The correct answer is Arabian Sea.

Key Points

• The Arabian Sea is a part of the northern Indian Ocean, bounded by the Indian subcontinent on the east, the Arabian Peninsula on the west, and the Horn of Africa on the southwest.
• The region is a crucial route for global maritime trade and is often prone to piracy activities, especially near the Gulf of Aden and Somali waters.
• The Indian Navy plays a significant role in ensuring the security of maritime trade routes in this area, conducting regular anti-piracy operations to safeguard international shipping.
• Wing Commander Akshay Saxena played a pivotal role in these operations, contributing to the safety and security of maritime activities in the Arabian Sea.
• Due to its strategic importance, the Arabian Sea has been a focus area for international naval coalitions combating piracy and ensuring the free movement of trade.
• India's proactive role in anti-piracy operations in the Arabian Sea highlights its commitment to global maritime security.

 Additional Information

• Bay of Bengal
• The Bay of Bengal is the northeastern part of the Indian Ocean, bordered by India and Sri Lanka to the west, Bangladesh to the north, and Myanmar and the Andaman and Nicobar Islands to the east.
• It is primarily known for its cyclonic activities and is less prone to piracy compared to the Arabian Sea.
• The region is significant for fishing, shipping routes, and energy exploration.
• Gulf of Thailand
• The Gulf of Thailand is situated in Southeast Asia, bordered by Thailand, Cambodia, and Vietnam.
• It is primarily known for its tourism and fishing activities, rather than piracy-related issues.
• The region supports major economies in Southeast Asia through its marine resources.
• Andaman Sea
• The Andaman Sea lies to the southeast of the Bay of Bengal and is bordered by the Andaman and Nicobar Islands, Myanmar, and Thailand.
• It is known for marine biodiversity and its role as a route for regional maritime trade.
• While piracy is rare in this region, it is monitored for illegal fishing and smuggling activities.

Given Table:

According to the given condition:

Given: 398*

Here, no rule applies.

3 → coded as C

9 → coded as N

8 → coded as B 

* → coded as S

So, 398* → Coded as CNBS

Hence, "Option 3" is the correct answer.

The logic followed here is:

Given: #: DZT :: QMG: %

Option 1) ​# = OYV, % = PYT → OYV: DZT :: QMG: PYT

Option 2) # = YPG, % = KUL → YPG: DZT :: QMG: KUL

​

Option 3) # = ZTY, % = VMH → ZTY: DZT :: QMG: VMH

Option 4) # = YUO, % = VRL → YUO: DZT :: QMG: VRL

Hence, "Option 4" is the correct answer.

Shortcut Trick Let the longer side be L and the shorter side be L − 21. Given: Area = 5 × Perimeter L(L − 21) = 5 × 2(L + L − 21) ⇒ L2 − 21L = 10(2L − 21) L2 − 21L = 20L − 210 ⇒ L2 − 41L + 210 = 0 By factoring: (L − 35)(L − 6) = 0. Since L > 21, L = 35. ∴ The correct answer is 35 cm.

Alternate Method Given: Let longer side (l) = x cm Then shorter side (b) = (x − 21) cm Formula Used: Area of Rectangle = l × b Perimeter of Rectangle = 2(l + b)

Calculations: ⇒ Area = 5 × Perimeter ⇒ x(x − 21) = 5 × [2(x + x − 21)] ⇒ x2 − 21x = 10(2x − 21) ⇒ x2 − 21x = 20x − 210 ⇒ x2 − 41x + 210 = 0 ⇒ x2 − 35x − 6x + 210 = 0 ⇒ x(x − 35) − 6(x − 35) = 0 ⇒ (x − 35)(x − 6) = 0 ⇒ x = 35 or x = 6 ⇒ Since b = x − 21, x must be greater than 21. ∴ x = 35. ∴ The correct answer is 35 cm.

Additional Information Properties of Rectangle A rectangle is a quadrilateral with four right angles. Opposite sides are equal and parallel. Diagonal length = √(l2 + b2). Quadratic Roots For x2 − (Sum of roots)x + (Product of roots) = 0, the roots are found by splitting the middle term or using the formula. Area and Perimeter Relations The numerical equality of area and perimeter (or their multiples) is a common geometric problem solved using algebraic equations.

The Correct answer is Sambhar Lake

Key Points

• Sambhar Lake is the largest inland saline wetland in India.
• It is located in the state of Rajasthan, near the towns of Sambhar, Jaipur, and Ajmer.
• The lake covers an area of around 190 to 230 square kilometers, depending on the season.
• Sambhar Lake is a major source of salt production in India, contributing significantly to the salt industry.
• The lake is fed by several rivers, including the Mendha, Rupangarh, Khari, and Khandela rivers.
• It is recognized as a Ramsar site, which designates it as a wetland of international importance.
• The lake is also a key ecological habitat for migratory birds, including the flamingos, pelicans, and storks.
• The saline nature of the lake is due to the high concentration of salt deposits formed over time.
• Sambhar Lake has significant cultural and religious importance, being mentioned in ancient Indian texts like the Mahabharata.

 Additional Information

• Wular Lake
• Wular Lake is one of the largest freshwater lakes in India.
• It is located in the state of Jammu and Kashmir.
• The lake is fed by the Jhelum River and is important for fisheries and agriculture.
• It plays a crucial role in maintaining the hydrological balance of the region.
• Pulicat Lake
• Pulicat Lake is a brackish water lagoon located on the border of Andhra Pradesh and Tamil Nadu.
• It is the second-largest lagoon in India after the Chilika Lake.
• The lake is known for its bird sanctuary, which attracts migratory birds like flamingos.
• Chilika Lake
• Chilika Lake is the largest coastal lagoon in India and is located in the state of Odisha.
• It is a major habitat for aquatic life and migratory birds.
• The lake is designated as a Ramsar site and is known for its rich biodiversity.

The logic followed here is:

PNQ : QQO

And,

UQR : VTP

​Similarly,

Option 1) ​OHM : PKK

Hence, "Option 1" is the correct answer.

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

According to the question,

Required condition: Number - Symbol - Number

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

Thus, there are more than three such symbols which are immediately preceded by a number and also immediately followed by another number.

Hence, "Option 3" is the correct answer.

Given: Seven people, D, E, F, G, L, M and N, are sitting in a row, facing north. 

1) Only M sits to the left of N.

2) Only four people sit between M and L. 

3) Only F sits between G and D, and G is not an immediate neighbour of L. 

After positioning F, G and D only one position is left which will be occupied by the only person left i.e. E.

Thus, E sits at the extreme right of the line.

Hence, "Option 1" is the correct answer.

The Correct answer is Option 2.

Key Points

• The International Monetary Fund (IMF) is a global organization that provides economic forecasts and policy advice to its member countries.
• In its April 2025 forecast, the IMF projected the US GDP growth rate for 2025 to be 0.018 or 1.8%.
• The IMF’s forecasts are crucial as they provide insights into the global economic outlook and influence policy decisions worldwide.
• The projection reflects a moderate growth trend for the United States economy, considering factors such as macroeconomic policies, global trade dynamics, inflation, and labor market conditions.
• This growth rate is indicative of a stable but cautious economic recovery, potentially impacted by external factors like geopolitical tensions, supply chain disruptions, or monetary policy adjustments by the Federal Reserve.
• Such projections play a significant role in helping governments, businesses, and investors plan their strategies and assess risks in the economic environment.
• The accuracy of IMF forecasts depends on continuous monitoring and updates based on real-time economic indicators.

 Additional Information

• About the IMF
• The IMF was established in 1944 during the Bretton Woods Conference and officially began operations in 1945.
• The IMF's headquarters is located in Washington, D.C., United States.
• It has 190 member countries and works to foster global monetary cooperation, secure financial stability, facilitate international trade, promote high employment and sustainable economic growth, and reduce poverty.
• The IMF provides economic analysis and forecasts through reports such as the World Economic Outlook (WEO).
• Incorrect Options
• Options like 0.025, 0.034, and 0.037 are incorrect as they do not align with the IMF's official April 2025 forecast for US GDP growth.

Given Table:

According to the given condition:

Given: 5#64%

Here, I rule applies i.e. first element is a number and the last a symbol.

5 → coded as G

# → coded as N

6 → coded as P 

4 → coded as K

% → coded as A

So, 5#64% → Coded as GNPKA.

Hence, "Option 2" is the correct answer.

Shortcut Trick

A number is divisible by 81 if the sum of its digits is divisible by 81 (for very large numbers) or if it is a multiple of 81.

More simply, any number divisible by 81 must also be divisible by 9 (Sum of digits must be a multiple of 9).

Check sum of digits for 5265: 5 + 2 + 6 + 5 = 18. Since 18 is divisible by 9, check 5265 ÷ 81.

5265 ÷ 81 = 65.

∴ The correct answer is 5265.

Alternate Method

Given: Numbers (1) 5232, (2) 5854, (3) 5265, (4) 4678.

Formula Used: Divisibility rule of 81. A number is divisible by 81 if the quotient is an integer when divided by 81.

⇒ Option 1: 5232 ÷ 81 ≈ 64.59 (Not divisible)

⇒ Option 2: 5854 ÷ 81 ≈ 72.27 (Not divisible)

⇒ Option 3: 5265 ÷ 81 = 65 (Exactly divisible)

⇒ Option 4: 4678 ÷ 81 ≈ 57.75 (Not divisible)

∴ The correct answer is 5265.

Additional Information

Divisibility by 9

A number is divisible by 9 if the sum of its digits is divisible by 9.

Divisibility by 3

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

Composite Divisibility

If a number is divisible by n^x, it must also be divisible by n. Here, 81 = 3⁴ = 9², so it must be divisible by 3 and 9.

The Correct answer is The first period contains 8 elements.

Key Points

• The modern periodic table arranges elements based on their atomic numbers in horizontal rows called periods and vertical columns called groups.
• The first period of the modern periodic table contains only two elements: Hydrogen and Helium.
• This is because the first energy level (shell) can hold a maximum of two electrons.
• Thus, the statement that the first period contains 8 elements is incorrect.
• Subsequent periods contain more elements due to the increasing capacity of energy levels to hold electrons.
• For example, the second period contains 8 elements, corresponding to the filling of the 2s and 2p orbitals.
• The periodic table is divided into blocks based on the sub-shells being filled (s, p, d, f blocks).
• The placement of elements reflects their properties and provides a systematic way to study chemical behavior.

 Additional Information

• Lanthanoids and actinoids are placed in separate panels at the bottom
• Lanthanoids and actinoids are the f-block elements of the periodic table.
• They are placed separately to maintain the structure and readability of the table.
• Lanthanoids are elements with atomic numbers 57 to 71, while actinoids are elements with atomic numbers 89 to 103.
• These elements exhibit unique electronic configurations and properties, such as their use in magnets, lasers, and nuclear reactors.
• Groups are the vertical columns, and periods are horizontal rows
• The modern periodic table has 18 groups and 7 periods.
• Groups are vertical columns where elements have similar valence electron configurations and chemical properties.
• Periods are horizontal rows representing elements with increasing atomic numbers.
• For example, elements in Group 1 are the alkali metals, while those in Group 17 are the halogens.
• The second and third periods each contain 8 elements
• The second period contains elements from Lithium to Neon, corresponding to the filling of 2s and 2p orbitals.
• The third period contains elements from Sodium to Argon, corresponding to the filling of 3s and 3p orbitals.
• This pattern reflects the quantum mechanical arrangement of electrons in atoms.

Shortcut Trick

Apply the Empirical Formula: Mode = 3 × Median − 2 × Mean.

Substitute the given values: Mode = 3(53) − 2(42).

Mode = 159 − 84 = 75.

∴ The correct answer is 75.

Alternate Method

Given:

Mean of the data = 42

Median of the data = 53

Formula Used:

The empirical relationship between the measures of central tendency is:

Mode = 3 × Median − 2 × Mean

Calculations:

⇒ Mode = 3 × 53 − 2 × 42

⇒ Mode = 159 − 84

⇒ Mode = 75

∴ The correct answer is 75.

Additional Information

Symmetrical Distribution

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

Skewed Distribution

For a moderately skewed distribution, the empirical formula provides an approximate relationship: Mode ≈ 3 × Median − 2 × Mean.

Given number: 1865374

According to the question, 

The third digit from the left in the new number → 5

Hence, the correct answer is "Option 2".

The logic followed here is:

Option 1) QKHC                                                        

Option 2) FZWR                                                          

Option 3) WQNJ                                                          

Option 4) KEBW     

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

Hence, the correct answer is "Option 3"

The logic followed here is:

Given:

(19, 39, 44)

⇒ 19 × 2 + 1 → 38 + 1 = 39

⇒ 39 + 5 = 44

And,

(13, 27, 32)

⇒ 13 × 2 + 1 = 26 + 1 = 27

⇒ 27 + 5 = 32

So, checking each option one by one:

Option 1) (24, 45, 50)

⇒ 24 × 2 + 1 → 48 + 1 = 49 ≠ 45

⇒ 45 + 5 = 50

Option 2) (35, 61, 66)

⇒ 35 × 2 + 1 → 70 + 1 = 71 ≠ 61

⇒ 61 + 5 = 66

Option 3) (29, 49, 54)

⇒ 29 × 2 + 1 → 58 + 1 = 59 ≠ 49

⇒ 49 + 5 = 54

Option 4) (11, 23, 28)

⇒ 11 × 2 + 1 → 22 + 1 = 23

⇒ 23 + 5 = 28

Thus, out of all '(11, 23, 28)' follows the same logic.

Hence, the correct answer is "Option 4".

Given: Seven friends, I, J, K, L, M, N and R, are sitting in a row facing north.

1) No one sits to the right of M.

2) Only three people sit between M and R.

3) Only two people sit between R and L. 

4) K sits third to the left of I.

5) J sits to the immediate right of I. 

After positioning I, J and K only one position is left which will be occupied by the only person left i.e. N.

Thus, three people sit between N and L.

Hence, "Option 1" is the correct answer.

Shortcut Trick

Time taken by Pump (A) = 6 hours

Time taken by Pump + Leak (A + B) = 7.5 hours

Emptying time for Leak = (XY) ÷ (Y − X)

⇒ (6 × 7.5) ÷ (7.5 − 6) = 45 ÷ 1.5 = 30 hours

∴ The correct answer is 30 hr.

Alternate Method

Given: Filling time = 6 hr, Filling with leak = 7.5 (15/2) hr.

Formula Used: Total Work = LCM of time; Efficiency = Work ÷ Time.

⇒ Efficiency of Pump (A) = 5 units/hr

⇒ Efficiency of Pump + Leak (A + B) = 4 units/hr

⇒ Efficiency of Leak (B) = 4 − 5 = −1 unit/hr (negative sign denotes emptying)

⇒ Time taken by Leak to empty the tank = Total Work ÷ Efficiency of B

⇒ 30 ÷ 1 = 30 hours

∴ The correct answer is 30 hr.

Additional Information

Pipes and Cisterns Concept

Efficiency of an inlet pipe is taken as positive, while the efficiency of an outlet pipe (leak) is taken as negative.

Net Efficiency

If two pipes A and B work together, net efficiency = Efficiency of A + Efficiency of B. Total time = Total Work ÷ Net Efficiency.

Work-Time Relation

Time taken to complete a task is inversely proportional to the efficiency of the worker or pipe.

Shortcut Trick

Identify Leap Year: 2024 is a leap year (366 days).

Total days = 20 (Feb) + 31 (Mar) + 10 (Apr) = 61 days.

Interest Calculation: Interest = (3000 × 6 × 61/366) / 100

Since 6 × 61 = 366, Interest = 3000 / 100 = 30.

∴ The correct answer is ₹30.

Alternate Method

Given:

Principal (P) = ₹3,000

Rate (R) = 6% per annum

Time period = 9 February 2024 to 10 April 2024

Formula Used:

Simple Interest (SI) = (P × R × T) / 100

Calculations:

⇒ Number of days in February = 29 − 9 = 20 days (2024 is a leap year)

⇒ Number of days in March = 31 days

⇒ Number of days in April = 10 days

⇒ Total Days = 20 + 31 + 10 = 61 days

⇒ Time (T) in years = 61 / 366 years

⇒ SI = (3000 × 6 × (61/366)) / 100

⇒ SI = (3000 × 6 × 61) / (100 × 366)

⇒ SI = (3000 × 366) / (100 × 366)

⇒ SI = 3000 / 100

⇒ SI = ₹30

∴ The correct answer is ₹30.

Additional Information

Leap Year Calculation

A year is a leap year if it is divisible by 4. If it is a century year (ending in 00), it must be divisible by 400. Leap years have 366 days.

Day Counting Rule

In banking and financial interest calculations, normally the day of deposit is excluded and the day of withdrawal is included (or vice versa).

Simple Interest vs Compound Interest

Simple interest is calculated only on the principal, while compound interest is calculated on the principal plus accumulated interest from previous periods.

Shortcut Trick

Let the Cost Price (CP) of 1 book be 1 unit and Selling Price (SP) of 1 book be x units.

According to the question: 20 × SP = 6 × CP.

Ratio of SP to CP: SP/CP = 6/20 = 3/10.

Loss = CP − SP = 10 − 3 = 7 units.

Loss % = (Loss ÷ CP) × 100 = (7 ÷ 10) × 100 = 70%.

∴ The correct answer is 70% loss.

Alternate Method

Given: SP of 20 books = CP of 6 books. Formulas: Loss = CP − SP | Loss% = (Loss ÷ CP) × 100.

⇒ Let Cost Price (CP) of 1 book be Re. 1. ⇒ Cost Price of 20 books = Rs. 20. ⇒ Selling Price (SP) of 20 books = Cost Price of 6 books = Rs. 6. ⇒ Loss = CP − SP = 20 − 6 = Rs. 14. ⇒ Loss % = (Loss ÷ CP) × 100 = (14 ÷ 20) × 100. ⇒ Loss % = 7 × 10 = 70%.

∴ The correct answer is 70% loss.

Additional Information

Loss and Gain Percent

Profit or Loss is always calculated on the Cost Price unless otherwise stated in the problem.

Ratio Method

If CP of 'a' articles = SP of 'b' articles, then Profit or Loss % = ((a − b) ÷ b) × 100. Positive result denotes Profit, negative denotes Loss.

Given:

1) B is the father of C. 

2) Q is the sister of C.

3. T is the only sister of Q. 

4) T is the child of S.

5. M is the son of S's only son.

Thus, S is B's wife.

Hence, the correct answer is "Option 4".

The Correct answer is Nizamabad.

Key Points

• The headquarters of the National Turmeric Board, established in 2025, is located in Nizamabad.
• Nizamabad is a city in the state of Telangana, India, and is well-known for its turmeric production.
• The region is often referred to as the "Turmeric City" due to its significant contribution to the cultivation and trade of turmeric.
• The establishment of the National Turmeric Board aims to promote the turmeric industry, encourage better farming practices, and enhance the global market presence of Indian turmeric.
• Nizamabad has a strategic advantage due to its proximity to turmeric-growing regions and its established trade links for exporting turmeric products.
• The board is expected to work on enhancing research and development for turmeric, improving farmer incomes, and ensuring sustainable farming practices.

 Additional Information

• Kochi
• Kochi, located in the state of Kerala, is known as the "Queen of the Arabian Sea." It is a major port city and a hub for the spice trade in India.
• While Kochi plays a significant role in the spice industry, it is not specifically associated with turmeric production.
• Guntur
• Guntur is located in the state of Andhra Pradesh and is famous for the production of chili peppers.
• Although it is an important agricultural region, it is more associated with chili production than turmeric.
• Kolkata
• Kolkata, the capital of West Bengal, is known for its cultural heritage and as a major economic and trade center in eastern India.
• It does not have a direct or major role in turmeric production or trade.

According to the given information,

Thus, 'I' is coded as '8'.

Hence, "Option 1" is the correct answer.

The Correct answer is Kali Linux.

Key Points

• Kali Linux is a specialized operating system widely used in ethical hacking, penetration testing, and cybersecurity tasks.
• It is based on Debian Linux and comes with a wide array of pre-installed tools designed for digital forensics and information security.
• Kali Linux is maintained and developed by Offensive Security, a leading organization in cybersecurity training and solutions.
• Some of the popular tools included in Kali Linux are Nmap, Wireshark, Metasploit, John the Ripper, and Aircrack-ng.
• It supports a variety of platforms, including laptops, desktops, Raspberry Pi, and mobile devices.
• Kali Linux allows ethical hackers and security professionals to efficiently perform vulnerability assessments, security audits, and penetration testing.
• The operating system is open-source and provides strong community support, making it an excellent choice for cybersecurity enthusiasts and professionals.
• Kali Linux also includes advanced features such as customizable penetration testing environments, live boot options, and multi-language support.

 Additional Information

• Ubuntu LTS
• Ubuntu is a popular Linux distribution based on Debian, known for its user-friendly interface and robust performance.
• It is primarily used for general computing tasks, software development, and server management.
• Ubuntu LTS (Long Term Support) versions receive regular updates and security patches for up to five years, making it ideal for stable and reliable systems.
• While it is versatile, it lacks the specialized tools pre-installed in Kali Linux that are essential for penetration testing and ethical hacking.
• macOS Ventura
• macOS Ventura is the latest version of Apple's operating system for Mac computers.
• It is known for its seamless integration with Apple’s ecosystem, smooth user experience, and advanced features like Stage Manager and Continuity Camera.
• macOS is primarily designed for general computing tasks, creative work, and software development.
• While macOS supports some cybersecurity tools, it is not specifically tailored for penetration testing or ethical hacking.
• Windows 10
• Windows 10 is one of the most widely used operating systems globally, developed by Microsoft.
• It is primarily designed for general computing tasks, gaming, and office productivity.
• Windows supports third-party cybersecurity tools but lacks the pre-installed penetration testing features found in Kali Linux.
• It is not an ideal choice for ethical hacking due to its closed-source nature and limited customization options for security professionals.

Shortcut Trick

Compare marks directly with percentages since the Maximum Marks are the same.

621 marks → 69%

1 mark → 69 ÷ 621 %

522 marks → (69 ÷ 621) × 522 %

522 marks → (1 ÷ 9) × 522 = 58%

∴ The correct answer is 58%.

Alternate Method

Given: Marks of Kalpana = 621, Percentage of Kalpana = 69%, Marks of Sudha = 522.

Formula Used: Maximum Marks = (Obtained Marks ÷ Percentage) × 100

⇒ Let the Maximum Marks be M.

⇒ 69% of M = 621

⇒ (69 ÷ 100) × M = 621

⇒ M = (621 × 100) ÷ 69 = 900

⇒ Sudha's Percentage = (Marks Scored ÷ Maximum Marks) × 100

⇒ Percentage = (522 ÷ 900) × 100

⇒ Percentage = 522 ÷ 9 = 58%

∴ The correct answer is 58%.

Additional Information

Percentage Change

Percentage change = (Difference ÷ Original Value) × 100. Useful for comparing growth or decline.

Passing Marks Concept

Passing Marks = Total Marks × Passing Percentage. Often used in exam-based word problems.

Base Value consistency

When the base (Total Marks) is the same, values and percentages are directly proportional.

The Correct answer is Mouse.

Key Points

• A mouse is a crucial input device that translates physical movement, such as dragging or clicking, into digital signals for a computer system.
• It is widely used for tasks like navigation, object selection, and manipulation in graphical environments (e.g., operating systems, video games).
• The movement of the mouse is detected by either mechanical components (in older models) or advanced optical sensors (in modern devices).
• These movements are then converted into corresponding cursor movements on the computer screen, allowing precise control.
• The mouse often comes with additional buttons and a scroll wheel, enabling users to execute commands such as clicking, dragging, scrolling, and double-clicking.
• It can be connected to a computer via a USB cable or wirelessly through Bluetooth.
• The mouse has become an essential tool for interactive user interfaces and is pivotal in various fields such as designing, gaming, and data management.

 Additional Information

• Scanner
• A scanner is an input device used to convert physical documents or images into digital format.
• It is not used for real-time navigation or object manipulation, but rather for digitizing printed material.
• Examples of scanners include flatbed scanners and barcode scanners.
• Microphone
• A microphone captures audio signals (sound) and converts them into digital signals for processing by a computer.
• It is used primarily for applications such as voice recording, speech recognition, and communication.
• However, it does not assist in navigation or graphical tasks.
• Keyboard
• A keyboard is an input device that allows users to input text, commands, and shortcuts into a computer system.
• It is primarily used for typing and interacting with software but does not convert physical movement into digital signals for graphical tasks.
• Modern keyboards often come with additional function keys and media controls.

Shortcut Trick

Assume all 34 notes are of ₹100 denomination.

Total amount → 34 × 100 = ₹3,400.

Excess amount → 3,400 − 3,100 = ₹300.

Difference in denomination → 100 − 50 = ₹50.

Number of ₹50 notes → 300 ÷ 50 = 6.

∴ The correct answer is 6.

Alternate Method

Given:

Total amount = ₹3,100

Total number of notes = 34

Denominations = ₹50 and ₹100

Calculations:

⇒ Let the number of ₹50 notes be x and ₹100 notes be y.

⇒ x + y = 34 --- (Equation 1)

⇒ 50x + 100y = 3,100

⇒ 50(x + 2y) = 3,100

⇒ x + 2y = 62 --- (Equation 2)

⇒ Subtracting (Equation 1) from (Equation 2): (x + 2y) − (x + y) = 62 − 34

⇒ y = 28

⇒ x = 34 − 28 = 6

∴ The correct answer is 6.

Additional Information

Linear Equation Method

Standard algebraic approach using variables to represent quantities and equating them to the total value and count.

Alligation Method

A faster way to find ratios by comparing weighted averages of two different groups to the overall mean value.

Denomination Problems

Total Value = (Quantity₁ × Face Value₁) + (Quantity₂ × Face Value₂).

The Correct answer is China.

Key Points

• The McMahon Line is the boundary line that separates India from China.
• It was drawn during the Simla Convention of 1914, between British India and Tibet, with the presence of China.
• The line is named after Sir Henry McMahon, the then Foreign Secretary of British India, who represented India in the negotiations.
• This line is situated in the northeastern region of India, specifically along the state of Arunachal Pradesh, which China often claims as part of its territory.
• The McMahon Line runs for approximately 550 miles (885 kilometers).
• While India recognizes the McMahon Line as its legal boundary, China disputes this line, leading to border tensions between the two nations.
• The region around the McMahon Line is geopolitically sensitive and has been the site of conflicts, including the Sino-Indian War of 1962.

 Additional Information

• Pakistan
• India shares its western border with Pakistan, marked primarily by the Radcliffe Line.
• The Radcliffe Line was drawn during the partition of India in 1947.
• The border between India and Pakistan is highly sensitive, with disputes over regions such as Kashmir.
• Nepal
• India shares an open border with Nepal, which is marked by the Mahakali River in certain regions.
• The India-Nepal Treaty of Peace and Friendship (1950) governs the bilateral relationship between the two countries.
• Citizens of both countries can travel across the border without requiring a visa or passport.
• Bhutan
• India shares its northeastern border with Bhutan.
• The border is defined by geographical features such as the Himalayas.
• India and Bhutan maintain strong diplomatic ties, and India assists Bhutan in its development projects.

Shortcut Trick

Ratio of time = 80 : 64 = 5 : 4

Weighted Average Speed = [(Speed₁ × Time Ratio₁) + (Speed₂ × Time Ratio₂)] ÷ Total Ratio

Average Speed = [(20 × 5) + (65 × 4)] ÷ (5 + 4)

Average Speed = [100 + 260] ÷ 9 = 360 ÷ 9 = 40 m/min

∴ The correct answer is 40 m/min.

Alternate Method

Given:

Speed₁ = 20 m/min, Time₁ = 80 min

Speed₂ = 65 m/min, Time₂ = 64 min

Formula Used:

Average Speed = Total Distance ÷ Total Time

Distance = Speed × Time

Calculations:

⇒ Distance₁ = 20 × 80 = 1600 m

⇒ Distance₂ = 65 × 64 = 4160 m

⇒ Total Distance = 1600 + 4160 = 5760 m

⇒ Total Time = 80 + 64 = 144 min

⇒ Average Speed = 5760 ÷ 144

⇒ Average Speed = 40 m/min

∴ The correct answer is 40 m/min.

Additional Information

Average Speed (Equal Distances)

When two equal distances are covered at speeds u and v, Average Speed = (2 × u × v) ÷ (u + v).

Relative Speed

If two objects move in the same direction, relative speed is |u − v|. In opposite directions, it is (u + v).

Unit Conversion

To convert kmph to m/s, multiply by 5/18. To convert m/s to kmph, multiply by 18/5.

The correct answer is Article 51A (i).

Key Points

• Article 51A outlines the Fundamental Duties of citizens under Part IV-A of the Indian Constitution.
• Article 51A (i) specifically mentions the duty of every citizen of India to safeguard public property and to abjure violence.
• The Fundamental Duties were added to the Constitution through the 42nd Amendment Act, 1976, based on the recommendations of the Swaran Singh Committee.
• These duties aim to remind citizens of their responsibility to contribute to the nation's well-being and ensure a harmonious social environment.
• The provision under Article 51A (i) is crucial for promoting a sense of responsibility among citizens to protect public assets and ensure that violence is avoided in public life.
• Public property refers to assets owned collectively by society, such as parks, government buildings, public transport, and infrastructure.
• Abjuring violence is essential for maintaining peace and order in society, ensuring that differences are resolved through non-violent means.

 Additional Information

• Article 51A (h)
• Article 51A (h) mandates citizens to develop the scientific temper, humanism, and the spirit of inquiry and reform.
• This duty emphasizes fostering a culture of critical thinking and rationality among Indian citizens.
• Article 51A (k)
• Article 51A (k) obligates parents or guardians to provide opportunities for education to their children or wards between the ages of six and fourteen years.
• This duty is in alignment with the Right to Education (RTE) Act, 2009.
• Article 51A (j)
• Article 51A (j) enjoins citizens to strive towards excellence in all spheres of individual and collective activity so that the nation constantly rises to higher levels of achievement.
• This duty encourages citizens to work towards both personal growth and the nation's development.

The Correct answer is Grid pattern streets.

Key Points

• The Harappan Civilization, also known as the Indus Valley Civilization, is renowned for its advanced urban planning and architectural design.
• One of the most unique and distinguishing features of Harappan town planning was the use of a grid pattern for streets.
• In this grid system, the streets were laid out in a structured pattern, intersecting at right angles, which created a well-organized city layout.
• This planning allowed for the division of the city into blocks or sectors, with separate areas designated for residential, commercial, and public activities.
• The grid system facilitated efficient drainage systems, as the streets were often equipped with advanced sewage channels and covered drains made of burnt bricks.
• This level of planning reflects the technical and engineering skills of the Harappan people, who prioritized hygiene, organization, and accessibility.
• Examples of cities with this type of layout include Mohenjo-Daro, Harappa, and Lothal.
• The grid pattern streets also indicate that the civilization had a centralized authority to regulate and implement urban planning policies.

 Additional Information

• Irregular housing layout
• The Harappan Civilization's urban planning was the opposite of irregular housing layouts. Houses were built in a standardized manner using baked bricks, with uniform sizes and layouts.
• Each house had access to a private well and drainage system, indicating a focus on uniformity and hygiene.
• Underground temples
• There is no evidence of underground temples in the Harappan Civilization. The Harappan culture is not known for monumental temple structures, unlike later Indian civilizations.
• Instead, they focused on functional urban structures like the Great Bath at Mohenjo-Daro, which may have had a ritualistic or communal purpose.
• Circular forts
• The Harappans did not construct circular forts. Instead, they built rectangular fortified areas or citadels for administrative and protective purposes.
• These citadels were often raised on mud-brick platforms to safeguard against flooding.

Shortcut Trick

For half-yearly compounding, the Rate is halved and Time is doubled.

New Rate = 2% ÷ 2 = 1% per half-year | Periods (n) = 1 × 2 = 2

Effective Rate for 2 periods = x + y + (xy/100) ⇒ 1 + 1 + (1 × 1)/100 = 2.01%

Compound Interest = 2.01% of ₹6,70,000 ⇒ 6,70,000 × 0.0201 = ₹13,467

∴ The correct answer is ₹13,467.

Alternate Method

Given: Principal (P) = ₹6,70,000, Annual Rate (R) = 2%, Time (T) = 1 year.

Formula Used: Amount (A) = P(1 + r/100)ⁿ and CI = A − P

⇒ Half-yearly rate (r) = 2% ÷ 2 = 1%

⇒ Number of half-years (n) = 1 × 2 = 2

⇒ A = 6,70,000 × (1 + 1/100)²

⇒ A = 6,70,000 × (1.01)²

⇒ A = 6,70,000 × 1.0201 = ₹6,83,467

⇒ CI = 6,83,467 − 6,70,000

⇒ CI = ₹13,467

∴ The correct answer is ₹13,467.

Additional Information

Half-Yearly Compounding Rule

When interest is compounded half-yearly, the annual rate R becomes R/2 and the time T becomes 2T.

Effective Rate Formula

For two periods with rate r%, the effective percentage rate is calculated as [r + r + (r×r)/100] %.

CI vs SI for 2 Years

The difference between Compound Interest and Simple Interest for 2 years is P(R/100)².

Shortcut Trick

Given: √3 tanA = 3 sinA

⇒ √3 (sinA/cosA) = 3 sinA

⇒ cosA = √3/3 = 1/√3

Value required: 2√3 cosecA × tanA = 2√3 (1/sinA) × (sinA/cosA) = 2√3/cosA

⇒ 2√3 ÷ (1/√3) = 2√3 × √3 = 6

∴ The correct answer is 6.

Alternate Method

Given: √3 tanA = 3 sinA

Formula Used: tanA = sinA/cosA, cosecA = 1/sinA

⇒ √3 (sinA/cosA) = 3 sinA

⇒ 1/cosA = 3/√3

⇒ cosA = √3/3 = 1/√3

⇒ Base (B) = 1, Hypotenuse (H) = √3

⇒ Perpendicular (P) = √(H² − B²) = √(3 − 1) = √2

⇒ Target expression = 2√3 cosecA × tanA

⇒ Target expression = 2√3 × (H/P) × (P/B) = 2√3 × (H/B)

⇒ Target expression = 2√3 × (√3/1)

⇒ 2 × 3 = 6

∴ The correct answer is 6.

Additional Information

Trigonometric Identities

Fundamental relations: tanA = sinA/cosA, cotA = cosA/sinA, and sin²A + cos²A = 1.

Reciprocal Ratios

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

Pythagoras Theorem

In a right-angled triangle, P² + B² = H² where P is perpendicular, B is base, and H is hypotenuse.

The Correct answer is 0.89%.

Key Points

• As per the Socio-Economic Caste Census (SECC) 2011, a certain percentage of households were classified as the poorest of the poor.
• The SECC 2011 was a comprehensive survey conducted to identify households living below the poverty line and collect data about their socio-economic conditions.
• The classification as "poorest of the poor" is based on multiple indicators such as income levels, assets, housing conditions, and access to basic amenities.
• The correct percentage in this context is 0.0089, which denotes the proportion of households identified under this category.
• This data is crucial for the formulation of targeted policies and programs by the government to address extreme poverty and improve the living conditions of affected households.
• SECC 2011 not only aids in identifying beneficiaries for various welfare schemes but also provides a detailed understanding of socio-economic disparities across different regions of India.

 Additional Information

• Socio-Economic Caste Census (SECC) 2011
• SECC 2011 was conducted jointly by the Ministry of Rural Development, Ministry of Housing and Urban Poverty Alleviation, and the Registrar General of India.
• The SECC collected data on various aspects such as education, employment, caste, housing, and income levels.
• The SECC was instrumental in identifying beneficiaries for government schemes like Pradhan Mantri Awas Yojana and National Food Security Act.
• Indicators Used for Classification
• The classification of households under categories like "poorest of the poor" was based on indicators such as household income, access to drinking water, sanitation facilities, and employment type.
• These indicators help in determining the extent of deprivation and socio-economic challenges faced by households.

Given: Seven boxes D, E, F, G, S, T and U are kept one over the other.

1. Only F is kept above E.

2. Only four boxes are kept between E and D.

3. Only two boxes are kept between T and U.

4. G is kept immediately above S.

5. U is not kept immediately above G.

Thus, G box is kept fourth from the top.

Hence, the correct answer is "Option 3".

Shortcut Trick

Combined efficiency of A + B = 1/15

Efficiency of A = 1/17

Efficiency of B = 1/15 − 1/17 = 2/255

Time for B to do 2/3 work = (2/3) ÷ (2/255) = (2/3) × (255/2) = 85 days

∴ The correct answer is 85 days.

Alternate Method

Given: Time taken by (A+B) = 15 days, Time taken by A = 17 days.

Formula Used: Total Work = LCM of days; Efficiency = Total Work ÷ Days

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

⇒ Efficiency of B = 17 − 15 = 2 units/day

⇒ Two-third of the total work = 2/3 × 255 = 170 units

⇒ Time taken by B alone = 170 ÷ 2 = 85 days

∴ The correct answer is 85 days.

Additional Information

Work and Efficiency Relationship

Efficiency is inversely proportional to the time taken to complete a task. Efficiency = Work ÷ Time.

Fractional Work

To find the time for a fraction of work, multiply the total time required for the full work by that fraction: Time_part = Fraction × Total Time.

Pipes and Cisterns

This concept follows the same logic as Time and Work, where filling pipes have positive efficiency and outlet pipes have negative efficiency.

The Correct answer is National Green Tribunal.

Key Points

• The National Green Tribunal (NGT) is a specialized judicial body established under the National Green Tribunal Act, 2010.
• Its primary purpose is to handle cases related to environmental protection and the conservation of forests and other natural resources.
• The NGT has the authority to take suo motu cognisance of environmental issues, which means it can initiate action on its own based on media reports or other information, as in the case of the news about 350 turtles found dead on the shore.
• Such cases are critical for addressing violations of environmental laws and ensuring compliance with the principles of sustainable development and environmental justice.
• The tribunal is empowered to provide relief, compensation, and restitution of property and the environment in such cases.
• The NGT operates in a time-bound manner to ensure swift disposal of cases and is guided by principles of natural justice.
• This tribunal has jurisdiction over all civil cases where a substantial question relating to the environment is involved, including those arising under laws like the Environment (Protection) Act, 1986, Forest (Conservation) Act, 1980, and Air (Prevention and Control of Pollution) Act, 1981.

 Additional Information

• Supreme Court of India
• The Supreme Court is the highest judicial authority in India, established under Article 124 of the Constitution.
• It primarily deals with constitutional matters, appeals from lower courts, and cases of national importance.
• While the Supreme Court can address environmental issues, it does not typically take suo motu cognisance of specific environmental cases like the NGT does.
• High Court of Tamil Nadu
• The High Court of Tamil Nadu is the principal civil court of original jurisdiction in Tamil Nadu and handles cases under its territorial jurisdiction.
• Though High Courts can hear environmental cases, they generally do not have the specialized expertise or mandate of the NGT for addressing environmental violations.
• High Court of Odisha
• The High Court of Odisha is the highest judicial body in the state of Odisha.
• It can hear cases concerning environmental issues within its state jurisdiction but lacks the pan-India jurisdiction and specialized focus of the NGT.

The correct answer is Banihal Pass.

Key Points

• Banihal Pass is located in the Pir Panjal range of the Himalayas.
• This pass lies at an altitude of approximately 2,832 meters (9,291 feet).
• It connects the Kashmir Valley with the outer Himalayas and is an important route for transportation.
• The Jawahar Tunnel, one of the largest tunnels in India, is situated near the pass and facilitates travel between Jammu and Srinagar.
• Historically, Banihal Pass served as a crucial pathway for traders and travelers moving between the Kashmir Valley and other parts of India.
• The pass is surrounded by breathtaking landscapes and is known for its scenic beauty.

 Additional Information

• Shipki La
• Shipki La Pass is located in the Himachal Pradesh region of India.
• This pass is situated on the Indo-China border and serves as a trade route between India and Tibet.
• It is part of the Greater Himalayas, not the Pir Panjal range.
• The river Sutlej enters India through Shipki La Pass.
• Zoji La
• Zoji La Pass is located on the National Highway 1 in the Indian state of Jammu and Kashmir.
• It connects Srinagar and Leh, serving as a gateway to the Ladakh region.
• Zoji La lies in the Greater Himalayas and is one of the highest passes in the region.
• This pass is known for its challenging terrain and extreme weather conditions.
• Nathu La
• Nathu La Pass is located in the state of Sikkim, India.
• It is an important pass along the Indo-China border and serves as a trade route between the two countries.
• Nathu La is part of the Eastern Himalayas, not the Pir Panjal range.
• This pass is renowned for its strategic significance and high-altitude location.

The Correct answer is Article 324.

Key Points

• Article 324 of the Indian Constitution provides for the establishment of the Election Commission of India (ECI).
• The Election Commission is responsible for the superintendence, direction, and control of elections to the Parliament, State Legislatures, and offices of the President and Vice-President of India.
• This article vests the power of conducting free and fair elections in an independent constitutional body, ensuring the democratic framework of the country.
• The Election Commission is a permanent and independent body to ensure that elections are conducted in a fair and unbiased manner.
• The Commission consists of the Chief Election Commissioner (CEC) and other Election Commissioners as the President may appoint.
• The powers and functions under Article 324 ensure autonomy and authority to the Election Commission to maintain the integrity of the electoral process in India.
• It is a vital provision to safeguard the principle of free and fair elections, which is the cornerstone of a democratic system.

 Additional Information

• Article 326
• Article 326 deals with the elections to the House of the People and to the Legislative Assemblies of States based on adult suffrage.
• It provides that every citizen who is not less than 18 years of age and is not otherwise disqualified under the Constitution or law is entitled to vote.
• Article 325
• Article 325 prohibits discrimination on the grounds of religion, race, caste, or sex in the electoral process.
• It ensures that no person is ineligible for inclusion in the electoral rolls on these discriminatory grounds.
• Article 327
• Article 327 gives the Parliament the power to make laws with respect to all matters relating to elections to the Legislature.
• This includes the preparation of electoral rolls, the conduct of elections, and any other related matters.

Given:

Evaluate: 81 × 112

Formula used:

Direct multiplication formula: Multiply the two numbers directly.

Calculation:

81 × 112

⇒ Break it into simpler parts: (81 × 100) + (81 × 12)

⇒ (8100) + (972)

⇒ 8100 + 972 = 9072

∴ The correct answer is option (3).

The Correct answer is 30°.

Key Points

• The total approximate latitudinal extent of India is 30°, ranging from 8°4'N to 37°6'N.
• This latitudinal span contributes significantly to the diverse climatic zones found across India, including tropical, subtropical, and temperate regions.
• The southernmost point of India is Indira Point, located at 6°45'N in the Nicobar Islands.
• The northernmost point of India lies in the Union Territory of Ladakh and is near 37°6'N.
• The latitudinal extent plays a crucial role in determining the duration of daylight hours across various regions of the country.
• This span also influences the distribution of natural vegetation, agriculture, and even monsoonal patterns.
• It is important for geographical studies and helps understand India's position in the global context.

The Correct answer is Alexander Fleming.

Key Points

• Alexander Fleming discovered the antibacterial properties of a Penicillium fungus in 1929.
• He observed that a mold, later identified as Penicillium notatum, had killed bacteria surrounding it in a petri dish.
• This discovery led to the development of penicillin, the world’s first widely effective antibiotic.
• Penicillin was instrumental in treating bacterial infections during World War II, saving countless lives.
• Fleming’s work earned him the Nobel Prize in Physiology or Medicine in 1945, shared with Ernst Boris Chain and Howard Florey, who helped mass-produce penicillin.
• Penicillin revolutionized medicine and is considered one of the greatest discoveries in the field of microbiology and pharmacology.

 Additional Information

• Paul Ehrlich
• Paul Ehrlich was a German scientist known for his work on immunology and the development of the first chemotherapy agent.
• He discovered the drug Salvarsan, which was used to treat syphilis.
• Ehrlich introduced the concept of a "magic bullet"—a drug that could target disease-causing organisms without harming the host.
• Antonie van Leeuwenhoek
• Antonie van Leeuwenhoek was a Dutch scientist who is known as the "Father of Microbiology."
• He was the first to observe and describe microorganisms, such as bacteria and protozoa, using a microscope.
• His discoveries laid the foundation for the field of microbiology.
• Marie Curie
• Marie Curie was a Polish-French scientist known for her groundbreaking research on radioactivity.
• She was the first woman to win a Nobel Prize and the only person to win Nobel Prizes in two different sciences (Physics and Chemistry).
• Her discoveries of radium and polonium were instrumental in the development of nuclear science and medicine.

The Correct answer is 52%.

Key Points

• The Global Risks Perception Survey (GRPS) 2025 is a component of the Global Risks Report, which is published annually by the World Economic Forum (WEF).
• The survey gathers inputs from a wide range of stakeholders, including business leaders, economists, policymakers, and risk experts.
• As per the GRPS 2025, 52% of respondents believe that the turbulence outlook over the next two years will be significant.
• The term "turbulence outlook" refers to the anticipated volatility and uncertainty in global systems due to factors like geopolitical tensions, economic crises, climate change, and technological risks.
• This perception underscores the growing concerns about global instability and the need for robust mitigation strategies.
• The GRPS is a critical tool for identifying and prioritizing global risks, enabling policymakers and organizations to develop strategies to address these challenges effectively.

 Additional Information

• Global Risks Report
• The Global Risks Report is published annually by the World Economic Forum (WEF).
• It highlights the most pressing risks facing the world and provides insights into their potential impact and interconnectedness.
• The report is based on data from the Global Risks Perception Survey and expert analysis.
• It covers risks across categories such as economic, environmental, geopolitical, societal, and technological risks.
• Importance of Understanding Risk Perception
• Risk perception is crucial for policymaking, as it helps governments and organizations prioritize and allocate resources effectively.
• It also aids in developing resilience strategies to mitigate the impact of potential crises.
• Understanding risk trends allows for better preparation in areas such as disaster management, economic policy, and environmental protection.

The Correct answer is Pulses.

Key Points

• In February 2025, the Indian government announced a six-year program to boost the production of pulses. This initiative was introduced to reduce India's reliance on imports for this essential commodity.
• Pulses are an important source of plant-based protein and play a vital role in the Indian diet, especially for vegetarians.
• India is the world's largest producer, consumer, and importer of pulses, but domestic production has often fallen short of demand, leading to significant imports.
• The six-year program is expected to include measures such as government incentives, support for farmers, and the introduction of advanced agricultural techniques to increase yield.
• Pulses include varieties like chickpeas, lentils, black gram, green gram, and pigeon peas, which are extensively cultivated across different regions of India.
• The initiative aligns with India's larger goal of achieving self-sufficiency in agricultural production and reducing dependency on imported goods.
• Efforts to promote pulse production also contribute to the sustainability of agriculture, as pulses are known to enhance soil fertility by fixing nitrogen, reducing the need for chemical fertilizers.
• This program could also help stabilize the market prices of pulses, making them more affordable for consumers.
• The government may also encourage research and development in pulse cultivation, introducing disease-resistant and high-yield varieties.

 Additional Information

• Wheat
• Wheat is one of the staple crops in India and is mainly grown in the northern regions such as Punjab, Haryana, Uttar Pradesh, Bihar, and Madhya Pradesh.
• India is a leading producer of wheat, and the country exports this crop to various international markets.
• The focus on pulses is critical as wheat production is already significant, and there is less dependence on imports for wheat.
• Rice
• Rice is the primary food crop for a large part of India’s population, especially in southern and eastern states like West Bengal, Odisha, Andhra Pradesh, and Tamil Nadu.
• India is a major exporter of rice, including Basmati and non-Basmati varieties, and does not heavily rely on rice imports.
• Sugar
• Sugar production in India is already robust, with the country being one of the largest producers globally.
• Major sugar-producing states include Maharashtra, Uttar Pradesh, Karnataka, and Tamil Nadu.
• India exports sugar to several countries, reducing import dependence in this commodity.

Shortcut Trick

Treat the equation as a quadratic in terms of x⁻².

The factors for the quadratic y² − 10y + 9 = 0 are 9 and 1 (since 9 × 1 = 9 and 9 + 1 = 10).

Set x⁻² = 9 ⇒ x² = 1/9 ⇒ x = ± 1/3.

Set x⁻² = 1 ⇒ x² = 1 ⇒ x = ± 1.

∴ The correct answer is ± 1, ± 1/3.

Alternate Method

Given:

The equation is x⁻⁴ − 10x⁻² + 9 = 0.

Formula Used:

For an equation of the form ax²ⁿ + bxⁿ + c = 0, we use substitution (t = xⁿ) to solve it as a quadratic.

Calculations:

⇒ Let t = x⁻². Then, x⁻⁴ = (x⁻²)² = t².

⇒ substituting these in the original equation: t² − 10t + 9 = 0

⇒ t² − 9t − t + 9 = 0

⇒ t(t − 9) − 1(t − 9) = 0

⇒ (t − 9)(t − 1) = 0

⇒ t = 9 or t = 1

⇒ When t = 9: x⁻² = 9 ⇒ 1/x² = 9 ⇒ x² = 1/9 ⇒ x = ± 1/3

⇒ When t = 1: x⁻² = 1 ⇒ 1/x² = 1 ⇒ x² = 1 ⇒ x = ± 1

Combining the results, the roots are ± 1 and ± 1/3.

∴ The correct answer is ± 1, ± 1/3.

Additional Information

Substitution in Higher-Degree Equations

Equations like ax⁴ + bx² + c = 0 or ax⁻⁴ + bx⁻² + c = 0 are called equations reducible to quadratic form. They are solved by replacing the middle variable term with a single letter.

Discriminant Rule

The number of real roots depends on the discriminant (D = b² − 4ac). In this case, D = (−10)² − 4(1)(9) = 100 − 36 = 64, which is a perfect square, leading to rational roots for t.

Negative Exponents Property

Always remember that x⁻ⁿ = 1/xⁿ. When solving for x after finding t, ensure to take the reciprocal before calculating the square root.

Formula used:

Cross-multiplication: a/b = c/d ⇒ a × d = b × c

Calculation:

⇒ ? × ? = 56 × 504

⇒ ?² = 28224

⇒ ? = √28224

⇒ ? = 168

∴ The positive number is 168.

Shortcut Trick

Side of cube a = √³(1,09,41,048) = 222 cm.

Joining 5 cubes end to end creates a cuboid where Length = 5a, Width = a, and Height = a.

Lateral Surface Area (LSA) of cuboid = 2 × (L + W) × H = 2 × (5a + a) × a = 12a².

LSA = 12 × 222² = 12 × 49,284 = 5,91,408 cm².

∴ The correct answer is 5,91,408 cm².

Alternate Method

Given: Volume of each cube = 1,09,41,048 cm³, Number of cubes = 5.

Formula: Volume of cube = a³ | LSA of cuboid = 2(l + b)h

⇒ a³ = 1,09,41,048

⇒ a = √³(1,09,41,048) = 222 cm

⇒ For the cuboid: Length (l) = 5 × 222 = 1110 cm

⇒ Breadth (b) = 222 cm, Height (h) = 222 cm

⇒ LSA = 2 × (1110 + 222) × 222

⇒ LSA = 2 × 1332 × 222

⇒ LSA = 2664 × 222 = 5,91,408 cm²

∴ The correct answer is 5,91,408 cm².

Additional Information

Total Surface Area of Cuboid

TSA = 2(lb + bh + hl). For 5 cubes joined end to end, TSA = 22a².

Cube Root Calculation Trick

For 1,09,41,048: the last digit 8 implies the unit digit of cube root is 2. The remaining part 10941 lies between 22³ (10648) and 23³ (12167), so the root is 222.

Volume of Cuboid

Volume = Length × Breadth × Height. Here, it is 5 × individual cube volume.

The Correct answer is Canada.

Key Points

• In November 2024, Canada reported its first-ever presumptive human case of H5 bird flu.
• The H5 strain is a type of avian influenza virus that primarily affects birds but can occasionally infect humans.
• The case was classified as “presumptive” due to the need for further confirmation through comprehensive testing.
• This development marked a significant event as it raised concerns about the potential zoonotic transmission and health risks associated with the virus.
• The World Health Organization (WHO) and Canadian health authorities closely monitored the situation to assess the risks and provide guidance.
• Canada has a robust healthcare and surveillance system, which helped in identifying and managing the case promptly.
• The event underscored the importance of maintaining strict biosecurity measures to prevent the spread of avian influenza among birds and humans.
• Efforts were directed towards identifying the source of the infection and ensuring that similar cases were avoided in the future.

 Additional Information

• United States
• The United States has previously reported human cases of other types of avian influenza, but it has not been the first to report a presumptive H5 bird flu human case in November 2024.
• The country is known for its advanced epidemiological research and biosecurity measures.
• United Kingdom
• The United Kingdom has a well-established public health system but has not been associated with reporting the first human case of H5 bird flu in November 2024.
• It regularly monitors and manages avian influenza outbreaks, particularly in poultry farms.
• Australia
• Australia has a geographically isolated ecosystem, reducing the spread of diseases like avian influenza.
• While the country deals with biosecurity risks, it was not the first to report a human case of H5 bird flu in November 2024.

Shortcut Trick

Ratio of coins = 16 : 8 : 20

Ratio of values (in Paisa) = (16 × 50) : (8 × 25) : (20 × 10) = 800 : 200 : 200 = 4 : 1 : 1

Total value units = 4 + 1 + 1 = 6 units → ₹384

Value of 10 Paisa coins = (1/6) × 384 = ₹64 = 6400 Paisa

Number of 10 Paisa coins = 6400 ÷ 10 = 640 coins

∴ The correct answer is 640 coins.

Alternate Method

Given: Ratio of 50P : 25P : 10P coins = 16 : 8 : 20. Total amount = ₹384.

Formula Used: Total Value = ∑(Number of coins × Denomination value)

⇒ Let the number of coins be 16x, 8x, and 20x respectively.

⇒ Total value in Paisa = (16x × 50) + (8x × 25) + (20x × 10) = 384 × 100

⇒ 800x + 200x + 200x = 38400

⇒ 1200x = 38400

⇒ x = 38400 ÷ 1200 = 32

⇒ Number of 10 Paisa coins = 20x = 20 × 32 = 640

∴ The correct answer is 640 coins.

Additional Information

Coin Ratio vs Value Ratio

To convert coin ratio to value ratio, multiply each part by its face value. To convert value ratio to coin ratio, divide each part by its face value.

Unit Consistency

Always ensure both sides of the equation are in the same units (either all in ₹ or all in Paisa). Note: ₹1 = 100 Paisa.

Compound Ratio

The total value of a bag is the sum of the products of the number of coins of each denomination and their respective values.

Shortcut Trick

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

Substitute the given values: 4ab = (24)² − 268.

4ab = 576 − 268 = 308.

ab = 308 ÷ 4 = 77.

∴ The correct answer is 77.

Alternate Method

Given:

Sum of two numbers (a + b) = 24

Square of the difference (a − b)² = 268

Formula Used:

Standard expansion of binomial squares: (a + b)² = a² + b² + 2ab and (a − b)² = a² + b² − 2ab.

Calculations:

⇒ (a + b)² = 24² = 576

⇒ a² + b² + 2ab = 576 --- (Equation 1)

⇒ a² + b² − 2ab = 268 --- (Equation 2)

Subtracting Equation 2 from Equation 1:

⇒ (a² + b² + 2ab) − (a² + b² − 2ab) = 576 − 268

⇒ 4ab = 308

⇒ ab = 308 ÷ 4

⇒ ab = 77

The product of a and b is found to be 77, which matches Option (2).

∴ The correct answer is 77.

Additional Information

Fundamental Algebraic Identities

The relation between the sum and difference squares is: (a + b)² − (a − b)² = 4ab.

Sum of Squares Identity

Another useful identity is the sum of squares: (a + b)² + (a − b)² = 2(a² + b²).

Difference of Squares

The difference of two squares is factored as: a² − b² = (a − b)(a + b).

The logic followed here is:

Given: # : UEQ :: QAM : %

Option 1) ​# = CMY, % = ISE → CMY : UEQ :: QAM : ISE

Option 2) # = FMY, % = ISE → FMY : UEQ :: QAM : ISE

​

Option 3) # = CMY, % = ISO → CMY : UEQ :: QAM : ISO

Option 4) # = CMY, % = IUE → CMY : UEQ :: QAM : IUE

Hence, "Option 1" is the correct answer.

The Correct answer is Punjab and Haryana.

Key Points

• The Green Revolution was introduced in India during the 1960s to address food shortages and achieve self-sufficiency in food production.
• Punjab and Haryana were the initial focus regions for the Green Revolution because of their favorable conditions for agriculture, including fertile soil, adequate irrigation facilities, and progressive farmers.
• The success of the Green Revolution in these regions was largely due to the introduction of high-yielding varieties (HYVs) of seeds, chemical fertilizers, and pesticides.
• The availability of modern irrigation techniques, such as tube wells and canals, further boosted agricultural productivity in Punjab and Haryana.
• These regions became the breadbasket of India, contributing significantly to the nation's food grain production, particularly in wheat and rice.
• The Green Revolution transformed Punjab and Haryana into hubs of intensive farming, leading to increased agricultural output and reduced dependence on food imports.
• However, while it brought short-term benefits, it also caused long-term concerns like soil degradation, water depletion, and environmental pollution.

 Additional Information

• Odisha and Assam
• Odisha and Assam are regions in eastern India that are characterized by high rainfall and flood-prone areas, which make them less suitable for the initial implementation of the Green Revolution.
• These states primarily practice subsistence farming and have a significant dependence on traditional agricultural methods.
• Unlike Punjab and Haryana, they lacked the infrastructure and irrigation facilities required for the adoption of Green Revolution technologies during its early phase.
• Bihar
• Bihar has fertile land and significant agricultural potential, but during the initial phase of the Green Revolution, it faced challenges such as lack of irrigation facilities, low mechanization, and poor infrastructure.
• While Bihar eventually benefited from the Green Revolution, it was not among the regions initially targeted for its implementation.
• Tamil Nadu
• Tamil Nadu is located in southern India, where agriculture is largely dependent on monsoon rains and irrigation systems.
• Although Tamil Nadu later adopted Green Revolution practices, its initial focus was not as prominent as Punjab and Haryana due to different agricultural conditions and priorities.

The Correct answer is ISRO Propulsion Complex, Mahendragiri, Tamil Nadu.

Key Points

• The ISRO Propulsion Complex (IPRC) is located at Mahendragiri in the state of Tamil Nadu.
• It is a specialized facility of the Indian Space Research Organisation (ISRO) dedicated to the research, development, and testing of propulsion systems.
• The semi-cryogenic engine, an advanced technology, is being developed to enhance ISRO’s launch vehicle capabilities for carrying heavier payloads.
• The hot test conducted at IPRC is a crucial step for verifying the engine's performance, efficiency, and reliability.
• IPRC is equipped with sophisticated infrastructure for testing liquid propulsion engines and stages, making it the ideal location for such advanced testing.
• The engine is expected to play a vital role in the future missions of ISRO, including human spaceflight programs and heavy satellite launches.
• Mahendragiri has been a key site for ISRO's propulsion system development, contributing significantly to India's space exploration capabilities.

 Additional Information

• Vikram Sarabhai Space Centre, Thiruvananthapuram, Kerala
• It is named after Dr. Vikram Sarabhai, the father of the Indian space program.
• Located in Thiruvananthapuram, Kerala, it is ISRO's primary center for the development of launch vehicles, spacecraft systems, and payloads.
• This center specializes in the development and testing of solid propulsion systems, unlike the IPRC, which focuses on liquid propulsion.
• Satish Dhawan Space Centre, Sriharikota, Andhra Pradesh
• This is ISRO’s primary launch site, located on an island in Andhra Pradesh.
• It is responsible for the assembly, integration, and launch of satellite launch vehicles.
• While it plays a crucial role in launches, it does not specialize in propulsion system testing like IPRC.
• Liquid Propulsion Systems Centre, Mahendragiri, Tamil Nadu
• This center is also involved in the development of liquid propulsion systems for launch vehicles and satellites.
• However, the ISRO Propulsion Complex (IPRC) at Mahendragiri is the specific facility for conducting hot tests of semi-cryogenic engines.

The Correct answer is ₹25,000 crore.

Key Points

• The Union Budget 2025-26 announced the establishment of a Maritime Development Fund.
• This fund will have a total corpus of ₹25,000 crore.
• The primary objective of this fund is to boost the development and modernization of India's maritime sector.
• The maritime sector is crucial for India's economy as it handles approximately 95% of India's trade by volume and 70% by value.
• The establishment of the fund is expected to enhance port infrastructure, improve logistics efficiency, and promote sustainable practices within the sector.
• The fund will also support initiatives aimed at achieving the goals outlined in the Maritime India Vision 2030, which focuses on making India a leader in global maritime trade.
• This move aligns with the government's broader vision of leveraging India's strategic location and vast coastline to emerge as a maritime power.

The Correct answer is $640.3 billion.

Key Points

• According to the Economic Survey 2024-25, India's foreign exchange reserves stood at $640.3 billion at the end of December 2024.
• Foreign exchange reserves are crucial for a country's economic stability, as they help in managing exchange rate fluctuations, supporting imports, and maintaining confidence in the economy.
• India's foreign exchange reserves include foreign currency assets, gold reserves, Special Drawing Rights (SDRs), and Reserve Tranche Position (RTP) in the International Monetary Fund (IMF).
• The increase in foreign exchange reserves is indicative of India's strong economic performance, robust capital inflows, and a surplus in the balance of payments.
• Foreign exchange reserves serve as a buffer against external shocks, such as global financial crises or sudden capital outflows.
• India's reserves rank among the highest globally, reflecting its position as a resilient economy in the face of global uncertainties.

The Correct answer is English East India Company.

Key Points

• The English East India Company was established on 31st December 1600 through a royal charter issued by Queen Elizabeth I.
• This charter granted the company a monopoly over trade with all countries to the east of the Cape of Good Hope for a period of 15 years.
• The company's primary objective was to engage in the lucrative spice trade from the East Indies (modern-day Southeast Asia).
• The establishment of the English East India Company marked the beginning of British commercial and later political dominance in India.
• The company eventually transitioned from a trading corporation to a governing authority, playing a significant role in the colonization of India.
• The English East India Company was also involved in triangular trade, dealing in commodities like spices, tea, silk, and cotton.
• This company also laid the foundation for British imperial rule in India, which lasted until 1947.

 Additional Information

• Austrian East India Company
• The Austrian East India Company was established much later in the 18th century and was primarily focused on trade in the Indian Ocean region.
• It was not as influential or long-lasting as the English East India Company.
• Danish East India Company
• The Danish East India Company was founded in 1616 and focused on trade in India and Southeast Asia.
• The Danes had limited influence in India, with settlements like Tranquebar in Tamil Nadu.
• Spanish East India Company
• The Spanish East India Company is not a historically recognized entity. Spain was primarily involved in trade and colonization in the Americas rather than in India or Southeast Asia.

Shortcut Trick

Arrange the data in ascending order: 12, 19, 24, 56, 70, 71, 77, 80, 88, 98, 99.

Count the number of terms: n = 11 (which is odd).

The Median is the middle term: ((11 + 1) ÷ 2) = 6^th term.

The 6^th term in the sorted list is 71.

∴ The correct answer is 71.

Alternate Method

Given: Data set = {19, 98, 77, 24, 99, 71, 70, 56, 80, 12, 88}

Formula: Median = ((n + 1) ÷ 2)^th term (when n is odd)

The correct answer is Lushai Uprising.

Key Points

• The Lushai Uprising took place in the 19th century, not in the 20th century.
• This uprising occurred in 1877-79 in the regions now known as Mizoram.
• It involved the Lushai tribes rebelling against the British administration due to their intrusion into tribal territories and measures that threatened their autonomy.
• The uprising was a response to the British efforts to regulate the tribal way of life and prevent tribal raids into British-controlled areas.
• The British eventually subdued the rebellion, and the region was formally brought under British control through the creation of the Lushai Hills District.
• The Lushai Uprising holds historical significance as it reflects tribal resistance to colonial exploitation and intervention in their traditional way of life.

 Additional Information

• Kuki Uprising
• The Kuki Uprising took place during 1917-1919 in the Manipur region of Northeast India.
• It was a tribal revolt against the British policy of recruiting tribal men as laborers for World War I.
• The Kukis resisted colonial policies that disrupted their social and economic systems.
• Naga Revolt
• The Naga Revolt refers to the long-standing insurgency movement in the Northeast region of India.
• It gained momentum in the 20th century, with demands for Naga sovereignty and recognition of their distinct identity.
• The movement led to the formation of the Naga National Council and later the National Socialist Council of Nagaland.
• Bastar Rebellion
• The Bastar Rebellion (1910) occurred in the Bastar region of present-day Chhattisgarh.
• It was a tribal revolt against British colonial policies, particularly the exploitation of forests and tribal resources.
• The rebellion was led by tribal leaders like Gunda Dhur.

The Correct answer is Central Processing Unit.

Key Points

• The Central Processing Unit (CPU) is often referred to as the "brain of the computer".
• It is responsible for performing arithmetic, logic, control, and input/output operations as specified by the instructions in a program.
• The CPU comprises three key components:
• Arithmetic Logic Unit (ALU): Performs arithmetic and logical operations.
• Control Unit (CU): Directs the operations of the processor and coordinates with other computer components.
• Registers: Small storage units within the CPU used for quick data access.
• It processes data received from input devices and sends the output to output devices.
• The CPU interacts with the memory unit (RAM) to fetch, decode, and execute instructions.
• Modern CPUs are designed with multiple cores, allowing them to process multiple tasks simultaneously, improving performance.
• Examples of CPUs include processors from companies like Intel (e.g., Core i5, i7) and AMD (e.g., Ryzen 5, Ryzen 7).
• The performance of a CPU is measured in terms of its clock speed (e.g., GHz) and the number of cores.

 Additional Information

• Computer Processing Utility
• This term is incorrect as there is no such established term in computer science.
• The word "Utility" generally refers to software tools used for system maintenance or performance enhancement, not a hardware component like the CPU.
• Central Programming Unit
• This is an incorrect term. The CPU does not specifically deal with programming but rather the execution of instructions from programs.
• Programming is typically done using software tools like compilers, interpreters, or IDEs, not the CPU directly.
• Control Processing Unit
• This term is incorrect. While the CPU includes a Control Unit (CU), the entire unit is not referred to as the "Control Processing Unit."
• The Control Unit is just one of the components of the CPU, alongside the ALU and Registers.

Shortcut Trick

Net change in Sum = Correct value − Wrong value = 43 − 32 = +11

Change in Average = Net change in Sum ÷ Total observations = 11 ÷ 10 = +1.1

Correct Average = Old Average + Change in Average = 40 + 1.1 = 41.1

∴ The correct answer is 41.1.

Alternate Method

Given:

Total observations (n) = 10 | Old Average = 40 | Wrong value = 32 | Correct value = 43

Formula: Correct Average = (Old Sum − Wrong Value + Correct Value) ÷ n

⇒ Old Sum = Average × Number of observations = 40 × 10 = 400

⇒ Correct Sum = 400 − 32 + 43

⇒ Correct Sum = 411

⇒ Correct Average = 411 ÷ 10

⇒ Correct Average = 41.1

∴ The correct answer is 41.1.

Additional Information

Weighted Average

When two groups with averages A₁ and A₂ and sizes n₁ and n₂ are combined, the combined average is (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Arithmetic Mean Property

If each observation is increased by a constant value 'k', the new average also increases by 'k'. If multiplied by 'k', the new average becomes old average × k.

Correction Formula

Correct Average = Old Average + (Sum of Correct items − Sum of Incorrect items) ÷ Total items.

The Correct answer is Sri Lanka.

Key Points

• Sri Lanka is an island nation located in the Indian Ocean, southeast of India.
• It does not share a land boundary with India. Instead, it is separated from India by the Palk Strait and the Gulf of Mannar.
• The shortest distance between India and Sri Lanka is approximately 30 km, across the Adam's Bridge (Rama's Bridge or Ram Setu).
• Although there is no land boundary, the two nations share historical, cultural, and economic ties.
• Sri Lanka is often referred to as the "Pearl of the Indian Ocean" due to its unique shape and strategic location.

 Additional Information

• Myanmar
• Myanmar shares a land boundary with India along the northeastern region.
• The border length between India and Myanmar is approximately 1,643 km.
• Four Indian states share borders with Myanmar: Arunachal Pradesh, Nagaland, Manipur, and Mizoram.
• Myanmar is a part of the Bay of Bengal Initiative for Multi-Sectoral Technical and Economic Cooperation (BIMSTEC), which includes India as well.
• Bhutan
• Bhutan is a landlocked country in the Himalayan region and shares a land boundary with India.
• The India-Bhutan border is approximately 699 km long.
• Indian states sharing borders with Bhutan include Arunachal Pradesh, Assam, West Bengal, and Sikkim.
• The relationship between India and Bhutan is guided by the Treaty of Friendship (1949, revised in 2007).
• Afghanistan
• Afghanistan shares a land boundary with India at the northeastern tip of Jammu and Kashmir (now part of Ladakh under Indian administration) through the Wakhan Corridor.
• The Durand Line separates Afghanistan from Pakistan, and indirectly, it has implications for the Indian border.
• However, the region near the India-Afghanistan border is remote and sparsely populated.

Shortcut Trick

For a continued proportion a : b :: b : c, the relation is b² = ac.

Given b = 18 and c = 4a → a = c ÷ 4.

Substitute: 18² = (c ÷ 4) × c ⇒ 324 = c² ÷ 4.

c² = 324 × 4 = 1296.

c = √1296 = 36.

∴ The correct answer is 36.

Alternate Method

Given: a : b = b : c, c = 4a, b = 18

Formula Used: Product of means = Product of extremes

⇒ a/b = b/c

⇒ b² = ac

⇒ (18)² = a × (4a) [Since c = 4a]

⇒ 324 = 4a²

⇒ a² = 324 ÷ 4 = 81

⇒ a = 9

⇒ c = 4 × a = 4 × 9

⇒ c = 36

∴ The correct answer is 36.

Additional Information

Mean Proportional

If a, b, c are in continued proportion, then b is called the mean proportional between a and c, where b = √(ac).

Third Proportional

In the proportion a : b :: b : c, c is known as the third proportional to a and b, calculated as c = b²/a.

Fourth Proportional

If a, b, c, d are in proportion (a : b :: c : d), then d is the fourth proportional, where d = (b × c) ÷ a.

The Correct answer is Aishwarya Rai Bachchan.

Key Points

• Aishwarya Rai Bachchan is one of the most accomplished actresses in Indian cinema and has won numerous awards throughout her career.
• She is a former Miss World (1994) and is globally recognized for her beauty, grace, and acting skills.
• She has acted in a variety of films across multiple languages, including Hindi, Tamil, Telugu, Bengali, and English.
• Some of her critically acclaimed performances include roles in movies like Devdas, Guru, Chokher Bali, Raincoat, and Ponniyin Selvan.
• She has also been awarded the Padma Shri by the Government of India for her contributions to the arts.
• At the South Indian International Movie Awards (SIIMA) 2024, she won the Best Actress Award (Critics), highlighting her outstanding performance and dedication to her craft.
• SIIMA is a prestigious award ceremony that celebrates the excellence of South Indian cinema and includes categories for Telugu, Tamil, Kannada, and Malayalam films.

 Additional Information

• Alia Bhatt
• Alia Bhatt is a leading Bollywood actress known for her versatile performances in films such as Raazi, Gully Boy, and Gangubai Kathiawadi.
• She has also won several awards, including Filmfare Awards.
• In recent years, she has expanded her career internationally with her debut in Hollywood through the film Heart of Stone.
• Shraddha Kapoor
• Shraddha Kapoor is known for her roles in films like Aashiqui 2, Ek Villain, and Stree.
• She is popular for her charming screen presence and versatility in playing both romantic and thriller roles.
• She is also recognized for her singing abilities and has sung tracks in her movies.
• Deepika Padukone
• Deepika Padukone is a globally acclaimed actress known for her roles in films like Padmaavat, Bajirao Mastani, and Chennai Express.
• She has won multiple awards, including Filmfare Awards and has been named among the 100 most influential people in the world by Time magazine.
• She is also an advocate for mental health awareness and founded the Live Love Laugh Foundation.

The Correct answer is Section breaks allow for different page numbering schemes, headers, and footers within the same document, while page breaks only force content to the next page.

Key Points

• Section Breaks in MS Word allow users to divide a document into distinct sections, each with its own formatting.
• They facilitate the use of different page numbering styles such as Roman numerals, Arabic numbers, or no numbering in specific sections.
• Enable the customization of headers and footers for each section, making it possible to have unique content in these areas.
• Useful for documents where some pages require landscape orientation and others require portrait orientation, as section breaks allow for different page layouts.
• Provide flexibility to apply distinct margins, columns, and paper sizes to specific parts of a document.
• While Page Breaks only force the content to move to the next page, Section Breaks offer advanced formatting control that is essential in professional or lengthy documents.
• Ideal for creating reports, books, and proposals where formatting consistency and customizability are required across different sections.

Shortcut Trick

Working backwards using successive quotients 4, 5, 9 and last divisor 18:

Third divisor (HCF) = 18

Second divisor = 18 × 9 = 162

First divisor (Number 2) = 162 × 5 + 18 = 828

Dividend (Number 1) = 828 × 4 + 162 = 3474

LCM = (3474 × 828) ÷ 18 = 3474 × 46 = 159804

∴ The correct answer is 159804.

Alternate Method

Given: Quotients = 4, 5, 9; Last divisor = 18.

Formula Used: Dividend = (Divisor × Quotient) + Remainder; LCM × HCF = Product of two numbers.

⇒ Step 3: Last divisor is 18 and quotient is 9. Remainder is 0.

⇒ Divisor in Step 3 = 18 × 9 + 0 = 162. (This was the remainder of Step 2)

⇒ Step 2: Quotient is 5 and remainder is 18.

⇒ Divisor in Step 2 = 162 × 5 + 18 = 810 + 18 = 828. (This was the remainder of Step 1)

⇒ Step 1: Quotient is 4 and remainder is 162.

⇒ Dividend = 828 × 4 + 162 = 3312 + 162 = 3474.

⇒ Two numbers are 3474 and 828. HCF = 18.

⇒ LCM = (3474 × 828) ÷ 18 = 3474 × 46 = 159804.

∴ The correct answer is 159804.

Additional Information

Long Division Method for HCF

Also known as the Euclidean Algorithm, where the divisor of the last step (where remainder is zero) is the HCF.

LCM and HCF Relationship

For any two numbers 'a' and 'b', Product of numbers = HCF(a, b) × LCM(a, b).

Properties of HCF

HCF is always a factor of the difference between the two numbers and also a factor of their LCM.

Given:

Mr. KLM starts from Point A and drives 21 km towards the south.

He then takes a left turn, drives 7 km, turns left and drives 26 km.

He then takes a left turn and drives 11 km.

He takes a final left turn, drives 5 km and stops at Point P. 

Thus, Mr. KLM should drive 4 km (11 km - 7 km) in the east direction in order to reach Point A again.​

Hence, "Option 1" is the correct answer.

Given: (Left) 951 474 717 497 127 (Right)

According to the question:

So,

First digit of the highest number → 951 → 9

Third digit of the lowest number → 127 → 7

Thus, if the first digit of the highest number is subtracted from the third digit of the lowest number then the resultant will be → 7 - 9 → -2 

Hence, the correct answer is "Option 2".

Shortcut Trick

Net discount for 28% and 20% = 28 + 20 − (28 × 20) ÷ 100 = 48 − 5.6 = 42.4%.

Net discount for 42.4% and 10% = 42.4 + 10 − (42.4 × 10) ÷ 100.

⇒ 52.4 − 4.24 = 48.16%.

∴ The correct answer is 48.16%.

Alternate Method

Given: Successive discounts of 28%, 20%, and 10%.

Formula: SP = MP × (100 − d₁)% × (100 − d₂)% × (100 − d₃)%

Let the Marked Price (MP) be 100.

⇒ Selling Price (SP) = 100 × (72/100) × (80/100) × (90/100)

⇒ SP = 100 × 0.72 × 0.8 × 0.9 = 51.84.

⇒ Single Equivalent Discount = MP − SP = 100 − 51.84 = 48.16%.

∴ The correct answer is 48.16%.

Additional Information

Successive Discount Formula

For two successive discounts a% and b%, the single equivalent discount is (a + b − ab/100)%.

Marked Price & Selling Price

Discount is always calculated on the Marked Price (MP). SP = MP − Discount.

Given: (Left) 983 986 481 941 167 (Right)

According to the question:

So,

Third digit of the highest number → 986 → 6

First digit of the lowest number → 167 → 1

Thus, if the third digit of the highest number is subtracted from the first digit of the lowest number then the resultant will be → 1 - 6 → -5 

Hence, the correct answer is "Option 3".

The correct answer is Vidarbha.

Key Points

• Vidarbha was crowned the Ranji Trophy champion for the 2024-25 season, showcasing their dominance in Indian domestic cricket.
• The Ranji Trophy is one of the most prestigious domestic cricket tournaments in India, organized by the Board of Control for Cricket in India (BCCI).
• The tournament is named after Ranjitsinhji, the famous Indian cricketer, and it has been played since 1934-35.
• Vidarbha's cricket team represents the Vidarbha region in Maharashtra and is managed by the Vidarbha Cricket Association.
• Vidarbha has shown remarkable growth in recent years, with consistent performances in domestic cricket.
• Key players in the team’s success include seasoned cricketers and emerging talents who have contributed significantly to their victory.
• Vidarbha has previously won the Ranji Trophy titles in 2017-18 and 2018-19, making this their third title.
• Their victory highlights the strength of their domestic cricket infrastructure and the effective management by the Vidarbha Cricket Association.

 Additional Information

• Mumbai
• Mumbai holds the record for the most Ranji Trophy titles, with 41 titles to their name.
• They are known as the powerhouse of Indian domestic cricket, producing legendary cricketers such as Sachin Tendulkar, Sunil Gavaskar, and Rohit Sharma.
• Kerala
• Kerala is a relatively new entrant in the domestic cricket scene, and their performance has improved in recent years.
• Although they have not won the Ranji Trophy, the team has produced notable players like Sanju Samson.
• Tamil Nadu
• Tamil Nadu has won the Ranji Trophy twice, in 1954-55 and 1987-88.
• The state is known for its strong cricketing culture and has contributed players like Ravichandran Ashwin and Dinesh Karthik.

The Correct answer is Chaturang.

Key Points

• Chaturang is not a part of the Carnatic style of composition.
• It is a unique form of composition in the Hindustani classical music tradition.
• The term "Chaturang" translates to "four colors" or "four aspects," representing its structure, which includes four distinct components - lyrics, sargam (solfege), tarana, and rhythmic patterns.
• Chaturang is often composed to showcase the richness and diversity of Hindustani music.
• Unlike Carnatic music compositions, Chaturang does not follow the framework of Pallavi, Anupallavi, and Charanam, which are integral to Carnatic music.
• This distinction clearly separates Chaturang from the Carnatic style.

 Additional Information

• Varnam
• Varnam is a fundamental composition in Carnatic music and is often used as a warm-up piece for vocalists and instrumentalists.
• It combines intricate melodic patterns with rhythmic variations.
• Varnams are performed at the beginning of a concert and serve as an ideal demonstration of a raga’s structure and essence.
• Pallavi
• The Pallavi is the opening section of a Carnatic composition and acts as the main theme.
• It is repeated multiple times during a performance and forms the foundation for improvisation.
• It is a distinctive feature of Carnatic music compositions.
• Ragamalika
• Ragamalika translates to "garland of ragas" and is a type of composition in Carnatic music.
• It involves the use of multiple ragas within a single composition.
• Ragamalikas are often used to demonstrate the composer’s creativity and ability to transition smoothly between ragas.

The Correct answer is Its stable double-helical structure.

Key Points

• The double-helical structure of DNA is stabilized by hydrogen bonds between the nitrogenous bases and hydrophobic interactions among the base pairs.
• This stable structure ensures the faithful replication and preservation of genetic information across generations.
• The stability of DNA allows it to resist degradation and maintain its integrity, making it the most abundant genetic material.
• The backbone of DNA is made up of phosphate and deoxyribose sugar, which contributes to its chemical resilience.
• The structure also facilitates the precise pairing of bases (adenine with thymine, and cytosine with guanine), ensuring accurate genetic coding.
• The stability of DNA is further enhanced by its ability to interact with histones and other proteins, which help compact and protect it within chromosomes.

 Additional Information

• Its high mutation rate
• A high mutation rate would make DNA unstable and less reliable for preserving genetic information.
• While mutations play a role in evolution, excessive mutations can lead to genetic disorders and errors in replication.
• Its interaction with proteins
• DNA interacts with proteins like histones to form chromatin; however, this feature is not directly responsible for DNA being the most abundant genetic material.
• Protein interactions primarily help in packaging and regulation of genetic material.
• Its enzymatic roles
• DNA itself does not perform enzymatic roles; instead, enzymes like DNA polymerase and helicase act on DNA during replication and repair.
• Enzymatic roles are more relevant to RNA, which can act as a ribozyme (catalytic RNA).

Given number: 1862547

According to the question, 

Difference between the highest and lowest digits → 8 - 0 = 8

Hence, the correct answer is "Option 1".

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

Conclusions:

(I) Some drape are curtain → Does not follow (As all curtain are blinder and some blinder are drape. So it is possible but not definite.)

(II) Some blinder are screen → Follow (As all curtain are screen and all curtain are blinder. As whole curtains comes in both screen and binder, therefore it is true)

∴ Here, Only conclusion (II) follows.​

Hence, the correct answer is "Option 4".

The Correct answer is Each minister is the political head of his/her ministry.

Key Points

• The Union Council of Ministers is the executive authority in India, responsible for the administration of the country under the guidance of the Prime Minister.
• Each minister is designated as the political head of his/her ministry, meaning they are responsible for setting policies, making decisions, and ensuring the implementation of laws within their respective departments.
• Ministers work in collaboration with civil servants who are tasked with operational execution, providing expertise, and implementing policies laid down by the government.
• The political leadership of ministers ensures that the actions of their ministry align with the government’s vision and objectives, as well as the interests of the public.
• This structure is derived from the Westminster system, where the ministers are accountable to the legislature and indirectly to the public.
• The Union Council of Ministers operates under the framework of the Indian Constitution, particularly Articles 74 and 75, which define its composition, functions, and roles.

 Additional Information

• Ministers leave all work operations to be done by civil servants
• While civil servants play a crucial role in the implementation of policies, ministers do not leave all operations to them. Ministers act as the political heads, guiding the civil servants in alignment with government goals.
• Centralisation of power in local bodies
• This is incorrect because the Union Council of Ministers is responsible for national-level governance, not local bodies. Local governance is handled by Panchayati Raj Institutions and urban municipal bodies under the provisions of the Constitution.
• The abolition of the role of the Secretary
• The role of the Secretary is integral in ministries. Secretaries are senior civil servants who assist ministers by providing expertise, advice, and administrative support.
• They ensure the smooth functioning of ministries and the execution of policy decisions.

Shortcut Trick

Identify two Numbers whose Product is 45 and Sum is 14.

Factors of 45 are (1, 45), (3, 15), and (5, 9).

Only the pair (9, 5) satisfies the condition: 9 + 5 = 14 and 9 × 5 = 45.

Sum of Cubes = 9³ + 5³ = 729 + 125 = 854.

∴ The correct answer is 854.

Alternate Method

Given:

⇒ Sum of numbers (x + y) = 14

⇒ Product of numbers (xy) = 45

Formula Used:

⇒ x³ + y³ = (x + y)³ − 3xy(x + y)

Calculations:

⇒ x³ + y³ = (14)³ − 3 × 45 × (14)

⇒ x³ + y³ = 2744 − 135 × 14

⇒ x³ + y³ = 2744 − 1890

⇒ x³ + y³ = 854

The calculated value matches the third option.

∴ The correct answer is 854.

Additional Information

Sum of Cubes Identity

The expression can also be factored as x³ + y³ = (x + y)(x² − xy + y²).

Difference of Cubes

Similarly, for the difference, use the identity x³ − y³ = (x − y)(x² + xy + y²).

Square of a Sum

To find x² + y² independently, use (x + y)² − 2xy.

The logic followed here is:         

                                                                                                                                                       

Hence, the correct answer is "Option 3".