are renowned for their technical expertise and innovative training methods.
• Despite their strong presence, they did not win the gold medal in this specific event at the 2025 ISSF World Cup.
• A team from the USA
• The USA is another country with a significant influence in shooting sports.
• American shooters are known for their consistent performances and often dominate international tournaments.
• However, in this particular event, they did not secure the gold medal at the 2025 ISSF World Cup.
• A team from China
• China has been a powerhouse in shooting sports, excelling in various ISSF events.
• Chinese shooters are recognized for their discipline and rigorous training regimes.
• Although they are often contenders for gold, they did not win the title in this event at the 2025 ISSF World Cup.

Given: F, G, H, J, K and L live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it, number 2 and so on till the topmost floor is numbered 6.

1. F lives on an odd numbered floor.

2. Only two people live between F and L.

3. J lives immediately above L.

As there is no possible position for J in case 2, therefore is eliminated.

4) H lives immediately below K. 

As there is no possible position for K in case 1, therefore is eliminated.

After positioning K and H only one person is left which will be occupied by the only person left i.e. G.

Thus, two people live between G and K.

Hence, the correct answer is "Option 3".

Given:

Mr. X starts from Point L and drives 5 km towards the east.

He then takes a right turn, drives 6 km, turns right and drives 9 km.

He then takes a right turn and drives 2 km, turns left, drives 4 km.

He takes a final right turn, drives 4 km and stops at Point O.

Thus, Mr. X should drive 8 km (9 km + 4 km - 5 km) in the east direction in order to reach Point L again.​

Hence, "Option 3" is the correct answer.

Shortcut Trick

Let the total cost price for Anand be X.

Successive transactions: X × (152 ÷ 100) × (56 ÷ 100) = 4,788.

X × 1.52 × 0.56 = 4,788 ⇒ X = 4,788 ÷ 0.8512 = 5,625.

Original cost = Total cost − Repair expenses = 5,625 − 127 = 5,498.

∴ The correct answer is ₹5,498.

Alternate Method

Given → Final SP = ₹4,788, Loss% = 44%, Profit% = 52%, Repair = ₹127. Formulas: CP = SP × 100 ÷ (100 − Loss%) | CP = SP × 100 ÷ (100 + Profit%)

⇒ Bharath CP (Anand SP) = 4,788 × 100 ÷ (100 − 44) = 4,788 × 100 ÷ 56 = 8,550. ⇒ Anand Total CP = 8,550 × 100 ÷ (100 + 52) = 8,550 × 100 ÷ 152 = 5,625. ⇒ Original Cost = Total CP − Repair Expenses = 5,625 − 127 = 5,498.

∴ The correct answer is ₹5,498.

Additional Information

Total Cost Price

The total cost price includes the purchasing price plus any overhead expenses like repairs, transport, or labor.

Successive Transactions

When an item is sold multiple times, the SP of one becomes the CP for the next. Final SP = Initial CP × (100 ± P1)% × (100 ± P2)%.

The Correct answer is Theoretical basis for immunology.

Key Points

• Paul Ehrlich was awarded the Nobel Prize in Medicine in 1908 for his pioneering work in the field of immunology.
• He developed the side-chain theory, which explained how antitoxins (antibodies) are produced by the body to neutralize toxins.
• This work laid the theoretical foundation for understanding the immune system and how it responds to pathogens.
• Ehrlich also introduced the concept of a "magic bullet,” which referred to a targeted therapy that could treat diseases without harming the body.
• His discoveries were crucial for the development of immunotherapy, vaccines, and antibody-based treatments that are widely used in modern medicine.
• In addition to immunology, Ehrlich also contributed to the development of the first effective treatment for syphilis using a compound known as Salvarsan (arsphenamine).
• The Nobel Prize in 1908 was shared between Paul Ehrlich and Ilya Mechnikov, recognizing their contributions to immunology, with Mechnikov focusing on phagocytosis.

Additional Information

• Antibacterial effect of sulpha drugs
• The antibacterial effects of sulpha drugs were discovered in the 1930s, several years after Ehrlich's Nobel Prize.
• Sulpha drugs were the first effective antibiotics, and they marked the beginning of the modern era of antibacterial treatment.
• These drugs work by inhibiting the growth of bacteria, and they were widely used during World War II.
• Penicillin for treating infections
• Penicillin was discovered by Alexander Fleming in 1928, and its use as an antibiotic was developed later by Howard Florey and Ernst Boris Chain.
• This discovery occurred much later than Paul Ehrlich’s work and revolutionized the treatment of bacterial infections.
• Use of azodyes in textiles
• Although Paul Ehrlich worked with dyes, his Nobel Prize was not related to the use of azodyes in textiles.
• Azodyes are synthetic dyes used to color textiles and other materials, and they were significant in the chemical industry.

Shortcut Trick

If x + 1/x = k, then x² + 1/x² = k² − 2 and x⁴ + 1/x⁴ = (k² − 2)² − 2.

Given k = √5, first calculate the square term: (√5)² − 2 = 5 − 2 = 3.

Now calculate the fourth power term by squaring the result again: 3² − 2 = 9 − 2 = 7.

∴ The correct answer is 7.

Alternate Method

Given: x + 1/x = √5, where x > 0.

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

Step-by-step Calculation:

⇒ (x + 1/x) = √5

Squaring both sides:

⇒ (x + 1/x)² = (√5)²

⇒ x² + (1/x)² + 2 × x × (1/x) = 5

⇒ x² + 1/x² + 2 = 5

⇒ x² + 1/x² = 5 − 2 = 3

Again, Squaring both sides to find the fourth power:

⇒ (x² + 1/x²)² = 3²

⇒ (x²)² + (1/x²)² + 2 × x² × (1/x²) = 9

⇒ x⁴ + 1/x⁴ + 2 = 9

⇒ x⁴ + 1/x⁴ = 9 − 2 = 7

∴ The correct answer is 7.

Additional Information

Cube Identity

If x + 1/x = k, then the cubic value is given by x³ + 1/x³ = k³ − 3k.

Difference Identity

If x − 1/x = k, then the square value is x² + 1/x² = k² + 2.

Higher Power (x⁵ + 1/x⁵)

To find the fifth power, use the formula: x⁵ + 1/x⁵ = (x² + 1/x²)(x³ + 1/x³) − (x + 1/x).

Conversion Rule

If x + 1/x = k, then x − 1/x = √(k² − 4) for x > 1.

The logic followed here is:

ARCE - CARE - ECRA

And,

POLE - LPOE - ELOP

 

​Similarly,

Option 3) WORM - RWOM - MROW

Hence, "Option 3" is the correct answer.

Shortcut Trick

Combine the ratios by making the common term Q equal.

P : Q = 15 : 4 and Q : R = 3 : 1.

Multiplying first ratio by 3 and second by 4: P : Q : R = 45 : 12 : 4.

Total ratio parts = 45 + 12 + 4 = 61 units.

Given 61 units = 12,200 ⇒ 1 unit = 12,200 ÷ 61 = 200.

Share of R = 4 units = 4 × 200 = 800.

∴ The correct answer is 800.

Alternate Method

Given: Total Profit = 12,200, P : Q = 15 : 4, Q : R = 3 : 1.

Formula: Combined Ratio P : Q : R = (P × Q₂) : (Q₁ × Q₂) : (Q₁ × R).

⇒ Step 1: Ratio P : Q = 15 : 4 and Q : R = 3 : 1.

⇒ Step 2: To equate Q, P : Q : R = (15 × 3) : (4 × 3) : (4 × 1) = 45 : 12 : 4.

⇒ Step 3: Total sum of ratios = 45 + 12 + 4 = 61.

⇒ Step 4: Share of R = (Ratio of R ÷ Total Ratio) × Total Profit.

⇒ Step 5: Share of R = (4 ÷ 61) × 12,200 = 4 × 200 = 800.

∴ The correct answer is 800.

Additional Information

Ratio Balancing

When combining two ratios like A:B and B:C, multiply the first ratio by the B-value of the second, and the second ratio by the B-value of the first.

Profit Distribution

In a partnership or distribution, if the time period is constant, the Profit Share is directly proportional to the Investment Ratio.

Shortcut Trick

To form a triangle, we need to select any 3 non-collinear points.

Since no three vertices of a polygon are collinear, any selection of 3 vertices out of 10 will form a unique triangle.

Number of triangles = ¹⁰C₃ = (10 × 9 × 8) ÷ (3 × 2 × 1) = 120.

∴ The correct answer is 120 triangles.

Alternate Method

Given:

Number of sides of the polygon (n) = 10

Number of vertices of the polygon = 10

Formula Used:

The number of ways to select r objects from n distinct objects is given by the combination formula:

ⁿC_r = n! ÷ [r! × (n − r)!]

To form a triangle, we need exactly 3 vertices.

Calculations:

A polygon with 10 sides has exactly 10 vertices.

To form a triangle, we need to select any 3 vertices out of these 10 vertices.

Since no three vertices of a polygon are collinear, every unique combination of 3 vertices forms a unique triangle.

Therefore, the number of triangles that can be drawn is:

⇒ Number of triangles = ¹⁰C₃

⇒ Number of triangles = 10! ÷ [3! × (10 − 3)!]

⇒ Number of triangles = 10! ÷ [3! × 7!]

⇒ Number of triangles = (10 × 9 × 8) ÷ (3 × 2 × 1)

⇒ Number of triangles = 720 ÷ 6

⇒ Number of triangles = 120

Let us analyze why the other options are incorrect:

⇒ Option (2) 150: This value is incorrect because the maximum possible combinations of selecting 3 vertices from 10 is mathematically limited to 120.

⇒ Option (3) 125: This value is incorrect as it does not satisfy the combination formula ¹⁰C₃.

⇒ Option (4) 115: This value is incorrect because it is less than the actual number of possible triangles.

∴ The correct answer is 120 triangles.

Additional Information

Number of Diagonals in a Polygon

The number of diagonals in a polygon of n sides is given by the formula: n(n − 3) ÷ 2.

Triangles with No Common Sides

The number of triangles formed by joining the vertices of an n-sided polygon such that no side of the triangle is a side of the polygon is given by: ⁿC₃ − n − n(n − 4).

Triangles with Exactly One Common Side

The number of triangles that share exactly one side with an n-sided polygon is given by: n(n − 4).

Triangles with Exactly Two Common Sides

The number of triangles that share exactly two sides with an n-sided polygon is equal to the number of vertices, which is n.

Given:

0.$\overline{583}$

Formula used:

If x = 0.$\overline{abc}$, then x = $\dfrac{abc}{999}$

Calculation:

x = 0.$\overline{583}$

⇒ x = $\dfrac{583}{999}$

⇒ x = $\dfrac{583}{999}$ (already in simplest form)

∴ 0.$\overline{583}$ = $\dfrac{583}{999}$

The correct answer is Four Deputy Governors.

Key Points

• The Reserve Bank of India Act, 1934 governs the structure and functioning of the Reserve Bank of India (RBI).
• According to this Act, the RBI can have a maximum of four Deputy Governors at any point in time.
• The RBI's top management consists of the Governor and Deputy Governors, who play a critical role in decision-making and policy formulation.
• The Deputy Governors are responsible for overseeing various departments of the RBI, such as monetary policy, banking regulation, financial markets, and supervision.
• Of the four Deputy Governors, two are typically promoted from within the RBI, one is an economist or academic, and one is usually a commercial banker.
• The appointment of Deputy Governors is made by the Government of India, and they typically serve a term of three years, which may be extended.
• The presence of four Deputy Governors ensures that the RBI can efficiently handle its diverse and complex functions, including currency management, financial inclusion, and monetary stability.

Additional Information

• Reserve Bank of India Act, 1934
• This Act provides the foundational framework for the establishment, organization, and operation of the Reserve Bank of India.
• The Act outlines the objectives of the RBI, including ensuring monetary stability, regulating credit, and fostering economic growth.
• The Act also specifies the structure of the RBI, including the roles of the Governor, Deputy Governors, and other officials.
• Governor of the RBI
• The Governor is the chief executive officer of the RBI and is responsible for its overall functioning.
• They are appointed by the Government of India for a term of three years, which may be renewed.
• The Governor's role includes formulating and implementing monetary policy to achieve objectives like inflation control and financial stability.

Shortcut Trick

Speed of current = (Downstream speed − Upstream speed) ÷ 2

Speed of current = (47 − 19) ÷ 2

Speed of current = 28 ÷ 2 = 14 km/hr

∴ The correct answer is 14 km/hr.

Alternate Method

Given:

Downstream Speed (u) = 47 km/hr

Upstream Speed (v) = 19 km/hr

Formula Used:

Let Speed of Boat in Still Water be x and Speed of Current be y.

x + y = u (Downstream)

x − y = v (Upstream)

Calculations:

⇒ x + y = 47

⇒ x − y = 19

Subtracting the second equation from the first:

⇒ (x + y) − (x − y) = 47 − 19

⇒ 2y = 28

⇒ y = 28 ÷ 2

⇒ y = 14 km/hr

∴ The correct answer is 14 km/hr.

Additional Information

Speed of Boat in Still Water

It is the average of downstream and upstream speeds: x = (u + v) ÷ 2.

Relative Speed in Streams

Downstream speed is always greater than upstream speed because the current supports the boat's motion.

The Correct answer is 422 m.

Key Points

• IIT Madras launched its Hyperloop Test Track in 2025.
• The length of the test track is 422 meters, designed to study and develop hyperloop technologies.
• The hyperloop concept is a futuristic transportation system involving high-speed travel in a vacuum tube.
• India's first hyperloop test track was initiated by IIT Madras, marking significant progress in transportation innovation.
• Hyperloop systems aim to achieve speeds exceeding 1000 km/h, making them faster than airplanes over short distances.
• The test track allows researchers to experiment with concepts like magnetic levitation, vacuum sealing, and energy efficiency.
• It is part of India's effort to contribute to global hyperloop research and development, strengthening its position in cutting-edge technology.
• The project aligns with India's vision of sustainable and futuristic infrastructure for enhanced connectivity and reduced carbon emissions.

Additional Information

• 10 km
• Hyperloop test tracks of 10 km are typically designed for full-scale testing but are not currently implemented by IIT Madras.
• Such test tracks have been discussed or planned by other organizations globally for demonstrating long-distance capabilities.
• 100 m
• A 100-meter test track is often used for initial small-scale experiments, but IIT Madras opted for a larger track to study advanced hyperloop dynamics.
• 1 km
• A 1-kilometer hyperloop track is considered suitable for intermediate testing phases but does not match the actual length chosen by IIT Madras.

Shortcut Trick

Convert 20% to fraction: 20% = 1/5.

Ratio equation: (1/5) × First = (3/4) × Second.

Cross-multiply: First / Second = (3/4) × (5/1) = 15/4.

∴ The correct answer is 15 : 4.

Alternate Method

Given:

Let the first number be x and the second number be y.

Condition: 20% of x = 3/4 of y

Calculations:

⇒ (20/100) × x = (3/4) × y

⇒ (1/5) × x = (3/4) × y

⇒ x/y = (3/4) ÷ (1/5)

⇒ x/y = (3/4) × 5

⇒ x/y = 15/4

⇒ x : y = 15 : 4

∴ The correct answer is 15 : 4.

Additional Information

Percentage to Fraction Conversion

To convert a percentage to a fraction, divide by 100. Example: 20% = 20/100 = 1/5.

Ratio and Proportion

If a × x = b × y, then the ratio x : y is equal to b : a.

Successive Percentage

The net change for two successive percentage changes a% and b% is given by [a + b + (a × b)/100]%.

The Correct answer is Hockey Jharkhand.

Key Points

• Hockey Jharkhand emerged as the defending champions at the 15th Hockey India Senior Women National Championship 2025.
• They secured the championship title in the previous edition of the tournament held in 2024, showcasing their dominance in women's hockey.
• The team is known for its exceptional players, many of whom hail from the tribal regions of Jharkhand, an area known for producing talented hockey players.
• Jharkhand has a strong hockey culture and infrastructure, which has contributed to the development of skilled players and consistent performance in national-level tournaments.
• The team’s success is also attributed to the state government's support and initiatives in promoting hockey, especially among women.
• Hockey Jharkhand's victory highlights the growing prominence of women’s hockey in India, with teams from various states striving for excellence.

Additional Information

• Hockey Haryana
• Hockey Haryana is one of the top-performing teams in national hockey tournaments, with a strong track record in both men’s and women’s categories.
• The state has produced numerous players for the Indian national hockey team, thanks to its excellent training facilities and grassroots programs.
• Despite their strong performances, they were not the defending champions in the 15th edition of the tournament.
• Hockey Punjab
• Hockey Punjab is renowned for its contributions to Indian hockey, producing legendary players over the years.
• The state has a deep-rooted hockey culture, often excelling in men’s hockey but also showing significant improvement in women’s hockey in recent years.
• However, they did not win the championship title in 2024, making them ineligible as defending champions in 2025.
• Hockey Maharashtra
• Hockey Maharashtra has been striving to improve its performance in national tournaments, focusing on youth development and training programs.
• The team has shown potential but has yet to achieve consistent success at the national level, including the Hockey India Senior Women National Championship.

The logic followed here is:

Given: # : PKN :: TOR : %

Option 1) # = KPJ, % = YOJ → KPJ : PKN :: TOR : YOJ

Option 2) # = KFI, % = YTW → KFI : PKN :: TOR : YTW

​

Option 3) # = KFL, % = YPG → KFL : PKN :: TOR : YPG

Option 4) # = LJY, % = YVX → LJY : PKN :: TOR : YVW

Hence, "Option 2" is the correct answer.

Shortcut Trick

Use the direct percentage less formula: [r ÷ (100 + r)] × 100

Here, r = 17%

Required % = [17 ÷ (100 + 17)] × 100 = (17 ÷ 117) × 100

⇒ 1700 ÷ 117 ≈ 14.529%

∴ The correct answer is 14.53%.

Alternate Method

Given: A's salary is 17% more than B's salary.

Formula Used: Percentage Decrease = (Difference ÷ Higher Value) × 100

⇒ Let B's salary = 100

⇒ A's salary = 100 + 17% of 100 = 117

⇒ Difference = 117 − 100 = 17

⇒ Percentage by which B is less than A = (Difference ÷ A's salary) × 100

⇒ Required Percentage = (17 ÷ 117) × 100

⇒ Required Percentage = 1700 ÷ 117 = 14.5299...

⇒ Rounded to two decimal places = 14.53%

∴ The correct answer is 14.53%.

Additional Information

Base Change Property

When one value is x% more than another, the second is [x/(100+x)] × 100% less than the first.

Percentage Decrease Formula

Percentage Decrease = [(Initial Value − Final Value) ÷ Initial Value] × 100.

Successive Percentage Change

If a value changes by a% and then b%, net change is [a + b + (ab/100)]%.

Given: P, A, R, T, L and Y live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it, number 2 and so on till the topmost floor is numbered 6.

1) No one lives below R.

2) Only A lives above T.

3) R lives on the lowermost floor.

4) Only two people live between R and P.

5) Y lives on an even numbered floor.

After positioning Y only one person is left which will be occupied by the only person left i.e. L.

Thus, two people live between L and A.

Hence, the correct answer is "Option 3".

The logic followed here is:

Hence, "Option 2" is the correct answer.

Shortcut Trick

Net efficiency = Efficiency of Filling Pipe − Efficiency of Emptying Pipe

Total Capacity (LCM of 12, 21) = 84 units

Efficiency: Filling = 84 ÷ 12 = 7; Emptying = 84 ÷ 21 = 4

Net Efficiency = 7 − 4 = 3 units/hour

Time for half tank = (84 ÷ 2) ÷ 3 = 42 ÷ 3 = 14 hours

∴ The correct answer is 14 hours.

Alternate Method

Given: Filling time = 12 hours, Emptying time = 21 hours.

Formula Used: Time Taken = Total Work / Combined Efficiency

⇒ Total Capacity of tank = LCM(12, 21) = 84 units

⇒ Combined efficiency of both pipes = 7 − 4 = 3 units/hour

⇒ Target capacity (Half tank) = 84 ÷ 2 = 42 units

⇒ Time taken = 42 ÷ 3 = 14 hours

∴ The correct answer is 14 hours.

Additional Information

Net Work Done

When one pipe fills (rate x) and another empties (rate y), the net rate is (1/x − 1/y) per hour.

Pipes & Cisterns Sign Convention

Inlet pipes contribute positive efficiency while outlet (leak) pipes contribute negative efficiency.

Capacity vs Time

Time taken is inversely proportional to efficiency for a constant volume.

Shortcut Trick

Expenditure % = 100% − Savings % = 100% − 46% = 54%

Expenditure = 54% of ₹6,150

54/100 × 6150 = 0.54 × 6150 = ₹3,321

∴ The correct answer is ₹3,321.

Alternate Method

Given:

Monthly Salary = ₹6,150

Savings Percentage = 46%

Formula Used:

Expenditure = Salary − Savings

⇒ Savings Amount = 46% of 6150

⇒ Savings Amount = (46 ÷ 100) × 6150 = 0.46 × 6150 = ₹2,829

⇒ Expenditure = Total Salary − Savings Amount

⇒ Expenditure = 6150 − 2829 = ₹3,321

∴ The correct answer is ₹3,321.

Additional Information

Percentage Expenditure

Expenditure % = (Expenditure ÷ Total Income) × 100. It represents the portion of income spent.

Income-Savings-Expenditure Relation

Income is always the sum of Expenditure and Savings (Income = E + S). If one increases while income is constant, the other must decrease.

Successive Changes

If a salary increases by x% and then decreases by x%, the net change is always a decrease of x²/100%.

The logic followed here is:

Option 1) AH – CK

Option 2) KR – NU

​

Option 3) NU – PX

Option 4) EL – GO

​

Thus, out of all 'KR – NU' is the odd one out.

Hence, "Option 2" is the correct answer.

Shortcut Trick

Ratio of 1^st : 2^nd : 3^rd numbers = 4 : 2 : 1.

Total sum = 154 × 3 = 462.

Sum of ratio parts = 4 + 2 + 1 = 7 units.

7 units = 462 ⇒ 1 unit = 66.

First number = 4 units = 4 × 66 = 264.

∴ The correct answer is 264.

Alternate Method

Given: Average of three numbers = 154.

Formula Used: Sum = Average × Total Count of Numbers.

Let the third number be x.

⇒ Second number = 2 × x = 2x.

⇒ First number = 2 × 2x = 4x.

⇒ Sum of the three numbers = x + 2x + 4x = 7x.

⇒ Total Sum = 154 × 3 = 462.

⇒ 7x = 462

⇒ x = 462 ÷ 7 = 66.

⇒ First number = 4x = 4 × 66 = 264.

∴ The correct answer is 264.

Additional Information

Average or Arithmetic Mean

The average of n terms is the sum of terms divided by n. Sum = Average × n.

Ratio Scaling

When numbers are multiples of each other, assigning the smallest value as 1 unit helps in establishing a quick ratio chain.

Linear Equations in One Variable

Expressing all unknown values in terms of a single variable (x) simplifies the calculation of the sum or product.

The Correct answer is Desktop icons are only visual shortcuts and not the actual application files.

Key Points

• Desktop icons represent shortcuts to applications, files, or folders. They are essentially links to the actual application files stored elsewhere on the computer, such as in the "Program Files" directory or other system locations.
• Removing or deleting desktop icons does not affect the underlying application files or their functionality. The applications can still be accessed via the Start Menu, Taskbar, or their installation directories.
• The desktop in the Windows operating system serves as a user-friendly area for quick access but does not store the actual programs or files.
• Even if desktop icons are removed, users can utilize other navigation methods, such as the Windows Search functionality, to locate and run applications.
• This design ensures that the operating system remains functional and avoids dependency on the desktop for accessing programs.
• Windows OS uses a centralized file system, where application files are maintained in specific directories, ensuring their integrity and accessibility regardless of the presence of desktop icons.

Additional Information

• Desktop icons are system-critical files required to run applications
• This statement is incorrect because desktop icons are not system-critical files. They are merely shortcuts and do not impact the functionality or operation of application files.
• The actual application files are stored in designated system directories, such as "Program Files" or "AppData".
• Windows OS duplicates all application files in the desktop directory
• This statement is incorrect because Windows does not duplicate application files in the desktop directory. Desktop shortcuts are simple links pointing to the original files, not duplicate copies.
• Duplicating application files on the desktop would consume unnecessary storage space and cause inefficiencies.
• The desktop is a virtual memory area where applications run in the background
• This statement is incorrect because the desktop is not a virtual memory area. Virtual memory refers to the system's use of disk space to supplement RAM, while the desktop is a graphical user interface for file and application shortcuts.
• Applications run in the background using system resources, not the desktop area.

The Correct answer is Rajasthan.

Key Points

• Maand is a traditional form of folk music that originated in the state of Rajasthan, India.
• It is primarily associated with classical Rajasthani music and is a unique amalgamation of both classical and folk music.
• The Maand style is known for its melodious and soulful tunes, which were historically performed in the royal courts of Rajasthan.
• This form of music is often used to narrate stories of valour, love, and folklore, especially tales related to the Rajput kings.
• Famous Maand songs include "Kesariya Balam" and "Banko Chhiyo", which are widely acclaimed in Indian music traditions.
• The instruments commonly used in Maand music are sitar, sarangi, dholak, tabla, and harmonium, which complement the vocal renditions.
• Maand music holds a special place in Rajasthani culture and is an integral part of various festivals and celebrations in the state.

Additional Information

• Jharkhand
• Jharkhand has its own rich tradition of folk music, such as Jhumar, Domkach, and Paika, which are popular in tribal communities.
• These forms of music are often performed during festivals, weddings, and other cultural events.
• Uttar Pradesh
• Uttar Pradesh is renowned for its Thumri, Dadra, and Kajri, which are classical and semi-classical forms of music.
• It is also the birthplace of the Banaras Gharana, a prominent school of Indian classical music.
• Maharashtra
• Maharashtra is famous for its Lavani, a traditional form of folk music and dance.
• Lavani is characterized by its rhythmic beats and expressive lyrics, often performed to the accompaniment of the dholki.

The Correct answer is Anora

Key Points

• Anora won the Best Picture award at the 2025 Oscars.
• This film is recognized for its unique storytelling, exceptional cinematography, and powerful performances by its cast.
• Anora explores themes of identity, resilience, and transformation, making it resonate with audiences globally.
• The movie was directed by an acclaimed filmmaker known for their distinctive artistic vision and ability to create emotionally impactful narratives.
• Anora gained widespread critical acclaim and was celebrated for its innovative techniques and visual depth.
• The film stood out among other contenders due to its compelling plot and ability to connect deeply with viewers.
• Anora's win continues the tradition of recognizing cinematic works that push boundaries and contribute significantly to the art of filmmaking.

Additional Information

• Wicked
• Wicked is based on the popular Broadway musical of the same name, which is a prequel to The Wizard of Oz.
• The film explores the untold story of the Wicked Witch of the West and the Good Witch.
• It is known for its fantasy elements, vibrant visuals, and strong musical performances.
• Conclave
• Conclave is a political thriller set in the backdrop of the election of a new pope.
• The movie delves into the intricacies of Vatican politics and the secrets behind the papal elections.
• It is praised for its suspenseful narrative and exploration of power dynamics.
• The Brutalist
• The Brutalist is a historical drama that follows the journey of a Hungarian architect.
• The film portrays themes of immigration, ambition, and loss.
• It is notable for its stark visual style and portrayal of architectural marvels.

Given: (Left) 325 503 158 391 144 (Right)

According to the question:

So,

Second digit of the highest number → 503 → 0

First digit of the lowest number → 144 → 1

Thus, if the second digit of the highest number is added to the first digit of the lowest number then the resultant will be → 0 + 1 → 1

Hence, the correct answer is "Option 4".

The Correct answer is West Himalaya.

Key Points

• Valley of Flowers National Park is located in the West Himalaya region in the state of Uttarakhand, India.
• It is renowned for its stunning meadows of endemic alpine flowers and is a part of the Nanda Devi Biosphere Reserve.
• The Valley of Flowers is situated at an altitude ranging between 3,200 meters to 6,675 meters above sea level.
• It is a UNESCO World Heritage Site and is known for its extraordinary biodiversity, including rare and endangered species of flora and fauna.
• This park is home to several medicinal plants such as Aconitum heterophyllum and Dactylorhiza hatagirea.
• It is also famous for its association with Indian mythology, believed to be the place where Hanuman found the 'Sanjeevani Booti' to revive Lakshman.
• The park is a popular destination for trekkers and nature enthusiasts, and the route to the Valley of Flowers passes through Ghangaria village.
• It was discovered in 1931 by British mountaineers Frank S. Smythe and R. L. Holdsworth.

Additional Information

• Dhauladhar
• The Dhauladhar range is a part of the Lesser Himalayas located in Himachal Pradesh, India.
• It is known for its steep slopes and is a popular destination for trekking and mountaineering.
• Places like Triund and Mcleodganj are situated near this range.
• Pir Panjal
• The Pir Panjal range is the largest range of the Lesser Himalayas and is located in Jammu and Kashmir, Himachal Pradesh, and Uttarakhand.
• It is famous for the Banihal Pass and the Jawahar Tunnel, which connect Jammu to the Kashmir Valley.
• Karakoram
• The Karakoram range is located in the northernmost part of India and spans the borders of India, Pakistan, and China.
• It is home to K2, the second-highest peak in the world, and the Siachen Glacier, the highest battleground on Earth.

The Correct answer is Soviet dissident movement.

Key Points

• Benjamin Nathans is a historian and academic who authored the book "To the Success of Our Hopeless Cause."
• The book extensively explores the Soviet dissident movement, which arose during the Cold War period as a resistance to the oppressive and authoritarian policies of the Soviet Union.
• The movement consisted of activists, intellectuals, and ordinary citizens who sought to challenge censorship, political repression, and human rights violations under Soviet rule.
• Nathans delves into the lives and struggles of Soviet dissidents, highlighting their efforts to promote freedom of expression, democracy, and social justice.
• The book provides a comprehensive analysis of how these dissidents used tools like samizdat (self-published literature) and underground networks to communicate their ideas and spread awareness.
• The work is widely regarded as a scholarly masterpiece, contributing significantly to the understanding of Soviet history and the broader global human rights movement.
• Due to its detailed research and narrative, the book earned the Pulitzer Prize for General Nonfiction, recognizing its excellence in shedding light on a critical aspect of 20th-century history.

Additional Information

• Rise of AI
• The rise of AI refers to the rapid advancements in artificial intelligence technologies, which have transformed fields like healthcare, transportation, and finance.
• AI encompasses areas such as machine learning, natural language processing, and robotics.
• It is not related to the Soviet dissident movement or Benjamin Nathans' work.
• Environmental collapse
• This term addresses the degradation of ecosystems due to factors like climate change, deforestation, and pollution.
• Although a critical global issue, it is unrelated to the historical and political context of the Soviet Union explored by Benjamin Nathans.
• American healthcare crisis
• This topic revolves around the challenges in the U.S. healthcare system, such as rising costs, accessibility, and inefficiencies.
• While significant, it is not the focus of the book "To the Success of Our Hopeless Cause."

Shortcut Trick

The Mode is simply the observation that appears most frequently in the data set.

Count the occurrences: 20 appears 3 times, while 31, 33, and 35 appear 2 times each.

All other numbers (22, 25, 27, 29, 32, 34) appear only once.

Since 20 has the highest frequency, it is the mode.

∴ The correct answer is 20.

Alternate Method

Given: Observations = 20, 20, 20, 35, 29, 34, 25, 33, 35, 32, 33, 27, 22, 31, 31.

Formula: Mode = Value with the maximum frequency (f_max).

Let us tabulate the frequency of each observation:

⇒ Frequency of 20 = 3

⇒ Frequency of 31 = 2

⇒ Frequency of 33 = 2

⇒ Frequency of 35 = 2

⇒ Frequency of 22, 25, 27, 29, 32, 34 = 1 each

⇒ Comparing the frequencies, 3 is the highest value.

⇒ The observation corresponding to frequency 3 is 20.

∴ The correct answer is 20.

Additional Information

Mean (Arithmetic Average)

The sum of all observations divided by the total number of observations. Formula: Mean = (Σx_i) ÷ n.

Median

The middle value of a data set when arranged in ascending or descending order. For 15 observations, it is the 8^th term.

Empirical Relationship

For a moderately skewed distribution, the relationship is: Mode = 3 × Median − 2 × Mean.

Types of Mode

A data set can be unimodal (one mode), bimodal (two modes), or multimodal (more than two modes).

Decoding signs:

Given: 81 S 28 R 39 S (98 Q 7) = ?

81 S 28 R 39 S (98 Q 7) = ? ⇒ 81 + 28 - 39 + (98 ÷ 7) = ?

⇒ 81 + 28 - 39 + (98 ÷ 7) = ?

⇒ 81 + 28 + 14 - 39 = ?

⇒ 123 - 39 = ?

⇒ 84 = ?

Hence, "Option 4" is the correct answer.

The Correct answer is Linux Ubuntu.

Key Points

• Linux Ubuntu is an open-source desktop operating system based on the Linux kernel.
• It is developed and maintained by Canonical Ltd., a company founded in 2004.
• The operating system is freely available for everyone and can be modified and redistributed due to its open-source nature.
• Ubuntu offers a wide range of customization options and supports a vast number of software packages, making it suitable for both personal and professional use.
• This operating system is widely used for servers, development purposes, and as a desktop OS for general users.
• Ubuntu comes with a graphical user interface (GUI) and is known for its user-friendly features and robust security.
• It has several distributions, such as Ubuntu Desktop, Ubuntu Server, and Ubuntu Core, which cater to different user needs.
• Ubuntu's long-term support (LTS) versions provide updates and support for a span of five years, ensuring stability for users.
• Popular applications such as LibreOffice, Mozilla Firefox, and Thunderbird come pre-installed in Ubuntu.
• Ubuntu is used worldwide and is appreciated for its performance, security, and community support.

Additional Information

• Windows 11
• Windows 11 is a proprietary operating system developed by Microsoft Corporation.
• It is a successor to Windows 10 and was officially released on October 5, 2021.
• Windows 11 features a redesigned interface, improved performance, and multitasking capabilities.
• It does not qualify as open-source software because its source code is not freely available or modifiable.
• macOS
• macOS is a proprietary operating system developed by Apple Inc.
• It is designed for Apple's Macintosh computers and is known for its seamless integration with Apple hardware and software.
• macOS is a closed-source operating system, meaning its source code is not accessible or modifiable by the public.
• Android
• Android is an open-source operating system primarily designed for mobile devices.
• It is developed by Google and is based on the Linux kernel.
• Although Android is open-source, it is not typically considered a desktop operating system.

Shortcut Trick

For any standard cubic equation ax³ + bx² + cx + d = 0, the sum of the products of the roots taken two at a time is given by the formula c ÷ a.

Here, the given equation is x³ − 3x² + 4x − 12 = 0.

Comparing the coefficients, we have a = 1 and c = 4.

Sum of products taken two at a time = 4 ÷ 1 = 4.

∴ The correct answer is 4.

Alternate Method

Given:

The cubic equation is x³ − 3x² + 4x − 12 = 0.

Formula Used:

If α, β, and γ are the roots of the cubic equation ax³ + bx² + cx + d = 0, then:

The sum of the products of the roots taken two at a time is αβ + βγ + γα = c ÷ a.

Calculations:

By comparing x³ − 3x² + 4x − 12 = 0 with ax³ + bx² + cx + d = 0, we identify:

⇒ a = 1

⇒ b = −3

⇒ c = 4

⇒ d = −12

⇒ Sum of the products taken two at a time = c ÷ a

⇒ Sum of the products = 4 ÷ 1 = 4

∴ The correct answer is 4.

Additional Information

Sum of roots of a cubic equation

For a cubic equation ax³ + bx² + cx + d = 0, the sum of the roots (α + β + γ) is given by −b/a.

Product of roots of a cubic equation

For a cubic equation ax³ + bx² + cx + d = 0, the product of the roots (α×β×γ) is given by −d/a.

Roots of quadratic equation

For a quadratic equation ax² + bx + c = 0, the sum of roots is −b/a and the product of roots is c/a.

The Correct answer is New Delhi.

Key Points

• The International Conference on Carbon Markets Prakriti 2025 was held on 24-25 February 2025 in New Delhi, the capital city of India.
• New Delhi is a hub for national and international conferences, being the seat of the Indian government and home to key institutions and organizations.
• This conference focused on discussions related to carbon markets, a mechanism aimed at reducing greenhouse gas emissions through tradeable permits and credits.
• Carbon markets play a crucial role in achieving global targets set by the Paris Agreement to combat climate change.
• New Delhi has hosted several environmental and climate-related events due to its strategic importance and the presence of institutions like the Ministry of Environment, Forest and Climate Change and NITI Aayog.
• The event brought together policymakers, experts, and stakeholders to discuss strategies for creating and strengthening sustainable carbon markets.
• This aligns with India's commitment to achieving net-zero emissions by 2070, as stated in international forums such as COP26.
• New Delhi's infrastructure, connectivity, and availability of resources make it an ideal location for such high-level conferences.

Additional Information

• Mumbai
• Mumbai is the financial capital of India and a major hub for business and commerce.
• It is home to the headquarters of several multinational corporations, banks, and the Bombay Stock Exchange.
• While Mumbai hosts many corporate and financial conferences, environmental events like the Prakriti 2025 are less frequent here.
• Mumbai is also known for its proximity to the Arabian Sea and its challenges related to rising sea levels due to climate change.
• Chennai
• Chennai is a major industrial hub in southern India and is known for its automobile and IT industries.
• The city has hosted environmental conferences, particularly those focusing on coastal management and disaster resilience.
• Chennai faces challenges related to water scarcity and urban flooding, making it an important location for climate-related discussions.
• Kolkata
• Kolkata is an eastern Indian city known for its cultural heritage and intellectual contributions.
• The city has hosted conferences on sustainability and urban planning, particularly in the context of its riverine ecosystem and proximity to the Sundarbans.
• Kolkata faces environmental challenges such as air pollution and water management, making it a participant in discussions on carbon markets.

Shortcut Trick

Use the algebraic identity: (a + b)² − (a − b)² = 4ab.

Substitute the given values: 70² − 208 = 4ab.

4900 − 208 = 4692.

ab = 4692 ÷ 4 = 1173.

∴ The correct answer is 1173.

Alternate Method

Given:

Sum of numbers (a + b) = 70

Square of difference (a − b)² = 208

Formula Used:

(a + b)² = a² + b² + 2ab

(a − b)² = a² + b² − 2ab

Subtracting the two equations gives: (a + b)² − (a − b)² = 4ab

Calculations:

⇒ a + b = 70

⇒ Square both sides: (a + b)² = 70² = 4900

⇒ We know: (a − b)² = 208

⇒ Using the identity: (a + b)² − (a − b)² = 4ab

⇒ 4900 − 208 = 4ab

⇒ 4692 = 4ab

⇒ ab = 4692 ÷ 4

⇒ ab = 1173

∴ The correct answer is 1173.

Additional Information

Square of Sum Identity

(a + b)² = a² + b² + 2ab. This calculates the area of a square with side (a+b).

Square of Difference Identity

(a − b)² = a² + b² − 2ab. It represents the squared distance between two numbers.

Combined Identity for Product

ab = [(a + b)² − (a − b)²] ÷ 4. This is a direct way to find the product if sum and difference are known.

Sum of Squares

a² + b² = [(a + b)² + (a − b)²] ÷ 2. This is useful for finding the sum of individual squares.

The logic followed here is:

Hence, "Option 4" is the correct answer.

The logic followed here is:

72 is related to 9 ⇒ 72 ÷ 8 = 9 

And,

24 is related to 3 ⇒ 24 ÷ 8 = 3

Similarly,

64 is related to ⇒ 64 ÷ 8 = 8

Hence, "Option 1" is the correct answer.

Shortcut Trick

One-third of number + 10 = 65

One-third of number = 65 − 10 = 55

Original number = 55 × 3 = 165

Sum of digits = 1 + 6 + 5 = 12

∴ The correct answer is 12.

Alternate Method

Given: Result after increasing one-third of a number by 10 is 65.

Formula Used: Linear equation in one variable.

Let the original number be x.

⇒ (1/3) × x + 10 = 65

⇒ x/3 = 65 − 10

⇒ x/3 = 55

⇒ x = 55 × 3

⇒ x = 165

Sum of digits of 165:

⇒ 1 + 6 + 5 = 12

∴ The correct answer is 12.

Additional Information

Linear Equations

Equations of the form ax + b = c are solved by isolating the variable using inverse operations (subtraction first, then multiplication/division).

Sum of Digits

The sum of the digits of a number is used in divisibility rules; for example, a number is divisible by 3 if the sum of its digits is divisible by 3.

Fraction Manipulation

To find the whole from a fraction, multiply the fractional value by the reciprocal of the fraction.

Shortcut Trick

In an isosceles triangle, the two base angles are always equal.

Base Angle = (180° − Vertex Angle) ÷ 2

Base Angle = (180° − 44°) ÷ 2

Base Angle = 136° ÷ 2 = 68°

∴ The correct answer is 68° and 68°.

Alternate Method

Given: The vertex angle of an isosceles triangle is 44°.

Formula Used: The sum of all interior angles of a triangle is 180°.

⇒ Let the measure of each base angle be x.

⇒ In an isosceles triangle, the angles opposite to the equal sides are equal.

⇒ Sum of angles = Vertex angle + Base angle 1 + Base angle 2

⇒ 180° = 44° + x + x

⇒ 180° = 44° + 2x

⇒ 2x = 180° − 44°

⇒ 2x = 136°

⇒ x = 136° ÷ 2 = 68°

∴ The correct answer is 68° and 68°.

Additional Information

Isosceles Triangle Theorem

If two sides of a triangle are congruent, then the angles opposite those sides are congruent (equal).

Angle Sum Property

The sum of the measures of the interior angles of any triangle is always 180°.

Equilateral Triangle

A triangle where all three sides are equal, resulting in all three angles being equal to 60°.

Shortcut Trick

When a right triangle is rotated about one of its perpendicular sides, that side becomes the height (h) and the other perpendicular side becomes the radius (r).

Rotation about 9 cm side ⇒ Height (h) = 9 cm and Radius (r) = 12 cm.

Volume of cone = (1/3) × π × r² × h = (1/3) × π × 12 × 12 × 9.

Volume = π × 144 × 3 = 432π cm³.

∴ The correct answer is 432π cm³.

Alternate Method

Given:

Sides of the right triangle = 9 cm, 12 cm, and 15 cm (Hypotenuse).

Rotation axis = 9 cm side.

Formula Used:

Volume of a Cone (V) = (1/3)πr²h

Calculations:

⇒ Radius (r) of the cone = 12 cm

⇒ Height (h) of the cone = 9 cm

⇒ Volume = (1/3) × π × (12)² × 9

⇒ Volume = (1/3) × π × 144 × 9

⇒ Volume = π × 144 × 3

⇒ Volume = 432π cm³

∴ The correct answer is 432π cm³.

Additional Information

Rotation about the other side

If rotated about the 12 cm side, then h = 12 cm and r = 9 cm. Volume = (1/3)π(9)²(12) = 324π cm³.

Slant Height of Cone

The hypotenuse of the right triangle always acts as the slant height (l) of the generated cone. l = √(r² + h²).

Surface Area of Cone

Curved Surface Area (CSA) = πrl and Total Surface Area (TSA) = πr(l + r).

The Correct answer is .xlsx

Key Points

• The .xlsx format is the default file format used in newer versions of MS Excel, such as Excel 2019 and later.
• .xlsx is based on the Office Open XML standard, which is a more efficient and secure file format compared to older formats.
• This format is designed to store structured data, including formulas, formatting, charts, and macros, in a compact and easily accessible manner.
• It supports advanced features like conditional formatting, data validation, and multi-sheet workbooks.
• The .xlsx format is also compatible with other software tools, allowing seamless data exchange and interoperability.
• Compared to older formats like .xls, it offers improved data compression, reducing file size without compromising data integrity.
• The adoption of the .xlsx format aligns with Microsoft's focus on enhancing performance and security in its applications.

Additional Information

• .xls
• .xls is the older file format used in earlier versions of MS Excel (up to Excel 2003).
• This format is based on the Binary Interchange File Format (BIFF), which has limited capabilities compared to .xlsx.
• It lacks support for advanced features such as enhanced graphics, larger datasets, and improved security.
• .csv
• The .csv format stands for Comma-Separated Values and is used for storing tabular data in plain text.
• It is ideal for simple data exchange between applications but does not support formulas, formatting, or multiple sheets.
• This format is widely used for data import/export but is not a default format in MS Excel.
• .pdf
• .pdf stands for Portable Document Format and is primarily used for sharing documents in a fixed layout.
• While MS Excel allows saving workbooks as .pdf, this format is not designed for editing or storing spreadsheet data.
• .pdf is more suitable for presentation purposes rather than active data manipulation.

Shortcut Trick

Ratio of students = 12 : 18 = 2 : 3.

Using the weighted average method: [(2 × 70) + (3 × 64)] ÷ (2 + 3)

⇒ (140 + 192) ÷ 5 = 332 ÷ 5 = 66.4.

∴ The correct answer is 66.4.

Alternate Method

Given:

Total students in the class = 30.

Number of first group (n₁) = 12 students, Average score (A₁) = 70.

Number of second group (n₂) = 30 − 12 = 18 students, Average score (A₂) = 64.

Calculations:

⇒ Total score of 12 students = 12 × 70 = 840.

⇒ Total score of remaining 18 students = 18 × 64 = 1152.

⇒ Total score of the entire class = 840 + 1152 = 1992.

⇒ Average score of the class = 1992 ÷ 30.

⇒ Average score of the class = 66.4.

∴ The correct answer is 66.4.

Additional Information

Combined Average Formula

The combined average of multiple groups is calculated as A = (n₁A₁ + n₂A₂ + ... + n_kA_k) ÷ (n₁ + n₂ + ... + n_k).

Deviation Method (Assumed Mean)

Pick an assumed average (a), then New Average = a + (Total Deviation ÷ Total Number). For this problem, if a = 64, deviation = [12 × (70 − 64)] ÷ 30 = 72 ÷ 30 = 2.4. So, 64 + 2.4 = 66.4.

Weighted Average Principle

When the size of groups is different, the group average with more members will pull the overall class average closer to its value.

The Correct answer is Imposition of heavy duties on Indian exports to Britain.

Key Points

• The British colonial policies imposed heavy duties and tariffs on Indian textile exports to Britain, making Indian goods less competitive in the British market.
• These discriminatory trade practices were designed to promote the British textile industry at the expense of the Indian textile industry.
• The imposition of high tariffs led to a significant decline in Indian textile exports, which were once renowned globally for their quality, craftsmanship, and uniqueness.
• Indian weavers and artisans faced severe hardships due to reduced demand for their goods, resulting in widespread unemployment and economic distress.
• The policy also forced Indian consumers to buy British-manufactured goods, which were imported into India without significant tariffs, further benefiting the British economy.
• This exploitation contributed to the deindustrialization of India during the colonial period, as traditional industries like textiles were deliberately undermined.
• The adverse impact of these policies on India's economy highlighted the exploitative nature of British colonial rule and the need for economic independence.

Additional Information

• Equal tariffs on imports and exports
• This option is incorrect because the British did not impose equal tariffs. They deliberately imposed unequal and discriminatory tariffs to favor their own industries.
• Free trade within India
• While free trade within India might sound beneficial, under British rule, this concept was manipulated to serve British economic interests rather than support Indian industries.
• Indian manufacturers faced competition from cheap British imports, which were often dumped in the Indian market.
• Export subsidies
• The British did not provide export subsidies for Indian textiles. Instead, they imposed restrictions and high duties to suppress Indian exports and promote British products.

Given: Seven people, A, B, L, M, N, S, and T are sitting in a row, facing north.

1) Only five people sit between T and A.

2) N sits to the immediate left of A.

3) Only one person sits between N and L.

4 ) M sits at some place to the left of S but at some place to the right of B. 

Thus, M sits third from the left end of the line.

Hence, "Option 1" is the correct answer.

According to the given information,

Thus, 'down' is coded as 'wk'.

Hence, "Option 3" is the correct answer.

The Correct answer is Ranji Trophy.

Key Points

• The Ranji Trophy is a prestigious domestic cricket tournament in India.
• It was established in the year 1934 and is named after Ranjitsinhji Vibhaji Jadeja, the famous Indian cricketer who played for England.
• The tournament is conducted by the Board of Control for Cricket in India (BCCI).
• The Ranji Trophy follows a first-class cricket format, which is played over multiple days.
• Teams representing various Indian states and cricket associations participate in the tournament.
• Vidarbha has been a strong contender in recent years and has won the Ranji Trophy in 2018 and 2019.
• Winning the Ranji Trophy is considered a stepping stone for players aiming to represent India in international cricket.
• The 2025 tournament win by Vidarbha highlights their continued excellence in domestic cricket.

Additional Information

• Vijay Hazare Trophy
• The Vijay Hazare Trophy is a domestic one-day cricket tournament in India.
• It was named after the legendary Indian cricketer Vijay Hazare.
• The tournament is played in a limited-overs format (50 overs per side).
• It provides a platform for players to showcase their skills in limited-overs cricket.
• Syed Mushtaq Ali Trophy
• The Syed Mushtaq Ali Trophy is a domestic T20 cricket tournament in India.
• It is named after the famous Indian cricketer Syed Mushtaq Ali.
• This tournament allows players to demonstrate their abilities in the shortest format of the game.
• Indian Premier League (IPL)
• The IPL is a globally popular franchise-based T20 cricket league hosted in India.
• It involves teams owned by private franchises and features top cricket players from around the world.
• The league is known for its high entertainment value and significant financial rewards.

The Correct answer is Rhinoviruses only infect the upper respiratory tract.

Key Points

• Rhinoviruses are the primary cause of the common cold and are responsible for more than 50% of cases.
• These viruses preferentially infect the upper respiratory tract, such as the nasal passages and throat.
• The upper respiratory tract provides a more suitable environment for rhinoviruses because of its lower temperature (about 33°C), which is optimal for their replication.
• The lower respiratory tract, including the lungs and alveoli, generally has a higher temperature (around 37°C), which is less conducive for rhinovirus survival and replication.
• Rhinoviruses lack mechanisms to effectively invade deeper tissues like the lungs or lower respiratory tract.
• Infections caused by rhinoviruses are typically mild and self-limiting, targeting the mucosal surfaces of the upper respiratory tract.
• Other viruses, such as influenza or respiratory syncytial virus (RSV), are more likely to cause lower respiratory tract infections.

Additional Information

• The virus is destroyed in the alveoli
• The alveoli are small air sacs in the lungs that are involved in oxygen exchange. While certain viruses may struggle to survive in this environment, this is not the primary reason the common cold is rarely a lower respiratory tract infection.
• Rhinoviruses do not typically reach the alveoli due to their preference for the upper respiratory tract.
• It requires a vector for lower tract transmission
• Rhinoviruses are transmitted via direct contact, airborne droplets, or contaminated surfaces, not through a vector like mosquitoes or ticks.
• Vector transmission is more commonly associated with diseases like malaria or dengue.
• Antibodies prevent it from entering the lungs
• While the immune system, including antibodies, plays a role in combating infections, the inability of rhinoviruses to infect the lower respiratory tract is primarily due to environmental and biological factors, not antibody interference.
• Antibodies are produced as part of the body's response to infection and do not specifically block rhinoviruses from entering the lungs.

The correct answer is Founding the first girls’ school in India.

Key Points

• Jyotiba Phule (also known as Jyotirao Phule) was a prominent social reformer, educationist, and activist from India.
• He is best remembered for his pivotal role in promoting education for women and the marginalized sections of society.
• In 1848, along with his wife Savitribai Phule, Jyotiba Phule founded the first girls' school in India in Pune, Maharashtra.
• This was a revolutionary step during an era when women's education was considered taboo and women were denied basic rights.
• Jyotiba Phule also worked tirelessly to eradicate the deeply entrenched caste system and promote social equality.
• He was a vocal critic of the Brahmanical social order and sought to uplift the Dalits and other marginalized communities.
• The establishment of the girls' school marked the beginning of a new era in women’s education in India and paved the way for future reforms in the field of education.
• His efforts earned him the title of Mahatma, meaning "Great Soul."

Additional Information

• Launching India’s first cooperative bank
• The first cooperative bank in India was the Anyonya Co-operative Bank, founded in 1889 in Baroda, Gujarat.
• While Jyotiba Phule was a social reformer, he was not associated with the establishment of a cooperative bank.
• Writing the Indian Constitution
• The Indian Constitution was drafted by the Constituent Assembly of India, chaired by Dr. B.R. Ambedkar.
• Jyotiba Phule passed away in 1890, long before the Constitution was written (1947-1949).
• Leading the 1857 revolt
• The 1857 revolt, also known as the First War of Indian Independence, was led by figures like Mangal Pandey, Rani Lakshmibai, Tatya Tope, and Bahadur Shah Zafar.
• Jyotiba Phule was a contemporary of the revolt but was more focused on social reforms and education rather than armed rebellion.

The Correct answer is Only 1 and 3.

Key Points

• Post the 1991 economic reforms in India, the agricultural sector underwent significant changes, particularly with the introduction of trade liberalization policies.
• Quantitative restrictions on imports of agricultural products were fully removed in April 2001, marking a major step toward integrating Indian agriculture into the global economy.
• India adopted an export-oriented policy, emphasizing production for international markets. This led to a shift from traditional food grain cultivation to the cultivation of cash crops such as cotton, sugarcane, and spices.
• The removal of quantitative restrictions and export-focused policies were aligned with the goals of the World Trade Organization (WTO), to which India is a signatory.
• This shift had significant implications for food security and rural livelihoods, as the focus on cash crops sometimes came at the expense of food grain production for the domestic market.

Additional Information

• Option 2: Increase in import duties
• Contrary to the claim in Option 2, import duties on agricultural products were not significantly increased after 1991. Instead, the focus was on reducing trade barriers to facilitate globalization and trade liberalization.
• India adhered to WTO norms that emphasized lower tariffs and reduced trade barriers for agricultural commodities.
• Quantitative restrictions (Option 1)
• The removal of quantitative restrictions was a significant policy change post-1991, and it allowed India to import agricultural products more freely.
• This policy aimed to integrate Indian agriculture with global markets, promoting competition and accessibility to diverse agricultural goods.
• Export-oriented policy (Option 3)
• India's post-1991 export-oriented policy led to an increased focus on cash crop production, which was economically lucrative in international markets.
• Examples of cash crops include tea, coffee, spices, cotton, and tobacco, which gained prominence over traditional food grains.
• This policy was aimed at earning foreign exchange and enhancing India's agricultural trade competitiveness globally.

Given: Seven boxes, D, E, F, G, S, T and U, are kept one over the other but not necessarily in the same order. 

1. Only E is kept above G. 

2. Only two boxes are kept above U.

3. U is kept immediately above T.

4. S is kept immediately above D.

5. S is not kept at third position from the bottom. 

After positioning S and D only one position is left which will be occupied by the only box left i.e. F.

Thus, three boxes are kept between F and E.

Hence, the correct answer is "Option 3".

The Correct answer is Axis Bank.

Key Points

• Axis Bank became the first Indian bank to launch near-real-time, 24/7 programmable USD clearing capabilities using JP Morgan’s Kinexys Digital Payments platform in March 2025.
• This innovative capability enables instant and automated cross-border payments, enhancing global financial connectivity.
• The partnership with JP Morgan underscores Axis Bank’s commitment to leveraging technology for providing seamless financial solutions to its customers.
• The Kinexys Digital Payments platform is known for its robust infrastructure that supports high-speed and secure payment processing.
• This move positions Axis Bank as a leader in digital banking innovation in India.
• The service is particularly beneficial for businesses engaged in international trade, enabling faster and more efficient transactions.
• This advancement aligns with the global trend of adopting programmable payments to enhance operational efficiency.
• It also reflects the growing importance of 24/7 banking services in today’s fast-paced financial environment.

Additional Information

• State Bank of India
• State Bank of India (SBI) is India's largest public sector bank, headquartered in Mumbai.
• SBI is known for its extensive network of branches and providing a diverse range of financial services.
• It serves customers across urban and rural areas and is instrumental in driving financial inclusion in India.
• Bandhan Bank
• Bandhan Bank is a relatively new private sector bank headquartered in Kolkata, India.
• The bank primarily focuses on providing banking services to the underprivileged and rural population.
• It began operations in 2015 and specializes in microfinance.
• Indian Bank
• Indian Bank is a prominent public sector bank headquartered in Chennai, India.
• The bank offers a range of services including retail banking, corporate banking, and treasury operations.
• It merged with Allahabad Bank in 2020 to expand its reach and services.

Given Table:

According to the given condition:

Given: @&238

Here, III rule applies i.e. their codes are to be changed to the code for 3

@ → coded as P

& → coded as D

2 → coded as T 

3 → coded as P

8 → coded as P

So, @&238 → Coded as PDTPP

Hence, "Option 3" is the correct answer.

The logic followed here is:

Option 1) YDGK

Option 2) GLOS

​

Option 3) EJNQ

Option 4) ZEHL

​

Thus, out of all 'EJNQ' is the odd one out.

Hence, "Option 3" is the correct answer.

Decoding the Symbols:

Given: E ÷ F + G – H x K

E ÷ F → E is the father of F.

F + G → F is the son of G. 

G – H → G is the sister of H.

H x K → H is the wife of K.

Thus, E is K's wife's sister's husband.

Hence, "Option 4" is the correct answer.

According to the given information,

Thus, 'G' is coded as '6'.

Hence, "Option 2" is the correct answer.

Given:

82 × 111

Formula used:

(a × (b + c)) = a × b + a × c

Calculation:

⇒ 82 × 111 = 82 × (100 + 11)

⇒ = 82 × 100 + 82 × 11

⇒ = 8200 + 902

⇒ = 9102

∴ 82 × 111 = 9102

The correct answer is Pulakesin II.

Key Points

• Pulakesin II, a renowned ruler of the Chalukya dynasty, is remembered for his military prowess and administrative skills.
• He defeated Harshavardhana on the Narmada frontier, halting Harsha's southern expansion.
• This event is prominently mentioned in the Aihole inscription, composed by Pulakesin II's court poet Ravikirti.
• The victory established the Narmada River as the northern boundary of Pulakesin II's empire and marked him as a powerful ruler in peninsular India.
• Pulakesin II's administration was marked by a strong central authority and a well-organized system of governance.
• The Chalukya dynasty, under his rule, reached its zenith, controlling large parts of modern-day Karnataka, Maharashtra, and Andhra Pradesh.
• He was a contemporary of Harshavardhana, and their conflict is a significant event in early medieval Indian history.

Additional Information

• Rajaraja Chola
• Rajaraja Chola I was a prominent ruler of the Chola dynasty, known for his military conquests and administrative reforms.
• He is renowned for building the Brihadeeswarar Temple at Thanjavur, a UNESCO World Heritage Site.
• His reign marked the expansion of the Chola Empire to Sri Lanka and parts of Southeast Asia.
• Narasimhavarman
• Narasimhavarman I, also known as Mamalla, was a ruler of the Pallava dynasty.
• He defeated the Chalukyas under Pulakesin II and captured the Chalukya capital, Vatapi (modern Badami).
• Narasimhavarman is famous for his contributions to architecture, including the rock-cut temples of Mamallapuram.
• Mahendravarman II
• Mahendravarman II was a ruler of the Pallava dynasty and the son of Narasimhavarman I.
• His reign was relatively short, and he is less prominent compared to other Pallava rulers.
• He continued the legacy of temple construction and cultural patronage started by his predecessors.

The Correct answer is A dispute between Karnataka and Tamil Nadu over water sharing.

Key Points

• The original jurisdiction of the Supreme Court in India is defined under Article 131 of the Indian Constitution.
• This jurisdiction allows the Supreme Court to adjudicate disputes between:
• The Government of India and one or more States
• Between two or more States
• However, disputes related to water sharing between states are excluded from the original jurisdiction of the Supreme Court.
• Such disputes are governed by the Inter-State River Water Disputes Act, 1956, and are handled by water tribunals, not the Supreme Court.
• The water-sharing dispute between Karnataka and Tamil Nadu is primarily related to the Cauvery River, which has been a long-standing issue.
• These disputes are resolved through dedicated mechanisms such as the Cauvery Water Disputes Tribunal rather than the Supreme Court's original jurisdiction.

Additional Information

• A commercial contract dispute between Gujarat and a private company
• Such disputes typically fall under the jurisdiction of civil courts or specialized tribunals, depending on the nature of the contract.
• They do not qualify as disputes between states or the central government under Article 131.
• A disagreement between Punjab and Haryana over territorial boundaries
• Disputes over territorial boundaries between states fall under the original jurisdiction of the Supreme Court.
• For example, boundary disputes can arise due to historical treaties or administrative decisions.
• A dispute between Maharashtra and the Centre over a constitutional law issue
• Constitutional law issues between states and the central government fall under the Supreme Court's original jurisdiction as defined in Article 131.
• Such issues typically involve interpretations of the Constitution or implementation of central laws.

Shortcut Trick

Put A = 45° in the expression.

⇒ [2(1/√2)/(1 − 1/√2) + 2(1/√2)/(1 + 1/√2)] × 3√((√2)² − 1)

⇒ [√2/((√2−1)/√2) + √2/((√2+1)/√2)] × 3(1) ⇒ [2/(√2−1) + 2/(√2+1)] × 3

⇒ 2[(√2+1 + √2−1)/(2−1)] × 3 ⇒ 2[2√2] × 3 = 12√2

Checking options: (2) 12 sec45°tan45° = 12 × √2 × 1 = 12√2.

∴ The correct answer is 12 secAtanA.

Alternate Method

Given: [2cosA/(1 − sinA) + 2cosA/(1 + sinA)] × 3√(sec²A − 1)

Formula Used: (1 − sin²A) = cos²A and (sec²A − 1) = tan²A

⇒ 2cosA [ (1 + sinA + 1 − sinA) / (1 − sin²A) ] × 3√tan²A

⇒ 2cosA [ 2 / cos²A ] × 3tanA

⇒ [ 4 / cosA ] × 3tanA

⇒ 4secA × 3tanA

⇒ 12secAtanA

∴ The correct answer is 12 secAtanA.

Additional Information

Trigonometric Identities

Fundamental identities: sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, and 1 + cot²θ = cosec²θ.

Reciprocal Relations

secA = 1/cosA, cosecA = 1/sinA, and tanA = sinA/cosA.

Substitution Method

For proving identities, substituting common angles like 0°, 30°, 45°, 60°, or 90° often simplifies complex expressions (avoiding undefined values).

The correct answer is Availability of water.

Key Points

• Availability of water is the most crucial factor influencing the compactness of rural settlements in dry regions like Rajasthan.
• In arid and semi-arid regions, water is a scarce resource, and its presence determines human settlement patterns.
• Villages tend to develop in a more compact form near water sources to ensure proximity and accessibility.
• Rajasthan faces extreme water scarcity due to its desert climate and low annual rainfall; thus, settlements often form around oases, wells, or tanks.
• Compact settlements help reduce the effort and time required to fetch water and allow better community management of water resources.
• Historically, people have relied on stepwells (baolis), tanks, and rainwater harvesting structures to meet their water needs, further influencing settlement patterns.
• In comparison, areas with abundant water sources generally feature dispersed settlements due to reduced dependency on a single water source.

Additional Information

• Groundwater salinity
• Groundwater salinity refers to the presence of high salt content in groundwater, which can render it unsuitable for drinking or irrigation.
• While groundwater salinity is an issue in Rajasthan due to its geological conditions, it does not directly influence the compactness of rural settlements.
• However, it may determine the location of settlements by pushing people to areas with better water quality.
• Soil fertility
• Soil fertility refers to the ability of soil to support plant growth by providing essential nutrients.
• While it is a crucial factor for agricultural settlements, it primarily influences land use and cropping patterns, rather than the compactness of settlements.
• In Rajasthan, due to the sandy and infertile soil, settlements are often concentrated near water sources rather than fertile lands.
• Altitude
• Altitude refers to the height of a location above sea level.
• While altitude can influence settlement patterns in hilly or mountainous regions, it is not a significant factor in the flat terrain of Rajasthan.
• In Rajasthan, the focus is more on water availability due to its arid climatic conditions.