Shortcut Trick

Ratio of numbers = 4 : 5 : 6

Since the numbers are in Arithmetic Progression, the Average is the middle term (5 units).

5 units = 40 ⇒ 1 unit = 8

Largest number (6 units) = 6 × 8 = 48

∴ The correct answer is 48.

Alternate Method

Given: Ratio = 4 : 5 : 6, Average = 40

Formula: Average = Sum of observations ÷ Total number of observations

⇒ Let the numbers be 4x, 5x, and 6x.

⇒ (4x + 5x + 6x) ÷ 3 = 40

⇒ 15x ÷ 3 = 40

⇒ 5x = 40

⇒ x = 8

⇒ Largest number = 6x = 6 × 8 = 48

∴ The correct answer is 48.

Additional Information

Average of AP

For any series in Arithmetic Progression, the Average is equal to (First term + Last term) ÷ 2 or the middle term if the number of terms is odd.

Ratio and Proportion

If quantities are in ratio a : b : c, their values can be assumed as ax, bx, and cx where x is the highest common factor.

Given: A, B, C, D, R, S, and T are sitting around a circular table facing the centre of the table.

1. S sits third to the right of R.

2. S sits to the immediate right of C.

3. C sits third to the left of A.

4. Only one person sits between D and T when counted from the left of T.

5. B is not an immediate neighbour of C.

Thus, three people sit between B and T when counted from the right of B.

Hence, the correct answer is "Option 1".

Shortcut Trick

Time for pump (A) = 8 hr

Time for pump + leak (A − B) = 28/3 hr

Total Capacity (LCM of 8, 28) = 56 units

Efficiency of Leak (B) = (56 ÷ 8) − (56 ÷ (28/3)) = 7 − 6 = 1 unit/hr

Time for Leak to empty = 56 ÷ 1 = 56 hr

∴ The correct answer is 56 hr.

Alternate Method

Given:

Filling time of Electric Pump (P) = 8 hours

Filling time with Leakage (P + L) = 9(1/3) hours = 28/3 hours

Formula Used:

Efficiency = Total Work ÷ Time

Time = Total Work ÷ Efficiency

Calculations:

⇒ Efficiency of Pump (P) = 56 ÷ 8 = 7 units/hr

⇒ Efficiency of (Pump + Leak) = 56 ÷ (28/3) = (56 × 3) ÷ 28 = 2 × 3 = 6 units/hr

⇒ Efficiency of Leak (L) = Efficiency of (P + L) − Efficiency of P

⇒ Efficiency of Leak (L) = 6 − 7 = −1 unit/hr (Negative sign denotes emptying)

⇒ Time taken by Leak to empty the tank = Total Capacity ÷ |Efficiency of Leak|

⇒ Time = 56 ÷ 1 = 56 hours

∴ The correct answer is 56 hr.

Additional Information

Pipes and Cisterns Concept

Filling pipes have positive efficiency, while leakage or outlet pipes have negative efficiency.

Leakage Formula

If a pipe fills a tank in 'x' hours and with a leak it takes 'y' hours, the leak empties it in (xy) ÷ (y − x) hours.

Total Work (Capacity)

LCM of individual time durations is the most efficient way to assume the total capacity of the tank.

The logic followed here is:

For HMP to KON

For USQ to XUO

The common pattern is a progressive letter shift of +3, +2, and -2 for each successive letter.

Checking the options:

Option 1) DLV to GNT

The pairs in the other options do not follow this pattern.

Thus, the pair DLV : GNT follows the same logic.

Hence, the correct answer is "Option 1".

Shortcut Trick

Convert fractional ratio to whole number ratio by multiplying by LCM of denominators (3, 5, 5) = 15.

New Ratio → (8/3 × 15) : (7/5 × 15) : (8/5 × 15) = 40 : 21 : 24.

Total units = 40 + 21 + 24 = 85 units.

Third monkey's share = (24/85) × 425 = 24 × 5 = 120.

∴ The correct answer is 120 bananas.

Alternate Method

Given: Total bananas = 425, Ratio = 8/3 : 7/5 : 8/5

Step 1: Simplify the given ratio.

⇒ Ratio = (8/3) : (7/5) : (8/5)

⇒ Multiplying by 15 → 40 : 21 : 24

Step 2: Calculate sum of the parts.

⇒ Sum = 40 + 21 + 24 = 85

Step 3: Relate sum to total quantity.

⇒ 85 units = 425

⇒ 1 unit = 425 ÷ 85 = 5

Step 4: Find share of the third monkey.

⇒ 24 units = 24 × 5 = 120

∴ The correct answer is 120 bananas.

Additional Information

Fractional Ratios

To simplify a : b : c in fractional form, multiply each term by the Lowest Common Multiple (LCM) of all denominators.

Ratio & Proportion

If a quantity 'Q' is divided in the ratio a:b:c, the share of the third part is calculated as [c / (a + b + c)] × Q.

The correct answer is ASCII represents characters using numeric codes in binary.

Key Points

• ASCII stands for American Standard Code for Information Interchange.
• It is a character encoding standard that represents text in computers, telecommunications, and other devices.
• ASCII uses numeric codes in binary, ranging from 0 to 127, to represent characters such as letters, digits, and symbols.
• For example, the ASCII code for the uppercase letter 'A' is 65, and its binary equivalent is 01000001.
• ASCII is widely used in programming, data storage, and communication systems as a foundational text encoding scheme.

Additional Information

• LAN (Local Area Network)
• A LAN is a network that connects computers and devices within a limited geographical area, such as a home, school, or office.
• It enables resource sharing, including files, printers, and internet connections.
• Unlike WAN (Wide Area Network), LAN covers a smaller area and typically offers higher data transfer speeds.
• CD (Compact Disc)
• A CD is an optical storage medium used to store data such as music, videos, and software.
• Unlike magnetic storage, CDs use laser technology to read and write data.
• CDs can be categorized as CD-ROM (read-only), CD-R (recordable), and CD-RW (rewritable).
• Unicode
• Unicode is a universal character encoding standard that extends ASCII to represent characters from multiple languages and scripts.
• Unlike ASCII, which is limited to 128 characters, Unicode supports over 140,000 characters.
• It ensures consistent representation of text across different systems and platforms.
• Binary Number System
• The binary number system uses only two digits: 0 and 1.
• Computers operate using binary because it aligns with the digital nature of electronic circuits (on/off states).
• Binary forms the foundation of all computer processing, data storage, and communication.

The correct answer is March 2027.

Key Points

• V Anantha Nageswaran is the Chief Economic Adviser (CEA) to the Government of India.
• The term of the Chief Economic Adviser has been extended till March 2027, ensuring continuity in economic policy advisory.
• V Anantha Nageswaran was appointed as the CEA on January 28, 2022, succeeding Krishnamurthy Subramanian.
• As CEA, Nageswaran plays a crucial role in preparing key economic documents like the Economic Survey and advising the government on fiscal and monetary policies.
• The extension is intended to leverage his expertise in guiding India’s economic strategies amidst global uncertainties.

Additional Information

• Role of the Chief Economic Adviser:
• The CEA is responsible for providing expert advice on economic matters to the Ministry of Finance.
• Prepares the Economic Survey, an important annual document outlining India’s economic performance and future outlook.
• Acts as an interface between policymakers and economists to ensure evidence-based decision-making.
• Economic Survey:
• An annual flagship report prepared by the Ministry of Finance under the guidance of the CEA.
• It provides a detailed analysis of trends in the economy over the past year and suggests reforms for sustainable growth.
• India’s Fiscal Policy:
• Focuses on taxation and government spending to regulate economic activity.
• Aims at achieving macroeconomic objectives like growth, employment, and inflation control.
• Global Economic Uncertainty:
• Factors such as inflation, geopolitical tensions, and monetary tightening by central banks worldwide impact India’s economic strategies.
• The CEA's role is critical in navigating these challenges through informed policy recommendations.

The given three-digit numbers are: 617, 335, 930, 459, 571.

Now,

The highest number is 930. Its first digit is 9.

The lowest number is 335. Its third digit is 5.

Perform the addition.

Add the first digit of the highest number 9 to the third digit of the lowest number 5.

9 + 5 = 14.

Hence, the correct answer is "Option 2".

Shortcut Trick

Use the direct Empirical Formula relation: Mode − Median = 2 × (Median − Mean).

Given: Mode − Median = 46.36.

Substitute the value: 46.36 = 2 × (Median − Mean).

Median − Mean = 46.36 ÷ 2 = 23.18.

∴ The correct answer is 23.18.

Alternate Method

Given: Median = Mode − 46.36 ⇒ Mode − Median = 46.36.

Formula: The empirical relationship between Mean, Median, and Mode is Mode = 3 × Median − 2 × Mean.

⇒ Mode = 3 × Median − 2 × Mean

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

⇒ Mode − Median = 2 × Median − 2 × Mean

⇒ 46.36 = 2 × (Median − Mean)

⇒ Median − Mean = 46.36 ÷ 2

⇒ Median − Mean = 23.18

∴ The correct answer is 23.18.

Additional Information

Empirical Formula

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

Symmetric Distribution

In a perfectly symmetrical distribution, the Mean, Median, and Mode are all equal (Mean = Median = Mode).

Mean-Mode Relation

The difference Mean − Mode = 3 × (Mean − Median) is another common form of this empirical rule.

The given code language is:

Thus, 'O' is coded as '4'.

Hence, the correct answer is "Option 2".

The correct answer is Article 51A (d).

Key Points

• Article 51A (d) of the Constitution of India mandates that it is the Fundamental Duty of every Indian citizen to "defend the country and render national service when called upon to do so."
• Fundamental Duties were added to the Indian Constitution by the 42nd Amendment Act, 1976, based on the recommendations of the Swaran Singh Committee.
• These duties are enshrined under Part IVA of the Constitution.
• The objective of incorporating Fundamental Duties is to remind citizens of their moral obligations toward the nation and to uphold the spirit of patriotism.
• There are currently 11 Fundamental Duties listed in Article 51A of the Indian Constitution.

Additional Information

• 42nd Amendment Act, 1976
• It is also known as the "Mini Constitution" of India due to the significant changes it brought to the Constitution.
• It introduced Fundamental Duties, added the words "Socialist," "Secular," and "Integrity" to the Preamble, and curtailed the power of the judiciary, among other changes.
• Swaran Singh Committee
• The Swaran Singh Committee was constituted in 1976 to recommend the inclusion of Fundamental Duties in the Constitution.
• It was named after Swaran Singh, the then Minister of External Affairs.
• Fundamental Duties
• The Fundamental Duties are non-justiciable, meaning they cannot be enforced by the courts.
• They serve as a moral code of conduct for citizens to contribute positively to society and the nation.
• Part IVA of the Constitution
• Part IVA was added to the Constitution by the 42nd Amendment Act, 1976.
• It contains only one Article, Article 51A, which enumerates the Fundamental Duties.

The correct answer is Donald Trump assassination attempt.

Key Points

• The Washington Post won the 2025 Pulitzer Prize for Breaking News Reporting for its comprehensive and timely coverage of an assassination attempt on Donald Trump, the former President of the United States.
• The incident occurred in 2024 during a public event, where a failed assassination attempt led to widespread media attention and security concerns.
• The Washington Post's team was recognized for their accuracy, depth of investigation, and real-time updates during and after the event.
• The coverage included detailed reporting on the attack, the suspect's motives, and the response of law enforcement agencies.
• The Pulitzer committee praised the newspaper's efforts in providing clarity and factual information amidst an evolving and highly sensitive situation.

Additional Information

• Pulitzer Prize for Breaking News Reporting
• Established in 1942, this category honors distinguished reporting on breaking news events by an individual or team.
• Entries often showcase real-time coverage, investigative depth, and public impact.
• It is one of the most prestigious awards in journalism, presented annually by Columbia University.
• Donald Trump's Public Appearances
• As a prominent political figure, Trump's public events often attract both supporters and detractors.
• Heightened security measures are a norm due to his polarizing influence and global recognition.
• Assassination Attempts on Political Leaders
• Historically, political leaders worldwide have been targets of assassination attempts due to their influential roles.
• Such events often lead to increased security protocols and public debates on safety measures.
• Examples include attempts on leaders like John F. Kennedy, Ronald Reagan, and Indira Gandhi, among others.
• Role of Media in Crisis Reporting
• Media plays a crucial role in providing verified information during crises to prevent misinformation and panic.
• Investigative journalism often aids in uncovering critical facts, ensuring accountability and transparency.
• Organizations like The Washington Post are known for their commitment to journalistic integrity in such scenarios.

Shortcut Trick

Savings percentage = 100% − 52% = 48%.

Given 48% = ₹7,740.

Expenses = 52%.

Value of 52% = (7,740 ÷ 48) × 52 = 161.25 × 52 = ₹8,385.

∴ The correct answer is ₹8,385.

Alternate Method

Given:

Expenditure = 52% of Monthly Income

Savings = ₹7,740

⇒ Let Monthly Income be I.

⇒ Savings = Income − Expenditure

⇒ 48% of I = 7,740

⇒ (48/100) × I = 7,740

⇒ I = (7,740 × 100) ÷ 48

⇒ I = 16,125

⇒ Monthly Expenses = 52% of 16,125

⇒ Monthly Expenses = 0.52 × 16,125 = 8,385

∴ The correct answer is ₹8,385.

Additional Information

Income Formula

Total Income is always the sum of Expenditure and Savings (I = E + S).

Percentage Change

If income increases by x% and expenditure by y%, the new savings can be calculated using the Base Change method.

Ratio Method

Convert percentages to fractions to simplify: 52% = 13/25. If Income is 25 units, Expense is 13 units and Savings is 12 units.

The correct answer is Can override the decision of his council.

Key Points

• The Regulating Act of 1773 established the office of the Governor-General of Bengal, who was assisted by an executive council of four members.
• The Governor-General was empowered to make rules and regulations for the civil government of Fort William in Bengal.
• The Governor-General had the power to control and superintend the presidencies of Madras and Bombay in matters of war and peace.
• However, the Governor-General could not override the decision of his council; decisions were to be taken collectively, and in the event of a tie, the Governor-General held the casting vote.
• This limitation was an attempt to ensure checks and balances within the colonial administration.

Additional Information

• Regulating Act of 1773:
• The first attempt by the British Parliament to regulate the affairs of the East India Company and its territories in India.
• It marked the beginning of parliamentary control over the Company's administration in India.
• It restricted the private trade of Company officials and sought to address administrative corruption.
• Governor-General of Bengal:
• The Regulating Act designated the Governor of Bengal as the Governor-General of Bengal.
• Warren Hastings was the first Governor-General under the Act.
• Executive Council:
• The Governor-General's Executive Council consisted of four members appointed by the Court of Directors of the East India Company.
• It functioned as a decision-making body, with the Governor-General having the casting vote.
• Limitations of the Regulating Act:
• The Act failed to provide adequate checks on the Governor-General's powers.
• Conflicts often arose between the Governor-General and his council members due to the lack of clarity in decision-making authority.
• This led to the enactment of the Pitt's India Act of 1784, which introduced further reforms.

The given three-digit numbers are: 103, 678, 217, 111, 537.

Now,

The highest number is 678. Its second digit is 7.

The lowest number is 103. Its first digit is 1.

Perform the addition.

Add the second digit of the highest number 7 to the first digit of the lowest number 1.

7 + 1 = 8.

Hence, the correct answer is "Option 1".

The question contains a slightly confusing set of interchange rules. However, based on the options, the most logical and correct interpretation of the rules is that ‘+’ and ‘×’ are interchanged and ‘−’ and ‘÷’ are interchanged.

The given equation is:

612 ÷ 45 + 13 × 936 − 78 = ?

After applying the interchange rules, the equation becomes:

612 − 45 × 13 + 936 ÷ 78 = ?

Now, we solve the equation following the BODMAS rule:

= 612 − 45 × 13 + 936 ÷ 78

= 612 − 585 + 12

= 27 + 12 = 39

Hence, the correct answer is "Option 4".

The correct answer is It said disability rights are a part of fundamental rights..

Key Points

• The Supreme Court of India, in March 2025, declared that disability rights are an integral part of fundamental rights under the Indian Constitution.
• This landmark decision emphasized the enforcement of the Rights of Persons with Disabilities Act, 2016, ensuring equality, dignity, and inclusion for persons with disabilities.
• The judgment underscored Article 21 of the Constitution, which guarantees the right to life with dignity, and linked it to the rights of individuals with disabilities.
• It mandated that public and private entities must ensure reasonable accommodations for persons with disabilities to eliminate discrimination.
• The ruling reinforced the idea that accessibility, equal opportunities, and non-discrimination are essential for fostering an inclusive society.

Additional Information

• Rights of Persons with Disabilities Act, 2016 (RPwD Act):
• It replaced the Persons with Disabilities (Equal Opportunities, Protection of Rights, and Full Participation) Act, 1995.
• The Act recognizes 21 types of disabilities, including mental illness, autism, and dwarfism.
• It ensures rights such as education, employment, and social security for persons with disabilities.
• It mandates a reservation of 4% in government jobs and 5% in educational institutions for persons with benchmark disabilities.
• Fundamental Rights under the Indian Constitution:
• Fundamental rights are guaranteed under Articles 12–35 of the Indian Constitution.
• Article 21 guarantees the right to life and personal liberty, which includes the right to live with dignity.
• Equality before law (Article 14) and prohibition of discrimination (Article 15) are key provisions supporting disability rights.
• Reasonable Accommodation:
• It refers to necessary and appropriate modifications to ensure persons with disabilities can enjoy their rights equally.
• Examples include ramps in buildings, assistive technologies, or extended time during examinations.
• Global Framework on Disability Rights:
• The United Nations Convention on the Rights of Persons with Disabilities (UNCRPD) was adopted in 2006.
• India ratified the UNCRPD in 2007, committing to its principles of equality, non-discrimination, and accessibility.

The correct answer is Alluvial soil.

Key Points

• Alluvial soil is the dominant soil type found in the Great Plains of India.
• It is formed by the deposition of silt, sand, and clay brought down by rivers like the Ganga, Yamuna, Brahmaputra, and their tributaries.
• The Great Plains are a part of the Indo-Gangetic-Brahmaputra plain, which is one of the most fertile regions in the world.
• Alluvial soils in the region are highly suitable for agriculture, supporting the cultivation of crops like wheat, rice, sugarcane, and pulses.
• These soils are rich in nutrients such as potash and lime but are generally deficient in nitrogen and phosphorus.

Additional Information

• Alluvial Soil:
• It is categorized into two types: Khadar (new alluvium), which is found closer to riverbanks, and Bhangar (old alluvium), located farther from rivers.
• Khadar soils are more fertile due to frequent river depositions, while Bhangar soils contain kankar (calcareous concretions).
• Formation of Alluvial Soil: This soil is formed by the action of rivers and is transported and deposited over time, creating extensive plains and deltas.
• Distribution in India: Alluvial soils are extensively found in the northern plains, including Punjab, Haryana, Uttar Pradesh, Bihar, and West Bengal, and along river valleys in other parts of the country.
• Agricultural Importance: Due to their fine texture, good water-retention capacity, and nutrient content, alluvial soils are considered ideal for intensive agricultural activities.
• Soil Management: Regular use of fertilizers and crop rotation practices are necessary to replenish nutrients and maintain soil fertility.

Shortcut Trick

Area of a sector can be calculated directly if the arc length (l) and radius (r) are known.

Shortcut formula: Area = (1 ÷ 2) × l × r

⇒ Area = 0.5 × 5 × 16.2

⇒ Area = 2.5 × 16.2 = 40.5

∴ The correct answer is 40.5 units².

Alternate Method

Given:

Radius (r) = 16.2 units

Arc length (l) = 5 units

Formula Used:

Area of Sector = (l × r) ÷ 2

Calculations:

⇒ Area = (5 × 16.2) ÷ 2

⇒ Area = 81 ÷ 2

⇒ Area = 40.5

∴ The correct answer is 40.5 units².

Additional Information

Arc Length Formula

The length of an arc (l) is given by (θ ÷ 360) × 2πr, where θ is the central angle in degrees.

Sector Area (θ method)

Area of a sector can also be calculated as (θ ÷ 360) × πr².

Perimeter of Sector

The total boundary of a sector is l + 2r, which includes the arc length and two radii.

The correct answer is Iron.

Key Points

• Iron is an essential nutrient required for the synthesis of hemoglobin, a protein in red blood cells responsible for oxygen transport in the body.
• Iron deficiency leads to a condition called iron-deficiency anemia, which directly reduces the oxygen-carrying capacity of blood.
• The primary symptoms of iron-deficiency anemia include fatigue, weakness, pale skin, and shortness of breath due to insufficient oxygen supply to tissues.
• Dietary sources of iron include red meat, poultry, fish, legumes, leafy green vegetables, and iron-fortified cereals.
• Iron absorption is enhanced by vitamin C, whereas substances like calcium and phytates can inhibit its absorption.

Additional Information

• Hemoglobin:
• Hemoglobin is a protein in red blood cells that binds to oxygen in the lungs and transports it to tissues throughout the body.
• Each hemoglobin molecule contains iron, which is critical for its oxygen-binding capacity.
• Iron-Deficiency Anemia:
• A condition where the body lacks sufficient iron to produce adequate amounts of hemoglobin.
• It is the most common type of anemia globally and can affect people of all ages.
• Types of Iron:
• Heme iron: Found in animal-based foods like meat and is more easily absorbed by the body.
• Non-heme iron: Found in plant-based foods and has lower bioavailability compared to heme iron.
• Iron Absorption:
• Vitamin C-rich foods like oranges and tomatoes enhance iron absorption.
• Calcium, tea, coffee, and whole grains may inhibit iron absorption when consumed together with iron-rich foods.
• Prevention and Treatment:
• Preventing iron deficiency involves consuming a balanced diet rich in iron and vitamin C.
• Iron supplements may be prescribed in cases of severe deficiency, under medical supervision.

The correct answer is The file ownership has changed..

Key Points

• An "Access is denied" error in Windows 11 can occur when the ownership of the file has changed.
• Ownership changes might happen if the file is moved from another user account, system, or network location.
• To resolve this issue, you need to take ownership of the file via the file's properties under the "Security" tab.
• Administrative privileges may be required to make changes to file ownership.
• This error can also occur if the file is locked by another process or user that has exclusive access to it.

Additional Information

• File Ownership in Windows
• File ownership determines which user or group has control over a file or folder.
• By default, the user who creates the file becomes its owner.
• Ownership can be transferred by administrators or through manual configuration.
• Steps to Take Ownership
• Right-click the file or folder and select "Properties."
• Navigate to the "Security" tab and click "Advanced."
• Under the "Owner" section, click "Change" and assign ownership to the desired user.
• Apply the changes to complete the process.
• Common Causes of File Ownership Issues
• Files restored from backups may retain their previous ownership settings.
• Files downloaded from the internet or external storage devices may have restricted ownership.
• Changes in user accounts or system updates can also affect file ownership.
• Other Possible Reasons for "Access Denied" Errors
• File permissions: The user may lack the necessary read/write permissions.
• File in use: The file might be open or locked by another process.
• Corrupt file or system: Issues with file integrity or the operating system can lead to errors.
• Antivirus software: Overly aggressive security software may block access to certain files.

Given: Each of P, Q, R, S, T, U and V has an exam on a different day of a week starting from Monday and ending on Sunday of the same week.

R has an exam on Thursday.

 

Exactly 4 people have their exam between U and T, neither of whom has an exam on Sunday.

S has an exam immediately before Q

U does not have an exam after Q.

 

P does not have an exam on Friday. 

And V sits at the remaining place.

4 people have an exam after Q.

Hence, the correct answer is "Option 4."

The correct answer is Diamond.

Key Points

• During the Harappan civilisation, ornaments were made using materials like ivory, carnelian, steatite, and gold.
• Diamond was not used for making ornaments in the Harappan era due to the lack of advanced mining technology and tools required to extract diamonds.
• Carnelian, a semiprecious stone, was widely used in bead-making and ornamentation, showcasing the Harappans' expertise in craftsmanship.
• Steatite, a soft stone, was extensively used for crafting beads and seals, reflecting its significance in Harappan material culture.
• Ivory was utilized to create intricate decorative items and ornaments, indicating the availability of elephants in the region.

Additional Information

• Carnelian:
• A reddish-orange semiprecious stone extensively used by the Harappans for bead-making.
• It was sourced locally or imported from regions like Gujarat and Afghanistan.
• Carnelian beads often underwent heat treatment to enhance their color and durability.
• Steatite:
• A soft stone used for seals, beads, and ornaments during the Harappan civilisation.
• Harappan seals made of steatite often featured animal motifs and inscriptions in the undeciphered script.
• Steatite items reflect the high level of artistic skill and intricate workmanship of the Harappans.
• Ivory:
• Ivory from elephant tusks was used to create various decorative objects and ornaments.
• The use of ivory indicates the presence of elephants in the Indus Valley region and trade in ivory goods.
• Ivory items were often meticulously crafted, showcasing the Harappans' mastery in carving.
• Diamond Extraction:
• Diamonds were not used in the Harappan civilisation due to the lack of advanced mining techniques.
• Diamond mining and usage became prominent in later periods, notably during the ancient Indian kingdoms.
• Early diamond sources in India were located in the Krishna River basin in modern-day Andhra Pradesh.

The correct answer is Mesopotamia.

Key Points

• The Harappan Civilization (also known as the Indus Valley Civilization) had extensive trade relations with Mesopotamia, as evidenced by archaeological findings.
• Trade items included goods like cotton textiles, beads, lapis lazuli, carnelian, and other semi-precious stones, which were highly valued in Mesopotamia.
• Mesopotamian records refer to a region called "Meluhha," believed to be the Indus Valley, indicating direct or indirect trade between these two ancient civilizations.
• Artifacts such as Harappan seals and weights have been discovered in Mesopotamia, corroborating the existence of trade links.
• These trade relations were facilitated via maritime routes across the Arabian Sea and overland routes through Persia and the Persian Gulf region.

Additional Information

• Harappan Seals:
• Seals made of steatite were a hallmark of Harappan culture and were used in trade for authentication and identification of goods.
• Some seals discovered in Mesopotamia have inscriptions resembling Harappan script, strengthening evidence of trade.
• Meluhha:
• In Mesopotamian texts, "Meluhha" is described as a distant land, rich in resources like timber, ivory, and lapis lazuli, believed to refer to the Indus Valley region.
• References to Meluhha occur in Sumerian and Akkadian records dating from around 2300 BCE.
• Trade Routes:
• Harappans utilized maritime routes across the Arabian Sea, connecting their ports like Lothal with Mesopotamia and other regions.
• Overland trade routes through Persia and the Oxus Valley also played a significant role in facilitating trade.
• Key Harappan Trade Ports:
• Lothal: A major port city that served as a trade hub with advanced dockyard facilities.
• Sutkagen Dor: A coastal settlement near present-day Pakistan, likely involved in maritime trade with Mesopotamia.

The correct answer is Rangma.

Key Points

• Rangma is a traditional war dance performed by the Naga tribes of Nagaland, symbolizing bravery and martial prowess.
• This dance is performed during ceremonies and festivals, particularly to commemorate victories in battles or to invoke courage.
• The dancers often wear traditional warrior attire, including headgear adorned with feathers and ornaments representing tribal identity.
• The dance movements mimic combat actions, showcasing the agility and fighting skills of the performers.
• Rangma dance is an integral part of the Naga culture, reflecting the community's strong warrior tradition and historical significance.

Additional Information

• Naga Tribes:
• The Nagas are a group of indigenous tribes residing primarily in Nagaland, northeastern India, as well as parts of Manipur, Arunachal Pradesh, and Myanmar.
• Each Naga tribe has its unique customs, traditions, and dialects, making their culture highly diverse.
• Traditional Dances of Nagaland:
• Other dances include the Sumi war dance, performed during festivals like Tuluni and Ahuna.
• These dances often serve as expressions of gratitude, celebration, and community bonding.
• Festivals of Nagaland:
• Hornbill Festival is the most prominent festival, showcasing the diverse cultural heritage of all Naga tribes.
• It is held annually in December and features traditional dances, music, arts, and crafts.
• Significance of War Dances:
• War dances in tribal communities often represent valor, unity, and preparation for battle.
• They also serve as a medium to pass down ancestral stories and warrior skills to younger generations.

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

C sits second to the left of D.

Only F sits between A and C.

B sits third to the left of F.

G is not an immediate neighbour of B. 

And E sits at the remaining place.

Thus, three people sit between A and D when counted from the left of D.

Hence, the correct answer is "Option 4".

The correct answer is Only 1 and 2.

Key Points

• The Supreme Court ruled that the Governor does not have the discretion to withhold assent to a Bill once it is re-passed by the legislature, as per the constitutional framework.
• The Court exercised its powers under Article 142 of the Constitution to declare 10 pending Bills as having received the Governor's assent, ensuring legislative processes are not unduly delayed.
• The judgment emphasized that withholding assent by the Governor without valid reasons undermines the legislative authority of the elected assembly.
• The decision reinforces the principle of cooperative federalism and ensures accountability of constitutional functionaries like Governors.
• The judgment did not include any provision for the Governor to reserve a re-enacted Bill for Presidential consideration, focusing solely on legislative assent processes.

Additional Information

• Article 142: It grants the Supreme Court wide discretionary powers to pass decrees or orders to ensure "complete justice" in any case, even if such actions are not explicitly provided in the statute.
• Role of the Governor: As per the Indian Constitution, the Governor acts as the constitutional head of the state and is required to act on the advice of the state council of ministers in most matters.
• Legislative Process: Once a Bill is passed by a state legislature, it is sent to the Governor for assent. The Governor can assent, withhold, return (if not a money Bill), or reserve it for Presidential consideration.
• Cooperative Federalism: This principle emphasizes the collaboration between the Union and state governments while respecting each other's jurisdictions as outlined in the Constitution.
• Judicial Review: The judiciary has the power to review the actions of constitutional authorities, including Governors, to ensure they act within their constitutional limits.

The correct answer is ₹10,000 crore.

Key Points

• The Tamil Nadu government has set an ambitious target of attracting ₹10,000 crore investments under its Tamil Nadu Space Industrial Policy 2025.
• The policy aims to position Tamil Nadu as a hub for space industry and research, leveraging the state’s strong industrial base and technological ecosystem.
• It seeks to promote growth in the space sector, including areas like satellite manufacturing, launch services, and ground station operations.
• The policy also focuses on fostering innovation by encouraging start-ups and academic institutions to participate in the space ecosystem.
• It is aligned with India’s vision of becoming a major player in the global space economy by enhancing domestic capabilities and infrastructure.

Additional Information

• Space Economy in India:
• India’s space economy is valued at approximately $9.6 billion, which is about 2% of the global space economy.
• It includes segments such as satellite services, ground equipment, and manufacturing.
• India’s space program is spearheaded by the Indian Space Research Organisation (ISRO), which has achieved several milestones globally.
• Global Space Industry Trends:
• The global space economy is expected to reach $1 trillion by 2040, driven by advancements in satellite technology and private sector investments.
• Key players include SpaceX, Blue Origin, and government agencies like NASA, ESA, and Roscosmos.
• Indian Space Start-ups:
• India has seen a surge in private space start-ups like Skyroot Aerospace, Agnikul Cosmos, and Pixxel.
• These start-ups focus on areas such as small satellite launches, payload development, and data analytics.
• Key Objectives of Tamil Nadu Space Industrial Policy:
• To develop world-class infrastructure for space-related industries.
• To attract investments in research, development, and manufacturing.
• To generate employment opportunities in the high-tech sector.
• To collaborate with ISRO and other global space agencies.

The correct answer is Rajasthan.

Key Points

• Rajasthan is renowned for its traditional water conservation systems, especially 'taanka' and 'kunds', which are designed to store rainwater efficiently.
• 'Kunds' are circular underground structures with sloping roofs that collect rainwater, making them ideal for arid regions.
• 'Taanka' is a technique used to store water in small tanks, usually found near households, ensuring water availability during dry seasons.
• These systems are vital in Rajasthan's desert climate, which experiences low and erratic rainfall, emphasizing the need for sustainable water management.
• Such indigenous methods highlight Rajasthan's commitment to water conservation and its cultural heritage of managing scarce resources effectively.

Additional Information

• Water Conservation Techniques in India:
• India employs several traditional water conservation methods, such as stepwells (baolis), johads, and check dams.
• These techniques are tailored to specific climatic and geographical conditions.
• Rainwater Harvesting:
• A modern adaptation of traditional systems, rainwater harvesting involves collecting and storing rainwater for domestic and agricultural use.
• It is widely promoted in India to address water scarcity issues, particularly in urban areas.
• Desert Climate of Rajasthan:
• Rajasthan is characterized by extreme temperatures, low rainfall (average annual rainfall of 100-400 mm), and arid conditions.
• Indigenous water conservation systems like 'kunds' and 'taankas' have played a pivotal role in sustaining life in such challenging environments.
• Historical Importance of Water Conservation:
• Traditional water systems like 'kunds' have been used for centuries and are examples of sustainable development practices.
• They showcase the ingenuity of communities in adapting to harsh climates while preserving resources.

Shortcut Trick

Combined efficiency (A+B) = Total Work ÷ Days = 56 ÷ 14 = 4

A efficiency = 56 ÷ 56 = 1

B efficiency = 4 − 1 = 3

Time for B to do 3/4 work = (3/4 × 56) ÷ 3 = 42 ÷ 3 = 14 days

∴ The correct answer is 14 days.

Alternate Method

Given: Time taken by (A+B) = 14 days, Time taken by A = 56 days.

Formula: 1/B = 1/(A+B) − 1/A

⇒ Efficiency of B = Efficiency of (A + B) − Efficiency of A

⇒ Efficiency of B = 4 − 1 = 3 units/day

⇒ Total Work = 56 units

⇒ 3/4 of Total Work = 56 × (3/4) = 42 units

⇒ Time taken by B = 42 ÷ 3 = 14 days

∴ The correct answer is 14 days.

Additional Information

Time and Efficiency Relationship

Time taken is inversely proportional to efficiency. Efficiency = Total Work ÷ Time.

Combined Work Formula

If two people work together, their combined efficiency is the sum of their individual efficiencies.

Fractional Work

Time for partial work = (Fraction × Total Work) ÷ Efficiency of the person.

The correct answer is Vijaya Kishore Rahatkar.

Key Points

• Vijaya Kishore Rahatkar was appointed as the Chairperson of the National Commission for Women (NCW) in October 2024.
• She has previously served in prominent leadership roles, including as the President of BJP Mahila Morcha.
• Her appointment reflects her extensive experience in advocacy for women's rights and empowerment in India.
• The NCW is a statutory body established under the National Commission for Women Act, 1990, tasked with addressing issues affecting women.
• The Chairperson plays a critical role in shaping policies and initiatives to ensure gender equality and protection of women's rights.

Additional Information

• National Commission for Women (NCW)
• The NCW was established in January 1992 under the National Commission for Women Act, 1990.
• Its primary role is to review legal provisions to safeguard women's rights and recommend measures for their effective implementation.
• The NCW also investigates specific complaints of violations of women's rights and monitors the functioning of laws relating to women.
• The commission aims to promote equality and fair treatment of women in various spheres, including employment and societal roles.
• Chairperson's Role
• The Chairperson leads the commission in formulating policies and strategies to address women's issues.
• They represent the NCW in interactions with government bodies, NGOs, and international organizations.
• The Chairperson is responsible for ensuring that the commission fulfills its mandate under the law.
• Key Functions of NCW
• Safeguarding rights guaranteed to women under the Constitution of India.
• Reviewing existing legislation and proposing amendments to address contemporary challenges faced by women.
• Creating awareness campaigns and programs to promote gender equality.
• Investigating complaints regarding women's issues and taking up cases with relevant authorities.
• Previous Chairpersons
• The NCW has had several notable leaders, including Rekha Sharma, who served as Chairperson before Vijaya Kishore Rahatkar.
• Past Chairpersons have contributed significantly to landmark initiatives and advocacy efforts for women's rights.

The logic followed here is:

Thus, the missing number in the series is 329.

Hence, the correct answer is "Option 2".

The correct answer is Only 1.

Key Points

• The Dharti Aaba Janjatiya Gram Utkarsh Abhiyan was launched in 2024 to ensure the holistic development of tribal areas.
• The scheme focuses on 25 interventions spanning health, education, and livelihood to improve the quality of life for tribal populations.
• It aims to address socio-economic disparities and promote sustainable development in tribal areas.
• Unlike the statement in Option 2, the scheme is not limited to only 10 states with scheduled areas. It encompasses a broader range of tribal regions.
• Option 3 is incorrect as the scheme was launched by another dignitary, not Vice President Jagdeep Dhankhar, and the launch details provided in the statement are inaccurate.

Additional Information

• Tribal Development:
• Tribal communities in India face challenges like inadequate access to education, healthcare, and sustainable livelihoods.
• Government schemes aim to bridge these gaps and ensure inclusive growth for tribal populations.
• Scheduled Areas:
• Scheduled Areas are regions identified under the Fifth Schedule of the Indian Constitution to protect tribal communities.
• These areas receive special administration and developmental support.
• Tribal Sub-Plan (TSP):
• The TSP strategy ensures that a fixed proportion of funds are allocated for tribal development under various central and state government schemes.
• It aims to address the socio-economic gaps in tribal regions.
• Jharkhand and Tribal Focus:
• Jharkhand is home to a significant tribal population and has been a focal point for tribal development initiatives.
• Efforts in the state include improving education, healthcare access, and preservation of tribal culture.

Shortcut Trick

Convert 18% and 4/5 to a common format for comparison.

18% of First Number (A) = 80% of Second Number (B) since 4/5 = 80%.

Ratio A : B = 80 : 18 = 40 : 9.

∴ The correct answer is 40 : 9.

Alternate Method

Given: 18% of first number = 4/5 of second number.

Formula Used: Percentage to Fraction conversion: x% = x/100.

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

⇒ (18/100) × x = (4/5) × y

⇒ (9/50) × x = (4/5) × y

⇒ x / y = (4/5) × (50/9)

⇒ x / y = (4 × 10) / 9

⇒ x / y = 40 / 9

∴ The correct answer is 40 : 9.

Additional Information

Percentage to Fraction Conversion

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

Ratio and Proportion

If a × X = b × Y, then the ratio X : Y is equal to b : a.

Fraction to Percentage

Multiply the fraction by 100 to get the percentage value. Example: 4/5 × 100 = 80%.

The correct answer is Indira Gandhi International Airport, Delhi.

Key Points

• Indira Gandhi International Airport (IGIA), located in Delhi, was the busiest airport in India in terms of passenger traffic for the financial year 2023-2024.
• IGIA serves as the primary hub for major airlines, including Air India, Vistara, and IndiGo, connecting domestic and international destinations.
• In FY 2023-2024, IGIA handled a record-breaking number of passengers, surpassing 70 million annual passengers as per Airports Authority of India (AAI) data.
• The airport has consistently ranked among the top in terms of passenger traffic due to its strategic location, advanced infrastructure, and efficient operations.
• IGIA also features Terminal 3 (T3), one of the largest passenger terminals in the world, handling both domestic and international flights.

Additional Information

• Passenger Traffic in India
• India's aviation sector is one of the fastest-growing in the world, with a significant increase in domestic and international passenger traffic.
• As of FY 2023-2024, the Airports Authority of India (AAI) reported a steady recovery post-COVID-19, with several airports achieving pre-pandemic traffic levels.
• Delhi, Mumbai, Bengaluru, and Hyderabad airports are among the busiest in the country in terms of passenger and aircraft movement.
• Indira Gandhi International Airport Overview
• IGIA is managed by Delhi International Airport Limited (DIAL), a consortium led by GMR Group.
• The airport has three operational terminals: T1 (domestic), T2 (domestic low-cost carriers), and T3 (mixed-use for international and domestic).
• It has won several awards, including the prestigious ACI Airport Service Quality (ASQ) awards.
• Key Growth Drivers for IGIA
• Delhi's central location and connectivity to major cities within India and abroad contribute to its high passenger traffic.
• Ongoing infrastructure development, including the expansion of runways and terminals, ensures capacity to handle future growth.
• Strategic partnerships with airlines and government initiatives like the UDAN scheme play a pivotal role in its success.
• Economic Impact of IGIA
• IGIA is a significant contributor to the Indian economy, supporting millions of jobs directly and indirectly.
• The airport also serves as a hub for cargo operations, facilitating international trade and commerce.

Given interchange rules:

• ‘+’ is replaced by ‘−’.
• ‘×’ and ‘÷’ are interchanged.

The given equation is:

55 ÷ 7 + 9 × 3 + 1 = ?

After applying the interchange rules, the equation becomes:

55 × 7 − 9 ÷ 3 − 1 = ?

Now, we solve the equation following the BODMAS rule:

= 55 × 7 − 9 ÷ 3 − 1

= 385 − 3 − 1

= 382 − 1 = 381

Hence, the correct answer is "Option 2".

Shortcut Trick

For the equation 3x² − 7x + 1 = 0, identify coefficients a = 3, b = −7, c = 1.

Calculate the Discriminant (D) = b² − 4ac = (−7)² − 4(3)(1) = 49 − 12 = 37.

Apply the Quadratic Formula directly: x = (−b ± √D) / 2a.

x = (7 ± √37) / (2 × 3) = (7 ± √37) / 6.

∴ The correct answer is (7 + √37)/6 and (7 − √37)/6.

Alternate Method

Given:

Quadratic equation: 3x² − 7x + 1 = 0

Formula Used:

For a quadratic equation ax² + bx + c = 0, the roots are given by:

x = (−b ± √(b² − 4ac)) / 2a

Calculations:

Comparing 3x² − 7x + 1 = 0 with ax² + bx + c = 0:

⇒ a = 3

⇒ b = −7

⇒ c = 1

Substitute these values into the formula:

⇒ x = (−(−7) ± √((−7)² − 4 × 3 × 1)) / (2 × 3)

⇒ x = (7 ± √(49 − 12)) / 6

⇒ x = (7 ± √37) / 6

The two roots are:

⇒ x₁ = (7 + √37) / 6

⇒ x₂ = (7 − √37) / 6

∴ The correct answer is (7 + √37)/6 and (7 − √37)/6.

Additional Information

Nature of Roots (D = b² − 4ac)

If D > 0, roots are real and distinct. If D = 0, roots are real and equal. If D < 0, roots are imaginary/complex.

Sum and Product of Roots

For ax² + bx + c = 0, the sum of roots (α + β) = −b/a and the product of roots (αβ) = c/a.

Quadratic Formula

Also known as the Sridharacharya formula, it is used to find roots when factorization is difficult.

Given:

Simplify: [(24 × 6) × { {2 ÷ 2} × (18 - (12 ÷ 2)) }]

Formula used:

Follow the BODMAS rule (Brackets, Orders, Division/Multiplication, Addition/Subtraction).

Calculation:

[(24 × 6) × { {2 ÷ 2} × (18 - (12 ÷ 2)) }]

⇒ [(24 × 6) × { {1} × (18 - 6) }]

⇒ [(24 × 6) × {1 × 12}]

⇒ [(24 × 6) × 12]

⇒ 144 × 12

⇒ 1728

∴ The correct answer is option (4).

The logic followed here is,

Option 1) # = FNW, % = SAJ

For # (FNW) to KSB

For NVE to % (SAJ)

Option 2) # = FUW, % = SAJ

For # (FUW) to KSB

The pattern derived from FUW to KSB is: (+5, -2, +5).

For NVE to % (SAJ)

Option 3) # = FNW, % = SAI

For # (FNW) to KSB

For NVE to % (SAI)

Option 4) # = FNW, % = SUY

 

For # (FNW) to KSB

For NVE to % (SUY)

 

Thus, the analogy holds true only for Option 1 where the pattern (+5, +5, +5) is consistent for both pairs. 

 

Hence, the correct answer is "Option 1".

The correct answer is Biscuits.

Key Points

• Biscuits are classified as a final good because they are ready for consumption and do not require further processing.
• In economics, a final good refers to a product that is ultimately consumed by the end-user rather than being used to produce another product.
• Examples of final goods include packaged foods like biscuits, clothing, and electronics, as they are produced for direct consumption.
• Intermediate goods like sugar, wheat, and flour are used as inputs for the production of final goods but are not sold directly to consumers for immediate use.
• The categorization of goods as intermediate or final depends on their use in the economy and the stage of production.

Additional Information

• Final Goods
• These are goods that have completed the production process and are ready for sale to the end consumer.
• Final goods contribute to the calculation of a country's Gross Domestic Product (GDP) as they represent consumption and investment.
• Examples include consumer goods like cars, refrigerators, and packaged food items.
• Intermediate Goods
• Intermediate goods are products used as inputs in the production of other goods.
• They are not included in GDP to avoid double counting since their value is already embedded in the final goods they help produce.
• Examples include raw materials like steel, flour, and sugar.
• Consumer Goods vs. Capital Goods
• Consumer goods are intended for direct consumption (e.g., biscuits, clothing).
• Capital goods, such as machinery and tools, are used to produce other goods and services but are not directly consumed.
• GDP Measurement
• Only final goods and services are included in GDP calculation to measure a country's economic output.
• The inclusion of intermediate goods would lead to inflated GDP figures due to double counting.

Conditions:

If the first element is a symbol and the last a number, the codes for these two (the first and the last elements) are to be interchanged.

If the first element is an odd number and the last an even number, the first and last elements are to be coded as .

If both second and third elements are perfect squares, the third element is to be coded as the code for the second element.

Given- 3 4 9 7

The 1st element is 3 (an odd number).

The 2nd element is 4 (a perfect square).

The 3rd element is 9 (a perfect square).

The last element is 7 (an odd number).

Rule No. (1): This condition does not apply because the first element (3) is a number, not a symbol.

Rule No. (2): This condition does not apply because the last element (7) is an odd number, not an even number.

Rule No. (3): This condition applies because the second element (4) is a perfect square and the third element (9) is also a perfect square. So, the code of the third element will be the code for the second element.

Based on the applicable rule (3), the third element will be coded as the code of the second element.

The code for 3 is F.

The code for 4 is G.

The code for 9 is B.

But, due to rule (3), 9 will be coded as G (the code for 4).

The code for 7 is M.

Thus, '3 4 9 7' is coded as → F G G M.

Hence, the correct answer is "Option 3".

Given:

$\dfrac{2}{9} \times \dfrac{27}{10} + \dfrac{6}{5} - 5$

Formula used:

Basic arithmetic operations for fractions

Calculation:

$\dfrac{2}{9} \times \dfrac{27}{10} + \dfrac{6}{5} - 5$

⇒ $\dfrac{(2 \times 27)}{(9 \times 10)} + \dfrac{6}{5} - 5$

⇒ $\dfrac{54}{90} + \dfrac{6}{5} - 5$

⇒ $\dfrac{3}{5} + \dfrac{6}{5} - 5$

⇒ $\dfrac{(3+6)}{5} - 5$

⇒ $\dfrac{9}{5} - 5$

⇒ $\dfrac{9}{5} - \dfrac{25}{5}$

⇒ $\dfrac{(9-25)}{5}$

⇒ $\dfrac{-16}{5}$

∴ The correct answer is option (2).

Shortcut Trick

Effective interest rate for 3 years = 20% × 3 = 60%

Total Amount = 100% (Principal) + 60% (Interest) = 160%

Given 160% → ₹8,640, so 1% = 8640 ÷ 160 = ₹54

Interest for 2 years = 20% × 2 = 40%

Simple Interest (2 yrs) = 40 × 54 = ₹2,160

∴ The correct answer is ₹2,160.

Alternate Method

Given: Amount (A) = ₹8,640, Rate (R) = 20% p.a., Time (T₁) = 3 years, Time (T₂) = 2 years.

Formula Used: A = P(1 + RT/100) and SI = (P × R × T) / 100

⇒ Amount = P + (P × 20 × 3) / 100

⇒ 8640 = P + 0.6P

⇒ 8640 = 1.6P

⇒ P = 8640 ÷ 1.6 = ₹5,400

⇒ SI (for 2 years) = (5400 × 20 × 2) ÷ 100

⇒ SI = 54 × 40 = ₹2,160

∴ The correct answer is ₹2,160.

Additional Information

Simple Interest Property

Simple interest remains constant for every year if the principal and rate are unchanged. SI for 'n' years = n × (SI for 1 year).

Effective Rate Method

Total interest percentage = (Rate × Time)%. This can be directly added to 100% to find the Amount percentage.

Amount Formula

The total sum at the end of the period is A = P + SI. In terms of P, A = P(1 + RT/100).

Shortcut Trick

Given: sinB = √3/2 ⇒ B = 60°.

Put B = 60° in √3 cosecB + secB − 4.

⇒ √3 × (2/√3) + 2 − 4

⇒ 2 + 2 − 4 = 0.

∴ The correct answer is 0.

Alternate Method

Given: sinB = √3/2

Formula Used: cosecB = 1/sinB; secB = 1/cosB; sin²B + cos²B = 1

⇒ sinB = √3/2 ⇒ Perpendicular(P) = √3, Hypotenuse(H) = 2

⇒ Base(B) = √(H² − P²) = √(2² − (√3)²) = √(4 − 3) = 1

⇒ cosecB = H/P = 2/√3

⇒ secB = H/B = 2/1 = 2

⇒ Expression = (√3 × 2/√3) + 2 − 4

⇒ Expression = 2 + 2 − 4 = 0

∴ The correct answer is 0.

Additional Information

Trigonometric Table Values (60°)

sin60° = √3/2, cos60° = 1/2, tan60° = √3, cot60° = 1/√3, sec60° = 2, cosec60° = 2/√3.

Reciprocal Identities

sinθ = 1/cosecθ, cosθ = 1/secθ, tanθ = 1/cotθ.

Pythagorean Triplets

For a right-angled triangle, a² + b² = c². Standard triplets include (3, 4, 5), (5, 12, 13), and (1, √3, 2).

Shortcut Trick

If Curved Surface Area (CSA) is half of Total Surface Area (TSA), then CSA = Area of 2 bases.

2πrh = 2πr² ⇒ h = r.

Given height (h) = 10 cm, so radius (r) = 10 cm.

Volume = πr²h = π × 10² × 10 = 1000π cm³.

∴ The correct answer is 1000π cm³.

Alternate Method

Given: Height (h) = 10 cm; CSA = 1/2 × TSA.

Formula Used: CSA = 2πrh; TSA = 2πr(h + r); Volume = πr²h.

⇒ 2πrh = 1/2 × [2πr(h + r)]

⇒ 2πrh = πr(h + r)

⇒ 2h = h + r

⇒ 2h − h = r ⇒ r = h

⇒ r = 10 cm

⇒ Volume = π × (10)² × 10

⇒ Volume = π × 100 × 10 = 1000π cm³

∴ The correct answer is 1000π cm³.

Additional Information

Surface Area of Cylinder

Curved Surface Area (CSA) = 2πrh and Total Surface Area (TSA) = 2πr(h + r).

Volume of Cylinder

The space occupied is given by Volume = πr²h.

Ratio of CSA to TSA

The ratio is h : (h + r). In this specific case, 1 : 2 implies h = r.

The correct answer is Click the 'File' tab and choose 'Save As'.

Key Points

• To save a new workbook in MS Excel, the 'Save As' option is used to specify the file name and location.
• The 'Save As' feature is accessible by clicking the 'File' tab in the Ribbon and selecting 'Save As' from the dropdown menu.
• This method allows users to save the file in various formats, such as .xlsx, .xls, .csv, or .pdf.
• Pressing 'Ctrl + S' directly saves the workbook if it has already been named; otherwise, it opens the 'Save As' dialog for new files.
• 'Save As' ensures that the user can specify file properties like name, type, and location before saving it.

Additional Information

• File Tab in MS Excel
• The 'File' tab is part of the Ribbon interface and provides access to options like 'Save', 'Save As', 'Open', 'Close', and 'Print'.
• It also includes settings for exporting, sharing, and account management.
• Keyboard Shortcuts for Saving in MS Excel
• Pressing Ctrl + S saves the current workbook. If unsaved, it opens the 'Save As' dialog box.
• Pressing F12 directly opens the 'Save As' dialog box.
• Difference Between 'Save' and 'Save As'
• 'Save' updates an existing file without changing its name or location.
• 'Save As' creates a new file, allowing the user to specify a new name, location, or file format.
• Common File Formats in Excel
• .xlsx: Default format for Excel workbooks.
• .xls: Legacy format for older versions of Excel.
• .csv: Comma-separated values format for plain-text data.
• .pdf: Portable Document Format for non-editable sharing.

Shortcut Trick

Initial population = 3,47,900

Decade 1 increase = 50% → Multiplying factor = 1.5

Decade 2 increase = 50% → Multiplying factor = 1.5

Final population = 3,47,900 × 1.5 × 1.5 = 3,47,900 × 2.25

Calculation: 347900 × (9/4) = 86975 × 9 = 7,82,775

∴ The correct answer is 7,82,775.

Alternate Method

Given: Initial population in 1921 = 3,47,900 | Time period = 1921 to 1941 (2 decades) | Growth rate = 50% per decade.

Formula Used: Final Population = P(1 + R/100)ⁿ

⇒ Population in 1931 = 3,47,900 + 50% of 3,47,900

⇒ Population in 1931 = 3,47,900 + 1,73,950 = 5,21,850

⇒ Population in 1941 = 5,21,850 + 50% of 5,21,850

⇒ Population in 1941 = 5,21,850 + 2,60,925

⇒ Population in 1941 = 7,82,775

∴ The correct answer is 7,82,775.

Additional Information

Successive Percentage Change

When a value changes by a% and then by b%, the net effective change is (a + b + ab/100)%.

Compound Growth Formula

Population growth usually follows the compound interest formula: A = P(1 + r/100)ⁿ where n is the number of time intervals.

Percentage to Fraction Conversion

For quick calculation, 50% increase means multiplying the base value by (1 + 1/2) = 3/2 or 1.5.

Given Expression: P + Q – R ÷ S x T

P + Q: P is the sister of Q.

Q – R: Q is the father of R.

R ÷ S: R is the son of S.

S x T: S is the daughter of T.

According to the given information, Family Tree Representation:

Therefore, P is the Daughter's husband's sister of T.

Hence, the correct answer is "Option 1"

Shortcut Trick

Rate of 25% → 1/4 increase. Multiplier for next year = 5/4. Multiplier for previous year = 4/5.

Population 2 years ago = 2,60,000 × (4/5)² = 2,60,000 × 16/25 = 1,66,400.

Population 3 years ago = 1,66,400 × 4/5 = 1,33,120.

Difference = 1,66,400 − 1,33,120 = 33,280.

∴ The correct answer is 33,280.

Alternate Method

Given: Current Population = 2,60,000, Rate of Increase = 25% per annum.

Formula Used: Population n years ago = P / (1 + R/100)ⁿ

⇒ Let Population 2 years ago be P₂ and 3 years ago be P₃.

⇒ P₂ = 2,60,000 ÷ (1 + 25/100)² = 2,60,000 ÷ (1.25)²

⇒ P₂ = 2,60,000 ÷ 1.5625 = 1,66,400

⇒ P₃ = 1,66,400 ÷ (1 + 25/100) = 1,66,400 ÷ 1.25

⇒ P₃ = 1,33,120

⇒ Difference = P₂ − P₃ = 1,66,400 − 1,33,120

⇒ Difference = 33,280

∴ The correct answer is 33,280.

Additional Information

Population Growth Formula

For constant growth R%, Population after n years = P(1 + R/100)ⁿ. For decrease, use (1 − R/100).

Successive Percentage Change

The net change for two successive years with rates r1 and r2 is [r1 + r2 + (r1×r2)/100]%.

Reverse Calculation Shortcut

If population increases by x/y, to find the previous value, multiply the current value by y/(x+y).

The correct answer is Demetrius.

Key Points

• Demetrius I, also known as Demetrius Aniketos ("the Invincible"), was an Indo-Greek king who ruled in the 2nd century BCE.
• He is credited with issuing coins that featured bilingual inscriptions in Greek and Kharosthi, a script used in ancient India.
• The bilingual nature of his coins reflects his efforts to integrate Greek and Indian cultures and communicate with the diverse populations of his realm.
• Demetrius’ coins often depicted symbols such as the elephant, which was significant in Indian culture, symbolizing his connection to the region he ruled.
• He expanded his rule into northwestern India, marking the beginning of the Indo-Greek kingdom's influence in the subcontinent.

Additional Information

• Indo-Greek Kingdom:
• The Indo-Greek kingdom was established in the regions of Bactria and northwestern India following the conquests of Alexander the Great.
• The blending of Greek and Indian cultures during this period is referred to as Greco-Buddhism.
• Bilingual Coinage:
• Indo-Greek coins were unique for their use of both Greek and Indian scripts, typically Greek on the obverse and Kharosthi or Brahmi on the reverse.
• This bilingual approach was aimed at uniting the multicultural populations under their rule.
• Kharosthi Script:
• Kharosthi was an ancient script used primarily in Gandhara (modern-day Pakistan and Afghanistan) and was derived from the Aramaic script.
• It was commonly used in inscriptions and coins during the Indo-Greek period.
• Symbolism on Coins:
• Indo-Greek coins often depicted symbols like elephants, lions, and the deity Zeus to appeal to both Greek and Indian traditions.
• These symbols also demonstrated the rulers' respect for local customs and beliefs.
• Demetrius' Contribution:
• Demetrius’ reign marked the beginning of Hellenistic influence in Indian art, culture, and governance, which persisted for centuries.
• He is considered a key figure in the history of cultural exchange between Greece and India.

The logic followed here is.

Option (1) 'YW-DV':

Option (2) 'VT-AR':

Option (3) 'GE - LC':

Option (4) 'TR - YP':

Thus, option 1 is odd one.

Hence, the correct answer is "Option 1".

The logic followed here is,

Option 1) # = GIM, % = RTY

For # (GIM) to LNR

 

For MOS to % (RTY)

 

 

Option 2) # = GIM, % = RTX

For # (GIM) to LNR

 

For MOS to % (RTX)

 

Since the pattern for GIM to LNR (+5, +5, +5) is the same as the pattern for MOS to RTX (+5, +5, +5),

Option 2 is correct.

Option 3) # = GIM, % = STX

For # (GIM) to LNR

For MOS to % (STX)

Option 4) # = HIM, % = RTX

For # (HIM) to LNR

For MOS to % (RTX)

Thus, the analogy holds true only for Option 2 where the pattern (+5, +5, +5) is consistent for both pairs.

Hence, the correct answer is "Option 2".

Given: Mr. Filix starts from Point A and drives 19 km towards the South.

He then takes a left turn, drives 5 km, turns left and drives 33 km.

He then takes a left turn and drives 9 km.

He takes a final left turn, drives 14 km and stops at Point P.

Point P is at a position of 4 km West of Point A.

To return to Point A from Point P, Mr. Filix must drive 4 km in the East direction.

Hence, the correct answer is "Option 2".

The pattern followed here is.

Thus, the missing term in the series is IC59.

Hence, the correct answer is "Option 3."

Shortcut Trick

Radius (r) = Diameter ÷ 2 = 4.2 ÷ 2 = 2.1 cm.

Volume of Sphere = (4/3) × π × r³.

Using π ≈ 22/7 ⇒ Volume = (4/3) × (22/7) × 2.1 × 2.1 × 2.1.

Simplified Calculation: 4 × 22 × 0.1 × 2.1 × 2.1 = 8.8 × 4.41 = 38.808 cm³.

∴ The correct answer is 38.8 cm³.

Alternate Method

Given:

Diameter (d) = 4.2 cm

Radius (r) = d/2 = 4.2/2 = 2.1 cm

Formula Used: Volume of sphere = (4/3)πr³

Calculations:

⇒ Volume = (4/3) × (22/7) × (2.1)³

⇒ Volume = (4/3) × (22/7) × 2.1 × 2.1 × 2.1

⇒ Volume = 4 × 22 × (2.1/3) × (2.1/7) × 2.1

⇒ Volume = 88 × 0.7 × 0.3 × 2.1

⇒ Volume = 88 × 0.21 × 2.1

⇒ Volume = 88 × 0.441

⇒ Volume = 38.808 cm³

⇒ Rounding to two decimal places = 38.81 cm³ ≈ 38.8 cm³

∴ The correct answer is 38.8 cm³.

Additional Information

Surface Area of a Sphere

The total surface area of a sphere is given by the formula 4πr².

Volume of a Hemisphere

A hemisphere is half of a sphere, so its volume is (2/3)πr³.

Curved Surface Area of a Hemisphere

The CSA of a hemisphere is 2πr², and the Total Surface Area (TSA) is 3πr².

The correct answer is Only 2 and 3.

Key Points

• National Payments Corporation of India (NPCI) operates innovative payment systems and solutions in India.
• Aadhaar Enabled Payment System (AePS): Allows basic banking services using Aadhaar authentication.
• UPI Lite: A simplified version of the Unified Payments Interface (UPI) for small-value offline transactions.
• NEFT (National Electronic Funds Transfer) is operated by the Reserve Bank of India (RBI), not NPCI.
• NPCI focuses on digital payment systems like UPI, AePS, RuPay, and IMPS to enhance financial inclusion.

Additional Information

• National Payments Corporation of India (NPCI):
• Established in 2008 under the guidance of the RBI and Indian Banks' Association (IBA).
• Key initiatives include UPI, RuPay, IMPS, BHIM, and AePS.
• Aims to create robust payment infrastructure and promote digital payments in India.
• Aadhaar Enabled Payment System (AePS):
• Facilitates cash withdrawal, balance inquiry, and fund transfer using Aadhaar authentication.
• Promotes financial inclusion by enabling banking services in rural and remote areas.
• Unified Payments Interface (UPI) and UPI Lite:
• UPI enables instant fund transfers between bank accounts using mobile devices.
• UPI Lite is designed for low-value transactions, especially in offline scenarios.
• National Electronic Funds Transfer (NEFT):
• An electronic payment system for transferring funds between banks in India.
• Operated by the Reserve Bank of India (RBI) to facilitate secure and reliable fund transfers.

The correct answer is Lahore Session, 1929.

Key Points

• The resolution for Poorna Swaraj (Complete Independence) was passed during the Lahore Session of the Indian National Congress in December 1929.
• Jawaharlal Nehru presided over the session, marking a significant moment in India's freedom struggle.
• The declaration of Poorna Swaraj was officially adopted on 26th January 1930, which was later commemorated as Republic Day after independence.
• The session also decided to boycott British goods and institutions to intensify the freedom struggle.
• The demand for complete independence replaced the earlier goal of dominion status, aligning the Congress with the aspirations of the masses.

Additional Information

• Indian National Congress (INC):
• Founded in 1885, the INC played a pivotal role in India's struggle for independence.
• It served as a platform for leaders like Gandhi, Nehru, Patel, and others to mobilize the masses.
• Poorna Swaraj:
• The term means "complete independence" and symbolized the ultimate goal of the Indian freedom struggle.
• It rejected any compromise with British rule and demanded self-rule for Indians.
• 26th January:
• This date was chosen for the Poorna Swaraj declaration and later became Republic Day in 1950 when the Indian Constitution came into effect.
• Boycott Movement:
• The INC decided to boycott British goods, titles, and institutions as part of its strategy to weaken colonial rule.
• This was a continuation of the Swadeshi Movement initiated earlier during the partition of Bengal.

The logic followed here is.

Option (1) 'MP - LK':

Option (2) 'KM - HJ':

Option (3) 'NP - KM':

Option (4) 'HJ - EG':

Thus, option 1 is odd one.

Hence, the correct answer is "Option 1".

Given: There are seven people (P, Q, R, S, T, U, V) with exams on a different day of a week, from Monday to Sunday.

Q has an exam on Saturday.

Only 4 people have exams between T and U, and neither has an exam on Monday.

U has an exam after P. 

P has an exam immediately after V, and R has an exam immediately before V.

And S has an exam on Monday.

R's exam is on Wednesday. The people with exams after Wednesday are V (Thursday), P (Friday), Q (Saturday), and U (Sunday).

4 people have exams after R.

Hence, the correct answer is "Option 1".

The correct answer is Industrial Town.

Key Points

• Kanpur, located in Uttar Pradesh, is one of the prominent industrial towns in India.
• It is known for its textile, leather, and chemical industries, which contribute significantly to its economy.
• During British rule, Kanpur was a major center for cotton and woolen textiles, earning it the nickname "Manchester of the East."
• The city's leather industry is globally recognized, making Kanpur a significant hub for leather goods production and export.
• Kanpur hosts several industrial estates, fostering growth in engineering, fertilizers, and plastics sectors.

Additional Information

• Industrial Town:
• It refers to a city or town primarily focused on industrial production and manufacturing.
• Such towns typically have factories, warehouses, and industrial estates as their key features.
• These towns often experience rapid urbanization due to employment opportunities in the industrial sector.
• Other Types of Towns:
• Administrative Towns: Serve as centers for governmental administration, e.g., New Delhi.
• Recreational Towns: Focus on tourism and leisure, e.g., Shimla.
• Transfer and Distribution Towns: Act as hubs for trade and transportation, e.g., Varanasi.
• Leather Industry in Kanpur:
• Kanpur's leather industry is one of the largest in India, producing shoes, belts, bags, and saddlery goods.
• The city exports leather products to the USA, UK, and other countries, contributing to India's foreign exchange earnings.
• Manchester of the East:
• Kanpur earned this title due to its significant role in textile production during the British era.
• The city hosted major textile mills such as Lal Imli Woolen Mills and Elgin Mills.

Shortcut Trick

Let the Marked Price (MP) be 100.

Successive Multiplier = (100 − 18)% × (100 − 24)% × (100 − 18)%.

Effective Price % = 100 × 0.82 × 0.76 × 0.82.

Effective Price % = 100 × 0.511024.

Effective Price % ≈ 51.10%.

∴ The correct answer is 51.10%.

Alternate Method

Given: Three consecutive discounts d₁ = 18%, d₂ = 24%, and d₃ = 18%.

Formulas: Selling Price (SP) = MP × (1 − d₁/100) × (1 − d₂/100) × (1 − d₃/100).

⇒ Assume Marked Price = 100.

⇒ Price after 1^st discount = 100 − 18 = 82.

⇒ Price after 2^nd discount = 82 − (24% of 82) = 82 − 19.68 = 62.32.

⇒ Price after 3^rd discount = 62.32 − (18% of 62.32) = 62.32 − 11.2176 = 51.1024.

⇒ Effective Price Percentage = (Final Price ÷ MP) × 100 = 51.10%.

∴ The correct answer is 51.10%.

Additional Information

Successive Discounts

When multiple discounts are applied one after another, the net discount is calculated on the reducing balance. Formula for two discounts: a + b − (ab ÷ 100).

Effective Price

The effective price is the final amount paid by the customer after all consecutive discounts have been subtracted from the Marked Price.

Shortcut Trick

The mode is the value that appears most frequently in a data set.

Count the occurrences of each number in the given observations.

Frequency of 27 = 4 times (Highest frequency).

Frequency of 20, 24, and 32 = 2 times each.

All other numbers appear only once.

∴ The correct answer is 27.

Alternate Method

Given: Observations = 35, 27, 27, 32, 25, 24, 27, 24, 32, 20, 31, 21, 29, 22, 27, 20, 26.

Formula: Mode = Value with the maximum frequency.

⇒ Frequency of 20 = 2

⇒ Frequency of 24 = 2

⇒ Frequency of 27 = 4

⇒ Frequency of 32 = 2

⇒ Frequency of other values (21, 22, 25, 26, 29, 31, 35) = 1 each

⇒ The value 27 has the maximum frequency of 4.

The correct answer is Ctrl + Shift + M.

Key Points

• The keyboard shortcut Ctrl + Shift + M is used in MS Word 365 to decrease or remove paragraph indentation.
• This command specifically reduces the left indentation of a paragraph by 0.5 inches (default setting).
• It is particularly useful for formatting documents quickly and efficiently, especially in professional or academic writing.
• Users can repeatedly press Ctrl + Shift + M to completely remove multiple levels of indentation, if applied.

Additional Information

• Paragraph Indentation
• Paragraph indentation refers to the space added to the left margin of a paragraph.
• It helps in visually distinguishing sections of text, improving document readability.
• MS Word Keyboard Shortcuts
• Ctrl + M: Increases paragraph indentation by 0.5 inches.
• Ctrl + Shift + T: Reduces hanging indentation in a paragraph.
• Ctrl + T: Increases hanging indentation of a paragraph.
• Formatting Options in MS Word
• MS Word provides a "Paragraph" section in the "Home" tab for adjusting indentation and spacing.
• Users can also access advanced options via the "Paragraph" dialog box for precise control.
• Customizing Shortcuts
• Users can customize keyboard shortcuts in MS Word by navigating to File > Options > Customize Ribbon > Keyboard Shortcuts.
• This allows assigning new shortcuts for frequently used commands, enhancing productivity.

The correct answer is To refer to a cell or range of cells using a more descriptive and easier-to-understand name in formulas.

Key Points

• A Named Range in MS Excel allows users to assign a meaningful name to a cell or group of cells, making formulas easier to read and understand.
• It simplifies complex formulas by replacing cell references (e.g., A1:B10) with descriptive names (e.g., "SalesData").
• Named Ranges enhance productivity by reducing errors and improving formula accuracy.
• They can be used across worksheets within the same workbook, enabling consistent references.
• Named Ranges are especially useful in dynamic reports and dashboards for automating calculations and data management.

Additional Information

• How to Create Named Ranges:
• Select the cell or range of cells you want to name.
• Go to the "Formulas" tab in the ribbon and click "Define Name."
• Provide a unique name and click "OK."
• Rules for Naming Ranges:
• Names cannot include spaces or special characters; use underscores (_) instead.
• Names must start with a letter, underscore, or backslash.
• Names are case-insensitive but must be unique within the workbook.
• Dynamic Named Ranges:
• Dynamic Named Ranges adjust automatically as data is added or removed.
• They can be created using Excel functions like OFFSET or INDEX.
• Applications of Named Ranges:
• Used in data validation rules for defining allowable inputs.
• Helpful in creating custom formulas for financial modeling and statistical analysis.
• Facilitates easier collaboration by making formulas more intuitive for other users.

Shortcut Trick

Since DE || AC, ΔBDE is similar to ΔBAC.

The ratio of their corresponding sides is BD : BA = 10 : (10 + 17) = 10 : 27.

Therefore, the ratio of their areas is Area(ΔBDE) : Area(ΔBAC) = 10² : 27² = 100 : 729.

Area of trapezium ADEC = Area(ΔBAC) − Area(ΔBDE) = 729 − 100 = 629.

Thus, the ratio of Area(ΔBDE) to Area(ADEC) is 100 : 629.

∴ The correct answer is 100:629.

Alternate Method

Given:

In ΔABC, DE || AC.

D is a point on AB and E is a point on BC.

BD = 10 cm

AD = 17 cm

Formula Used:

If two triangles are similar, the ratio of their areas is equal to the square of the ratio of their corresponding sides.

Area of trapezium ADEC = Area(ΔABC) − Area(ΔBDE)

Calculations:

First, find the total length of side AB:

⇒ AB = BD + AD

⇒ AB = 10 + 17 = 27 cm

Since DE || AC, we have:

⇒ ∠BDE = ∠BAC (Corresponding angles)

⇒ ∠BED = ∠BCA (Corresponding angles)

⇒ ΔBDE ∼ ΔBAC (By AA similarity criterion)

Now, the ratio of the areas of these similar triangles is:

⇒ Area(ΔBDE) / Area(ΔBAC) = (BD / AB)²

⇒ Area(ΔBDE) / Area(ΔBAC) = (10 / 27)²

⇒ Area(ΔBDE) / Area(ΔBAC) = 100 / 729

Let the area of ΔBDE be 100x and the area of ΔBAC be 729x.

The area of trapezium ADEC is given by:

⇒ Area(ADEC) = Area(ΔBAC) − Area(ΔBDE)

⇒ Area(ADEC) = 729x − 100x = 629x

Now, find the ratio of the area of ΔBDE to the area of trapezium ADEC:

⇒ Ratio = Area(ΔBDE) / Area(ADEC)

⇒ Ratio = 100x / 629x = 100 / 629

Thus, the required ratio is 100:629.

∴ The correct answer is 100:629.

Additional Information

Basic Proportionality Theorem (Thales Theorem)

If a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio: BD/AD = BE/EC.

Area Ratio of Similar Triangles

For any two similar triangles, the ratio of their areas is equal to the square of the ratio of any of their corresponding parts (sides, altitudes, medians, or angle bisectors).

Properties of Trapezium formed by Parallel Line

The area of the trapezium ADEC is always equal to the difference between the areas of the larger triangle ABC and the smaller triangle BDE.

The logic followed here is:

Logic: Second number = First number + 3.2**.**

Third number = Second number + 3.2

Let's verify this logic with the given sets:

For, (15, 18.2, 21.4)

⇒ First to Second: 15 + 3.2 = 18.2.

⇒ Second to Third: 18.2 + 3.2 = 21.4.

Here, the logic followed.

For, (19, 22.2, 25.4)

⇒ First to Second: 19 + 3.2 = 22.2.

⇒ Second to Third: 22.2 + 3.2 = 25.4.

Here, the logic followed.

Now, let's check the options based on this logic:

Option 1) (28, 30.2, 32.4)

⇒ First to Second: 28 + 3.2 = 31.2. (Given Second number is 30.2, 30.2 ≠ 31.2)

Here, logic not followed.

Option 2) (43, 46.2, 48.4)

⇒ First to Second: 43 + 3.2 = 46.2. (Matches)

⇒ Second to Third: 46.2 + 3.2 = 49.4. (Given Third number is 48.4, 48.4 ≠ 49.4)

Here, logic not followed.

Option 3) (24, 27.2, 30.4)

⇒ First to Second: 24 + 3.2 = 27.2. (Matches)

⇒ Second to Third: 27.2 + 3.2 = 30.4. (Matches)

Here, logic followed.

Option 4) (36, 39.2, 41.4)

⇒ First to Second: 36 + 3.2 = 39.2. (Matches)

⇒ Second to Third: 39.2 + 3.2 = 42.4. (Given Third number is 41.4, 41.4 ≠ 42.4)

Here, logic not followed.

Hence, the correct answer is "Option 3".

The correct answer is ProPublica.

Key Points

• ProPublica, an independent, nonprofit newsroom, won the Pulitzer Prize for Public Service in 2025.
• The Pulitzer Prize for Public Service is considered the most prestigious among the Pulitzer categories, awarded for impactful investigative journalism.
• ProPublica is known for its focus on stories that expose abuses of power and injustices, often leading to significant reforms.
• Its winning entry in 2025 highlighted investigations into systemic issues, including government accountability and corporate malfeasance.
• ProPublica's investigative journalism is funded through donations and grants, allowing it to remain independent and free of corporate or political influence.

Additional Information

• Pulitzer Prize:
• The Pulitzer Prizes are awards for achievements in newspaper, magazine, online journalism, literature, and musical composition within the United States.
• Established in 1917 by provisions in the will of Joseph Pulitzer, a Hungarian-American journalist and newspaper publisher.
• The awards are administered by Columbia University in New York City.
• Public Service is the only Pulitzer Prize category where the winner receives a gold medal instead of cash.
• Investigative Journalism:
• Investigative journalism involves in-depth reporting to uncover information often hidden from the public.
• It requires significant research and fact-checking to ensure the accuracy of the findings.
• This type of journalism often tackles issues like corruption, abuses of power, or systemic failures.
• It plays a crucial role in holding governments, corporations, and institutions accountable.
• ProPublica's Approach:
• ProPublica collaborates with other newsrooms to maximize the impact of its investigations.
• Its work often leads to legislative changes, policy reforms, and increased public awareness.
• ProPublica publishes its investigations online for free, making them accessible to a broad audience.
• It adheres to the highest standards of journalistic integrity and transparency.
• Importance of Public Service Journalism:
• Public service journalism aims to inform citizens and empower them to make educated decisions.
• It highlights pressing societal issues, encouraging public discourse and action.
• This form of journalism is vital for maintaining a well-functioning democracy.
• It often requires significant resources and commitment due to the complexity and sensitivity of the topics involved.

Shortcut Trick

Loss of 10% means SP₁ is 90% of CP.

Gain of 24% means SP₂ is 124% of CP.

Using the unitary method: 90% ⇒ 225.

1% ⇒ 225 ÷ 90 = 2.5.

124% ⇒ 2.5 × 124 = 310.

∴ The correct answer is 310.

Alternate Method

Given: Selling Price (SP₁) = 225, Loss% = 10%, Required Gain% = 24%.

Formulas: CP = SP × 100 ÷ (100 − Loss%); New SP = CP × (100 + Gain%) ÷ 100.

⇒ First, find the Cost Price (CP): CP = 225 × 100 ÷ (100 − 10) = 225 × 100 ÷ 90 = 250.

⇒ Now, find the New Selling Price (SP₂) for 24% gain: New SP = 250 × (100 + 24) ÷ 100.

⇒ New SP = 250 × 124 ÷ 100 = 2.5 × 124 = 310.

∴ The correct answer is 310.

Additional Information

Direct Ratio Method

When CP is constant, SP is directly proportional to (100 ± Profit/Loss%). Ratio SP₁ : SP₂ = (100 − L₁%) : (100 + P₂%).

Cost Price Base

Profit and Loss percentages are always calculated on the Cost Price (CP) unless stated otherwise in the question.

Shortcut Trick

Ratio of Men : Women : Children = 20 : 30 : 50 = 2 : 3 : 5.

Total weighted sum = (2 × 50) + (3 × 40) + (5 × 40) = 100 + 120 + 200 = 420.

Average weight of group = 420 ÷ (2 + 3 + 5) = 42 kg.

∴ The correct answer is 42 kg.

Alternate Method

Given:

Percentage of Men = 20%, Women = 30%.

Average weights: Men = 50 kg, Women = 40 kg, Children = 40 kg.

Formula:

Average Weight = (Total Weight of all People) ÷ (Total Number of People)

Calculations:

⇒ Percentage of Children = 100% − (20% + 30%) = 50%

⇒ Let total number of people in the group = 100

⇒ Number of Men = 20, Women = 30, Children = 50

⇒ Total weight = (20 × 50) + (30 × 40) + (50 × 40)

⇒ Total weight = 1000 + 1200 + 2000 = 4200 kg

⇒ Average weight of the group = 4200 ÷ 100 = 42 kg

∴ The correct answer is 42 kg.

Additional Information

Weighted Average

It is the average of a data set where different values have different levels of importance or frequency. Formula: Average = (n₁w₁ + n₂w₂ + ...) ÷ (n₁ + n₂ + ...).

Deviation Method

Pick an assumed average (e.g., 40) and calculate the net deviation. Here, 20% are +10 above 40, so Net Deviation = 20 × 10 = 200. Final Average = 40 + (200 ÷ 100) = 42 kg.

Shortcut Trick

Let A and B be present ages.

Equation 1: 6A + 4B = 156 → 3A + 2B = 78

Equation 2: 2B − 9A = 30 → 2B = 9A + 30

Substitute 2B in Eq 1: 3A + (9A + 30) = 78 → 12A = 48 → A = 4 years.

Then 2B = 9(4) + 30 = 66 → B = 33 years.

Sum of ages after 9 years = (4 + 33) + (9 × 2) = 37 + 18 = 55 years.

∴ The correct answer is 55 years.

Alternate Method

Given:

6A + 4B = 156 ... (i)

2B − 9A = 30 ... (ii)

Calculations:

⇒ Divide (i) by 2: 3A + 2B = 78

⇒ From (ii): 2B = 30 + 9A

⇒ Substitute in simplified (i): 3A + (30 + 9A) = 78

⇒ 12A = 48

⇒ A = 4 years

⇒ 2B = 30 + 9(4) = 66

⇒ B = 33 years

⇒ Present sum = 4 + 33 = 37 years

⇒ Sum 9 years later = 37 + (9 + 9) = 55 years

∴ The correct answer is 55 years.

Additional Information

Linear Equations in Two Variables

Solving for unknown ages using substitution or elimination methods based on given conditions.

Age Sum Transformation

If there are 'n' persons, the sum of their ages after 't' years increases by n × t.

Ratio of Ages

The difference between the ages of two people always remains constant over time.

The correct answer is The Chief Justice of India.

Key Points

• Article 124(2) of the Indian Constitution mandates the President of India to consult the Chief Justice of India (CJI) while appointing judges to the Supreme Court.
• The practice of consultation with the CJI ensures a system of checks and balances in the judicial appointment process.
• This consultation is binding on the President, as established by the Supreme Court’s judgments in the Second Judges’ Case (1993) and the Third Judges’ Case (1998).
• The collegium system, comprising the CJI and senior judges of the Supreme Court, plays a significant role in recommending names for judicial appointments.
• The President, while consulting the CJI, does not act solely on their advice but also takes into account the recommendations made by the Supreme Court Collegium.

Additional Information

• Collegium System:
• It is a system used for the appointment and transfer of judges in the Supreme Court and High Courts of India.
• The collegium comprises the CJI and the four senior-most judges of the Supreme Court.
• It was introduced through the Second Judges’ Case (1993), which gave primacy to the judiciary over the executive in judicial appointments.
• Second and Third Judges’ Cases:
• The Second Judges’ Case (1993) established the principle that the Chief Justice of India’s opinion holds primacy in judicial appointments.
• The Third Judges’ Case (1998) clarified the role of the collegium and expanded its composition to include four senior-most judges along with the CJI.
• Article 124 of the Indian Constitution:
• It deals with the establishment and composition of the Supreme Court, including the appointment of judges.
• Clause (2) of Article 124 specifies the consultation process for appointing judges.
• Role of the President:
• The President appoints Supreme Court judges based on the recommendations of the collegium.
• However, the President can seek clarification or reconsideration of the recommendation, but this is rare and usually non-binding.

Shortcut Trick

Fourth proportional to 7, 5, 14 is (5 × 14) ÷ 7 = 10.

Third proportional to A and 10 is 10² ÷ A = 100/A.

Given: 10 = 100/A ⇒ A = 10.

∴ The correct answer is 10.

Alternate Method

Given: Numbers for fourth proportional are 7, 5, 14. Numbers for third proportional are A and 10.

Formula Used: Fourth proportional (x) to a, b, c is given by x = (b × c) / a. Third proportional (y) to a, b is given by y = b² / a.

Calculations:

⇒ Let the fourth proportional be x.

⇒ 7 / 5 = 14 / x ⇒ x = (5 × 14) / 7 = 10.

⇒ Let the third proportional be y. Here y = x = 10.

⇒ A / 10 = 10 / y ⇒ A / 10 = 10 / 10.

⇒ A / 10 = 1 ⇒ A = 10.

∴ The correct answer is 10.

Additional Information

Mean Proportional

The mean proportional between two numbers a and b is √(a × b).

Continued Proportion

If a, b, c are in continued proportion, then a/b = b/c, which implies b² = ac.

Ratio and Proportion Properties

Product of extremes = Product of means. In a : b :: c : d, then a × d = b × c.

The logic followed here is:

Thus, the missing number in the series is 508.

Hence, the correct answer is "Option 2".

Shortcut Trick

Total Money Paid = (Number of dolls) × (Rate per doll)

Multiply (4x − 3y) and (x + y).

Term by term: 4x² + 4xy − 3xy − 3y² = 4x² + xy − 3y².

∴ The correct answer is ₹(4x² + xy − 3y²).

Alternate Method

Given:

Number of dolls = (4x − 3y)

Rate per doll = ₹(x + y)

Formula Used:

Total Cost = Quantity × Price

Calculations:

⇒ Total Money = (4x − 3y) × (x + y)

⇒ Total Money = 4x(x + y) − 3y(x + y)

⇒ Total Money = (4x × x) + (4x × y) − (3y × x) − (3y × y)

⇒ Total Money = 4x² + 4xy − 3xy − 3y²

⇒ Total Money = 4x² + xy − 3y²

∴ The correct answer is ₹(4x² + xy − 3y²).

Additional Information

Algebraic Multiplication

When multiplying two binomials (a + b) and (c + d), use the distributive property: a(c + d) + b(c + d) = ac + ad + bc + bd.

Like Terms

Only terms with the exact same variables and exponents (like 4xy and −3xy) can be added or subtracted to simplify the expression.

Law of Exponents

During multiplication of same bases, powers are added: x^m × xⁿ = x^m+n. For example, x × x = x¹⁺¹ = x².

Option 1) # = SFR, % = POS

For # (SFR) to QSO

 

For XZV to % (POS)

 

Option 2) # = TVR, % = UWS

For # (TVR) to QSO

 

For XZV to % (UWS)

 

Since the pattern for TVR to QSO (-3, -3, -3) is the same as the pattern for XZV to UWS (-3, -3, -3),

Option 2 is correct.

Option 3) # = TUR, % = UET

For # (TUR) to QSO

For XZV to % (UET)

Option 4) # = SVR, % = UWU

For # (SVR) to QSO

For XZV to % (UWU)

 

Hence, the correct answer is "Option 2".

Given:

1 is added to each odd digit and 2 is subtracted from each even digit in the number 7418536.

The new number formed is 8226644.

The digits 2, 6, and 4 appear more than once.

Thus, three digits appear more than once.

Hence, the correct answer is "Option 2".

Given series:

(Left) 7 € 2 5 3 ® 8 © 4 € 9 3 € 5 # % * 3 4 7 $ 1 (Right)

Condition to be checked:

Number → Symbol → Number

7 € 2 5 3 ® 8 © 4 € 9 3 € 5 # % * 3 4 7 7 $ 1

There are six such symbols in the above arrangement (7 € 2, 3 ® 8,  8 © 4, 4 € 9, 3 € 5, 7 $ 1).

Hence, the correct answer is "Option 4".

Shortcut Trick

Let the HCF be x.

Numbers are x, 11x, and 19x.

LCM of (1, 11, 19) × HCF = Given LCM

Since 1, 11, and 19 are coprime, their LCM is 1 × 11 × 19 = 209.

209 × x = 8778 ⇒ x = 8778 ÷ 209 = 42.

∴ The correct answer is 42.

Alternate Method

Given: Ratio of three numbers = 1 : 11 : 19 and LCM = 8778.

Formula: LCM of numbers = HCF × (Product of ratios if they are coprime).

⇒ Let the numbers be 1x, 11x, and 19x where x is the HCF.

⇒ LCM (x, 11x, 19x) = x × LCM (1, 11, 19)

⇒ Since 1, 11, and 19 have no common factors, LCM = x × 1 × 11 × 19 = 209x.

⇒ 209x = 8778

⇒ x = 8778 ÷ 209

⇒ x = 42

∴ The correct answer is 42.

Additional Information

LCM and HCF Relationship

For two numbers a and b, HCF(a, b) × LCM(a, b) = a × b. This does not directly apply to three or more numbers.

Coprime Numbers

If numbers are coprime, their HCF is 1 and their LCM is the product of the numbers.

Ratio Property

If the ratio of numbers is a:b:c and their HCF is k, then the numbers are ak, bk, and ck.

The correct answer is 100 Hz.

Key Points

• The relationship between frequency and period is defined as Frequency = 1 / Period.
• A sound wave with a period of 0.01 seconds has a frequency calculated as 1 / 0.01 = 100 Hz.
• Frequency is measured in Hertz (Hz), which represents the number of cycles per second.
• Sound waves with a frequency of 100 Hz fall within the range of human hearing, typically between 20 Hz to 20,000 Hz.
• The period and frequency are inversely related—if the period is short, the frequency is high, and vice versa.

Additional Information

• Frequency:
• Frequency refers to the number of oscillations or cycles a wave completes in one second.
• It is measured in Hertz (Hz), where 1 Hz equals one cycle per second.
• Period:
• The period is the time taken for one complete cycle of a wave.
• It is expressed in seconds and is the reciprocal of frequency.
• Sound Waves:
• Sound waves are longitudinal waves that travel through a medium (air, water, solids).
• They consist of compressions and rarefactions caused by vibrating objects.
• Human Hearing Range:
• Humans can typically hear frequencies ranging from 20 Hz to 20,000 Hz.
• Frequencies below 20 Hz are called infrasonic, and frequencies above 20,000 Hz are ultrasonic.