The Correct answer is Centre for Development of Telematics (C-DOT).

Key Points

• The Centre for Development of Telematics (C-DOT) is a premier Indian government-owned telecommunications technology development center.
• C-DOT collaborated with Sterlite Technologies Limited (STL) to test India's first Quantum Key Distribution (QKD) transmission in 2025.
• Quantum Key Distribution (QKD) ensures highly secure communication by leveraging the principles of quantum mechanics.
• This collaboration aims to boost cybersecurity in India, especially in critical sectors like defense, banking, and government operations.
• C-DOT, established in 1984, plays a significant role in developing indigenous telecommunication solutions and promoting self-reliance in the telecom sector.
• It has been instrumental in various telecom advancements, including the development of rural telecommunication systems and next-gen network technologies.

Additional Information

• Indian Institute of Technology (IIT)
• Indian Institutes of Technology (IITs) are a group of autonomous public technical universities in India.
• They are known for their excellence in engineering, technology, and research.
• While IITs work on various cutting-edge technologies, they were not involved in this specific QKD transmission project.
• National Institute of Technology (NIT)
• National Institutes of Technology (NITs) are premier engineering institutes in India.
• They focus on technical education and research but were not part of the Quantum Key Distribution project mentioned in the question.
• Centre for Development of Advanced Computing (C-DAC)
• C-DAC is an Indian research and development organization under the Ministry of Electronics and Information Technology.
• It is primarily known for its role in developing supercomputers and other advanced computing technologies.
• While C-DAC focuses on technological advancements, it was not involved in this specific QKD transmission collaboration.

Shortcut Trick

Ratio of Cost Price (CP) to Profit is 100 : 30 = 10 : 3.

Selling Price (SP) ratio = 10 + 3 = 13 units.

Given SP = 13 units = ₹ 2,938.

Value of 1 unit = 2,938 ÷ 13 = ₹ 226.

Profit = 3 units = 3 × 226 = ₹ 678.

∴ The correct answer is ₹ 678.

Alternate Method

Given: Profit% = 30%, Sales Income (SP) = ₹ 2,938.

Formulas: SP = CP × (100 + Profit%) ÷ 100 | Profit = SP − CP

⇒ Let the Cost Price (CP) be x.

⇒ 2,938 = x × (130 ÷ 100)

⇒ x = (2,938 × 100) ÷ 130 = ₹ 2,260.

⇒ Profit = SP − CP = 2,938 − 2,260 = ₹ 678.

∴ The correct answer is ₹ 678.

Additional Information

Relationship between CP, SP and Profit

Profit is always calculated on the Cost Price (CP) unless stated otherwise. Profit = SP − CP.

Profit Percentage

Profit% = (Profit ÷ CP) × 100. It represents the gain for every 100 units of cost.

The Correct answer is Primary memory is faster but has lower storage capacity, while secondary memory is slower but provides large storage capacity.

Key Points

• Primary memory, also known as RAM (Random Access Memory), is a type of memory that is directly accessible by the CPU and is used for temporary data storage during processing.
• It is extremely fast, which allows the CPU to quickly access and execute instructions.
• However, primary memory has a smaller storage capacity compared to secondary memory, making it unsuitable for long-term storage of large amounts of data.
• Secondary memory, such as hard drives, SSDs, or external storage devices, offers significantly higher storage capacities compared to primary memory.
• Secondary memory is slower in terms of read/write speeds but is designed for long-term storage of data, including files, applications, and operating system components.
• Primary memory is volatile, meaning data is erased when the power is turned off, while secondary memory is non-volatile and retains data even without power.
• This distinction makes primary memory suitable for active processing and secondary memory ideal for permanent storage.

Additional Information

• Option 1: Secondary memory is volatile, meaning data is lost when power is turned off, while primary memory is non-volatile and retains data
• This is incorrect because primary memory (RAM) is volatile, meaning it loses its data when the system is powered off, while secondary memory (e.g., hard drives, SSDs) is non-volatile and retains data even without power.
• Option 3: Both primary and secondary memory are directly accessible by the CPU for processing instructions
• This is incorrect because only primary memory (RAM) is directly accessible by the CPU. Secondary memory requires intermediate processes, such as loading data into RAM, before the CPU can access it.
• Option 4: Primary memory is used for long-term storage, while secondary memory is used for temporary storage of data
• This is incorrect as it reverses the roles of the two types of memory. Primary memory is used for temporary storage during active processing, while secondary memory is used for long-term data storage.

The Correct answer is Policies of British favouring sati, female infanticide and widow re-marriage.

Key Points

• The Revolt of 1857 was primarily driven by dissatisfaction among Indian rulers, soldiers, and civilians against British rule.
• The reasons for the revolt included political, social, economic, and military grievances.
• The policies of the British aimed at abolishing Sati, encouraging widow remarriage, and banning female infanticide were viewed positively by many reformists and did not significantly contribute to the rebellion.
• These reforms were designed to address social issues and were not directly linked to the anger that fueled the revolt.
• The major causes of the revolt were tied to issues such as religious interference, exploitation, and military discontent.
• The introduction of reforms like widow remarriage was progressive in nature and did not evoke widespread resentment comparable to other causes.
• Thus, this option is NOT considered one of the significant causes of the Revolt of 1857.

Additional Information

• Introduction of greased cartridge
• The introduction of the greased cartridge was one of the immediate causes of the Revolt of 1857.
• The cartridges were rumored to be greased with cow and pig fat, which insulted both Hindu and Muslim religious sentiments.
• This created widespread resentment among Indian soldiers, also known as sepoys, in the British army.
• Lack of contact between the ruler and the ruled
• The British administration was characterized by a lack of direct engagement with the local population.
• Policies were often implemented without understanding or addressing the grievances of the Indian populace.
• This alienation contributed to the widespread discontent among the people.
• Policy of Doctrine of Lapse
• The Doctrine of Lapse, introduced by Lord Dalhousie, allowed the British to annex Indian states if their rulers died without a male heir.
• This policy led to the annexation of many princely states such as Jhansi, Satara, and Nagpur, creating resentment among Indian rulers.
• The annexations were seen as a direct attack on the sovereignty of Indian rulers and fueled opposition to British rule.

The Correct answer is Gorakhpur.

Key Points

• Gorakhpur, a city in the Indian state of Uttar Pradesh, is set to establish India’s first Integrated Waste Management City cum-Learning Centre by September 2025.
• The initiative aims to create a garbage-free environment by managing waste effectively and educating the public about sustainable waste management practices.
• This project is aligned with India’s national goals of promoting sustainability and ensuring environmental conservation.
• The facility will serve as a learning hub for students, professionals, and the general public to understand the importance of integrated waste management.
• Technologies for waste segregation, recycling, and energy recovery are likely to be incorporated into the center to ensure effective waste management.
• This project reflects the commitment of local governance and stakeholders to address the issue of urban waste management innovatively and efficiently.

Additional Information

• Moradabad
• Moradabad, located in Uttar Pradesh, is known as the "Brass City of India" due to its prominent brass handicrafts industry.
• The city has not been highlighted for any specific integrated waste management projects as of now.
• Kanpur
• Kanpur is a major industrial city in Uttar Pradesh, recognized for its leather and textile industries.
• While Kanpur has faced challenges related to industrial pollution and waste management, it is not the location of the first Integrated Waste Management City.
• Agra
• Agra, famously known for the Taj Mahal, is a major tourist destination in India.
• The city has undertaken initiatives for solid waste management but is not the site for the first Integrated Waste Management City.

Decoding symbols:

Given: M × N ÷ O – P + Q

M × N → M is the wife of N.

N ÷ O → N is the father of O.

O – P → O is the brother of P.

P + Q → P is the sister of Q.

Here, M is Q's mother.

Hence, the correct answer is "Option 3".

The Correct answer is It dynamically resizes a formula's output range when the formula returns multiple values.

Key Points

• The Spill Range feature is part of the dynamic array functionality introduced in newer versions of MS Excel, such as Excel 365 and Excel 2019.
• When a formula returns multiple values, the output automatically "spills" into adjacent cells, creating a dynamic range.
• This eliminates the need for manually copying formulas into multiple cells, enhancing efficiency.
• The spill range is automatically updated when the formula is changed or when new data is added, ensuring a dynamic and responsive data structure.
• Common functions like SEQUENCE, SORT, FILTER, UNIQUE, RANDARRAY utilize spill ranges to dynamically display multiple outputs.
• If adjacent cells already contain data preventing the "spill," Excel will display a #SPILL! error, signaling a conflict in the output range.
• This feature is particularly useful for handling arrays and performing complex data manipulations with ease.

Additional Information

• Option 1: It allows multiple users to simultaneously edit different ranges within the same worksheet
• This feature is unrelated to the Spill Range functionality. Collaborative editing in Excel is supported through Excel Online or real-time co-authoring features in cloud-based versions.
• It enables teams to work together on the same file, but does not dynamically handle formula outputs.
• Option 2: It restricts data entry within a specific range of cells based on predefined criteria
• This refers to Data Validation, a tool used to limit or control the type of data entered into cells.
• Data validation is useful for ensuring accuracy and consistency but does not involve dynamic resizing or formula outputs.
• Option 4: It automatically saves the workbook to a cloud location at predefined intervals
• This describes the AutoSave feature available in Microsoft Office applications integrated with OneDrive or SharePoint.
• AutoSave ensures that your work is saved continuously to avoid data loss, but it does not relate to the handling of dynamic formula outputs.

The Correct answer is Brisbane.

Key Points

• The Indian External Affairs Minister inaugurated India’s 4th consulate in Brisbane in November 2024.
• The establishment of the consulate reflects India’s growing diplomatic presence in Australia.
• Brisbane is the capital city of Queensland, one of the largest states in Australia, and is known for its economic significance and cultural diversity.
• The city has a vibrant Indian diaspora, and the new consulate will serve their administrative and consular needs.
• The consulate will also enhance bilateral relations between India and Australia in sectors such as trade, education, and cultural exchange.
• India’s diplomatic footprint in Australia now includes consulates in Melbourne, Sydney, Perth, and Brisbane, along with the High Commission in Canberra.

Additional Information

• Perth
• Perth is the capital of Western Australia and is known for its mining and natural resource industries.
• India already has a consulate established in Perth to cater to the needs of the Indian diaspora in Western Australia.
• Melbourne
• Melbourne is renowned for its education sector and has a significant number of Indian students pursuing higher education.
• India’s consulate in Melbourne supports consular services for Victoria and Tasmania.
• Sydney
• Sydney is Australia’s largest city and a major hub for financial and cultural activities.
• India’s consulate in Sydney handles consular services for New South Wales and serves a large Indian community.

The Correct answer is Local government at the village level.

Key Points

• The Village Panchayat is the grassroots-level institution of the Panchayati Raj system in India.
• It is a part of the three-tier system of rural local governance which includes the Village Panchayat, Panchayat Samiti (block level), and Zila Parishad (district level).
• The Village Panchayat is responsible for the administration and development of rural areas.
• This system of governance was established under the provisions of the 73rd Constitutional Amendment Act, 1992.
• The head of the Village Panchayat is known as the Sarpanch, who is elected by the members of the Gram Sabha.
• The Village Panchayat performs various functions such as sanitation, water supply, rural development, primary education, and infrastructure development.
• It operates under the framework provided by the State Panchayati Raj Acts, with some variations across different states of India.
• The financial resources of the Village Panchayat include grants from the state government, local taxes, and other sources.

Additional Information

• A district-level administrative body
• This refers to the Zila Parishad, which operates at the district level.
• The Zila Parishad supervises and coordinates the activities of the Village Panchayats and Panchayat Samitis within its jurisdiction.
• It is responsible for planning and development at the district level.
• A block-level committee
• This refers to the Panchayat Samiti, which operates at the block level.
• It serves as a link between the Village Panchayat and the Zila Parishad.
• The Panchayat Samiti is responsible for implementing developmental programs at the block level.
• An urban municipal corporation
• This refers to an administrative body that governs urban areas, not rural areas.
• Urban municipal corporations are responsible for managing urban infrastructure, sanitation, waste management, and public services.
• They do not fall under the Panchayati Raj system, which is specific to rural governance.

The Correct answer is Triple-click on any word within the paragraph.

Key Points

• In MS Word 2019, selecting an entire paragraph quickly can save time and effort during editing tasks.
• Triple-clicking on any word within the paragraph is the fastest method to select the entire paragraph. This action highlights the entire block of text immediately.
• This functionality works in most modern versions of Microsoft Word, including the 2019 edition.
• The reason why triple-clicking works is that Word recognizes text structures like words, sentences, and paragraphs. Triple-clicking is a shortcut for paragraph selection.
• Using this shortcut eliminates the need to drag the cursor manually, which can be prone to errors, especially with large paragraphs or precise selections.
• This feature is part of Word's user-friendly design, ensuring efficiency in text formatting and editing.
• It is particularly useful in situations involving multi-paragraph documents, such as reports, essays, or official letters.

Additional Information

• Right-click and choose 'Paragraph'
• The right-click menu provides options for formatting and paragraph settings like alignment, spacing, and indentation, but it does not select the entire paragraph.
• This option is more suitable for customizing paragraph layout rather than for selection.
• Press and hold Alt while clicking the paragraph
• Pressing and holding Alt is used for rectangular selection or selecting specific areas of text, not for selecting an entire paragraph.
• This feature is helpful in creating columnar or block text selections.
• Double-click anywhere in the paragraph
• Double-clicking selects a single word, not the entire paragraph.
• It is a useful shortcut when you want to edit or format a specific word quickly.

The Correct answer is 2021.

Key Points

• The New Public Sector Enterprise (PSE) Policy was notified by the Government of India in the year 2021.
• This policy is aligned with the vision of Atma Nirbhar Bharat, which aims to make India self-reliant across various sectors.
• The policy provides guidance on strategic disinvestment and seeks to reduce the presence of the government in Public Sector Enterprises (PSEs) across all sectors of the economy.
• It emphasizes that the Government will only retain PSEs in strategic sectors, while in non-strategic sectors, PSEs will either be privatized or closed.
• The strategic sectors identified under the policy include areas such as atomic energy, defense, transport, telecommunications, banking, and insurance.
• The policy supports the Government’s effort to optimize resource allocation, enhance efficiency, and facilitate growth by allowing private sector participation in industries previously dominated by the public sector.
• Strategic disinvestment and privatization under the policy aim to unlock the potential of PSEs by improving their competitiveness, profitability, and operational efficiency.

Additional Information

• 2025
• This year is a future date and does not relate to the notification of the New Public Sector Enterprise Policy.
• 2024
• This is another future date and does not correspond to the introduction of the policy.
• 2023
• While 2023 is a recent year, the New Public Sector Enterprise Policy was already notified earlier in 2021.

The Correct answer is It began the antibiotic era.

Key Points

• The discovery of penicillin is considered a revolutionary event in the field of medicine because it marked the beginning of the antibiotic era.
• Penicillin was discovered by Alexander Fleming in 1928 when he observed that the fungus Penicillium notatum inhibited the growth of bacteria.
• It was the first naturally occurring antibiotic to be discovered and introduced for clinical use.
• Penicillin drastically changed the treatment of bacterial infections like pneumonia, syphilis, strep throat, and wound infections, saving millions of lives.
• Its introduction significantly reduced the mortality rate from infectious diseases, which were previously a leading cause of death.
• The success of penicillin paved the way for the discovery and development of other antibiotics, transforming the field of medicine and public health.
• During World War II, penicillin was mass-produced and used to treat soldiers, further proving its effectiveness and importance.
• It is considered one of the most important medical discoveries of the 20th century and has been instrumental in controlling infections globally.

Additional Information

• It was used for colouring bacteria
• Penicillin was not used for colouring bacteria. However, in microbiology, certain dyes like crystal violet and methylene blue are commonly used for staining bacteria to observe their structure.
• It treated pain rather than infections
• This is incorrect because penicillin is an antibiotic, which means it is used to treat bacterial infections, not pain. Painkillers like aspirin or paracetamol are used to manage pain.
• It was used only in animals
• Penicillin was first tested on animals to ensure its safety, but its primary use has been for humans. Later, it was also used in veterinary medicine to treat bacterial infections in animals.

Shortcut Trick

Base Average of 8 numbers = 15.

Deviation for 5 numbers = 5 × (18 − 15) = +15.

To balance, Net Deviation for remaining 3 numbers must be −15.

Deviation per remaining number = −15 ÷ 3 = −5.

Required Average = 15 − 5 = 10.

∴ The correct answer is 10.

Alternate Method

Given: Average of 8 numbers = 15, Average of 5 numbers = 18.

Formula: Total Sum = Average × Count of numbers

⇒ Total sum of 8 numbers = 8 × 15 = 120

⇒ Sum of first 5 numbers = 5 × 18 = 90

⇒ Sum of remaining 3 numbers = 120 − 90 = 30

⇒ Average of remaining 3 numbers = 30 ÷ 3 = 10

∴ The correct answer is 10.

Additional Information

Basic Average Formula

The arithmetic mean or average is calculated as the Sum of all observations ÷ Total number of observations.

Combined Average

If two groups have n₁ and n₂ elements with averages a₁ and a₂, the combined average = (n₁a₁ + n₂a₂) ÷ (n₁ + n₂).

Weighted Average Principle

The sum of deviations of all values from the average is always zero. This is the core of the deviation method shortcut.

Shortcut Trick

Net deviation in sum = (Correct scores) − (Wrongly recorded scores)

Net deviation = (25 + 30) − (35 + 28) = 55 − 63 = −8

Average correction = Net deviation ÷ Number of students = −8 ÷ 50 = −0.16

Actual Average = 45 − 0.16 = 44.84

∴ The correct answer is 44.84.

Alternate Method

Given: Total students = 50 | Initial Average = 45 | Wrong scores = 35, 28 | Correct scores = 25, 30

Formula: Actual Average = [ (Initial Average × N) − (Wrong Sum) + (Correct Sum) ] ÷ N

⇒ Total Initial Sum = 50 × 45 = 2250

⇒ Total Wrong Sum recorded = 35 + 28 = 63

⇒ Total Correct Sum to be recorded = 25 + 30 = 55

⇒ Correct Total Sum = 2250 − 63 + 55 = 2242

⇒ Actual Average = 2242 ÷ 50

⇒ Actual Average = 44.84

∴ The correct answer is 44.84.

Additional Information

Properties of Average

If every value in a data set is increased or decreased by a constant k, the mean (average) of the data set also increases or decreases by k.

Weighted Average

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

Correction Principle

New Average = Old Average + [ (Correct Value − Incorrect Value) ÷ Total Number of Items ]. This is the fastest way to solve entry-error problems.

Shortcut Trick

Let A's age be A and B's age be B.

From the first condition: 5A + B = 95 ⇒ B = 95 − 5A.

Substitute B in the second condition: A + 2.2(95 − 5A) = 63.

A + 209 − 11A = 63 ⇒ 10A = 146 ⇒ A = 14.6 years.

B = 95 − 5(14.6) = 95 − 73 = 22 years.

∴ The correct answer is 22 years.

Alternate Method

Given:

Condition 1: 5 × (A's age) + (B's age) = 95

Condition 2: (A's age) + 2.2 × (B's age) = 63

Calculations:

Let A's age be A and B's age be B.

⇒ 5A + B = 95 → (i)

⇒ A + 2.2B = 63 → (ii)

Multiply equation (ii) by 5 to eliminate A:

⇒ 5(A + 2.2B) = 5 × 63

⇒ 5A + 11B = 315 → (iii)

Subtract equation (i) from equation (iii):

⇒ (5A + 11B) − (5A + B) = 315 − 95

⇒ 10B = 220

⇒ B = 220 ÷ 10

⇒ B = 22

∴ The correct answer is 22 years.

Additional Information

Linear Equations in Two Variables

Equations of the form ax + by = c are solved using elimination or substitution methods to find values of unknown variables.

Ages Word Problems

Always translate phrases like "n times" into multiplication and "added to" into addition to form algebraic expressions accurately.

Given: (Left) 823 664 309 431 175 (Right)

According to the question:

So,

First digit of the highest number → 823 → 8

Third digit of the lowest number → 175 → 5

Thus, if the first digit of the highest number is added to the third digit of the lowest number then the resultant will be → 8 + 5 → 13 

Hence, "Option 3" is the correct answer.

Shortcut Trick Given a2 + b2 = 83 and ab = 6. Using identity: (a − b)2 = (a2 + b2) − 2ab = 83 − 12 = 71 → (a − b) = √71. Using identity: (a + b)2 = (a2 + b2) + 2ab = 83 + 12 = 95. The required ratio (a − b) / (a + b) is represented by the values √71 / 95. ∴ The correct answer is √71 / 95.

Alternate Method Given: a2 + b2 = 83 ab = 6 a > b Formula Used: (a − b)2 = a2 + b2 − 2ab (a + b)2 = a2 + b2 + 2ab

Calculations: ⇒ First, we find the numerator (a − b): ⇒ (a − b)2 = (a2 + b2) − 2(ab) ⇒ (a − b)2 = 83 − 2(6) = 83 − 12 = 71 ⇒ Since a > b, a − b = √71 ⇒ Next, we evaluate the sum term for the denominator: ⇒ (a + b)2 = (a2 + b2) + 2(ab) ⇒ (a + b)2 = 83 + 2(6) = 83 + 12 = 95 ⇒ The required value is expressed as the ratio of (a − b) to the squared sum component: ⇒ Ratio = √71 / 95 ∴ The correct answer is √71 / 95.

Additional Information Algebraic Square Identities (a + b)2 + (a − b)2 = 2(a2 + b2) and (a + b)2 − (a − b)2 = 4ab. Relationship between Sum and Difference (a + b)2 = (a − b)2 + 4ab. This is useful for converting between sum and difference when the product ab is known. Difference of Squares a2 − b2 = (a − b)(a + b). This factors the difference of two squares into the product of their root sum and difference.

The correct answer is Justice Bhushan Ramkrishna Gavai.

Key Points

• Justice Bhushan Ramkrishna Gavai is slated to become the 52nd Chief Justice of India (CJI) in May 2025.
• He is currently a judge of the Supreme Court of India.
• Justice Gavai is known for his significant contributions in the field of constitutional law and has delivered landmark judgments during his tenure.
• He hails from the state of Maharashtra and has an extensive legal career, including serving as a judge in the Bombay High Court before his elevation to the Supreme Court.
• The appointment of the Chief Justice of India is governed by the principle of seniority among the judges of the Supreme Court.
• The tenure of each Chief Justice is typically short, as it depends on their date of retirement, which is fixed at the age of 65 years.
• Justice Bhushan Ramkrishna Gavai will serve as the 52nd Chief Justice of India, continuing the legacy of upholding the Constitution of India.

Additional Information

• Justice Pamidighantam Sri Narasimha
• Justice Narasimha is a sitting judge of the Supreme Court of India and is considered an expert in constitutional matters.
• He was elevated to the Supreme Court in 2021 and has a distinguished career as an advocate before his judicial appointment.
• He is expected to serve as the 28th Chief Justice of India in the future.
• Justice Prashant Kumar Mishra
• Justice Mishra is a sitting judge of the Supreme Court and previously served as the Chief Justice of the Andhra Pradesh High Court.
• He has expertise in civil and criminal law and has contributed to the development of jurisprudence in India.
• Justice Sudhanshu Dhulia
• Justice Dhulia is also a sitting judge of the Supreme Court and has served as the Chief Justice of the Gauhati High Court.
• He is known for his work in the areas of administrative law and environmental law.

The logic followed here is:

Given: # : NQP :: HKJ : %

Option 1) # = QTO, % = EEG → QTO : NQP :: HKJ : EEG

Option 2) # = YTS, % = EUG → YTS : NQP :: HKJ : EUG

Option 3) # = QTS, % = EHG → QTS : NQP :: HKJ : EHG

Option 4) # = OMS, % = ERG → OMS : NQP :: HKJ : ERG

Hence, "Option 3" is the correct answer.

Shortcut Trick

Restore original production after a 20% decrease.

Using the formula for percentage increase required: Increase % = [r ÷ (100 − r)] × 100

Here, r = 20%

Required Increase = [20 ÷ (100 − 20)] × 100 = (20 ÷ 80) × 100 = 1/4 × 100 = 25%

∴ The correct answer is 25%.

Alternate Method

Given: Decrease in production = 20%

Formula Used: Production = Manpower/Hours × Efficiency (To restore original, we find the inverse ratio)

⇒ Let the initial production be 100 units.

⇒ After 20% decrease, new production = 100 − 20 = 80 units.

⇒ To restore original production, we need to increase from 80 back to 100.

⇒ Increase required = 100 − 80 = 20 units.

⇒ Percentage increase in working hours = (20 ÷ 80) × 100

⇒ Percentage increase = 1/4 × 100 = 25%

∴ The correct answer is 25%.

Additional Information

Percentage Change Invariance

If one quantity decreases by r%, the other must increase by [r ÷ (100 − r)] × 100 to keep the product constant.

Product Stability Ratio

Commonly applied in Price-Consumption and Time-Speed problems where the total expenditure or distance remains fixed.

Successive Percentage

Net change for successive x% and y% is [x + y + (xy/100)]%.

Given: D, E, F, G, M, N and O are sitting around a circular table, facing the centre of the table.

1) F sits third to the left of D.

2) N sits to the immediate left of D.

3) G sits to the immediate left of E.

4) E sits second to the left of O.

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

Thus, O sits fourth to the right of M.

Hence, "Option 3" is the correct answer.

Shortcut Trick

For a number to be divisible by 4, the last two digits must be divisible by 4.

The last two digits of 32043p88 are 88.

Since 88 is already divisible by 4 (88 ÷ 4 = 22), the value of p can be any digit from 0 to 9.

The maximum value of a single digit is 9.

∴ The correct answer is 9.

Alternate Method

Given: Eight-digit number = 32043p88

Divisibility Rule of 4: A number is divisible by 4 if the number formed by its last two digits is divisible by 4.

⇒ Last two digits of the number = 88

⇒ Check divisibility: 88 ÷ 4 = 22 (Remainder = 0)

⇒ Since 88 is divisible by 4, the entire number is divisible by 4 regardless of the value of p.

⇒ The digit p is at the hundreds place.

⇒ Possible values for p = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

⇒ The maximum value among these is 9.

∴ The correct answer is 9.

Additional Information

Divisibility by 2ⁿ

Divisibility by 2 requires last 1 digit to be even; by 4 (2²) requires last 2 digits; by 8 (2³) requires last 3 digits.

Divisibility by 3 and 9

A number is divisible by 3 or 9 if the sum of its digits is divisible by 3 or 9 respectively.

Divisibility by 11

Difference between the sum of digits at odd places and even places must be 0 or a multiple of 11.

The Correct answer is New Delhi, India.

Key Points

• The World Sustainable Development Summit (WSDS) is an annual flagship event organized by the Energy and Resources Institute (TERI).
• The summit focuses on sustainability concerns, climate change, and environmental issues to promote global cooperation.
• In March 2025, the WSDS was held in New Delhi, India, which is known for hosting several high-profile international events related to climate and sustainable development.
• The summit serves as a platform for policy-makers, researchers, industry representatives, and global leaders to discuss strategies for achieving sustainable development goals (SDGs).
• New Delhi, the capital city of India, is often chosen for such events due to its political significance, infrastructure, and accessibility.
• The WSDS 2025 emphasized themes like renewable energy, water conservation, climate action, and innovative technologies to address environmental challenges.
• The summit also featured the participation of international organizations, global experts, and national leaders to foster collaboration and exchange ideas on sustainability.
• TERI, headquartered in New Delhi, plays a key role in promoting research and innovation to mitigate climate change and enhance sustainable practices.

Additional Information

• Mumbai, India
• Mumbai is one of India’s largest metropolitan cities and a financial hub.
• While Mumbai hosts numerous business and trade-related summits, it is not commonly associated with major international sustainability-focused events like WSDS.
• The city is known for its economic significance and vibrant culture but lacks the political infrastructure required for hosting global policy summits.
• Bengaluru, India
• Bengaluru, often referred to as the Silicon Valley of India, is famous for its technology and innovation hubs.
• The city is a leader in research and development, especially in areas like IT and renewable energy.
• Although Bengaluru has a rich tradition of hosting tech-focused events, WSDS is traditionally held in New Delhi for its global outreach and political significance.
• Hyderabad, India
• Hyderabad is renowned for its pharmaceutical and biotechnology industries.
• The city has a growing reputation for hosting scientific and industrial conferences.
• However, WSDS is generally hosted in New Delhi to better align with national-level policy-making and international collaboration.

The logic followed here is:

Given: # : TVS :: IKH : %

Option 1) # = KNV, % = FXC → KNV : TVS :: IKH : FXC

Option 2) # = WOZ, % = UQE → WOZ : TVS :: IKH : UQE

Option 3) # = WYV, % = FHE → WYV : TVS :: IKH : FHE

Option 4) # = IOV, % = WEE → IOV : TVS :: IKH : WEE

Hence, "Option 3" is the correct answer.

The Correct answer is Dhiraj Bommadevara.

Key Points

• Dhiraj Bommadevara secured the bronze medal in the men's individual recurve event at the Archery World Cup 2025 Stage 1.
• This event is a part of the prestigious Archery World Cup series, which showcases the top archers from around the world.
• Dhiraj’s achievement is significant as it highlights the growing presence of Indian athletes in international archery competitions.
• He competed against some of the world’s best archers and displayed exceptional skill and determination to claim the bronze medal.
• This victory contributes to India’s reputation as a rising powerhouse in the field of archery.
• His success can inspire many aspiring athletes to pursue excellence in sports, particularly in archery.

Additional Information

• Abhishek Verma
• Abhishek Verma is an Indian archer who specializes in the compound category, not the recurve category.
• He has won multiple medals in international events, including the Asian Games and World Cups, in the compound discipline.
• Tarundeep Rai
• Tarundeep Rai is a veteran Indian archer who has represented India in several international competitions in the recurve category.
• He has previously won silver medals in the Asian Games but did not win the bronze medal in the 2025 World Cup Stage 1.
• Atanu Das
• Atanu Das is another prominent Indian recurve archer known for his performances in events like the Olympics and World Cups.
• He is a key figure in Indian archery but was not the one who won the bronze medal in this particular event.

Given: A, B, C, D, E and F live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it, number 2 and so on, till the topmost floor is numbered 6. B lives on an even numbered floor but not 6.

1) The sum of floors on which F and B live is 7.

2) B lives on an even numbered floor but not 6.

3. D lives immediately above C.

4) The sum of floors on which B and E live is 3.

After positioning E only one position is left which will be occupied by the only person left i.e. A.

Thus, three people live below D.

Hence, "Option 2" is the correct answer.

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 resultant 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, "Option 3" is the correct answer.

The correct answer is Slave Dynasty.

Key Points

• 'Adhai Din Ka Jhonpra', located in Ajmer, Rajasthan, is one of the earliest examples of Indo-Islamic architecture in India.
• It was constructed during the period of the Slave Dynasty (1206-1290 AD), founded by Qutb al-Din Aibak, a prominent ruler of the Delhi Sultanate.
• The structure was originally a Sanskrit college, which was converted into a mosque by Qutb al-Din Aibak in 1199 AD.
• The name 'Adhai Din Ka Jhonpra' (meaning "shed of two and a half days") is derived from a legend that suggests the mosque was built in just two and a half days.
• The mosque features a mix of Hindu, Jain, and Islamic architectural styles, showcasing the transition of Indian architectural traditions during the period.
• It is renowned for its intricate carvings, floral motifs, and calligraphy, which reflect the skilled craftsmanship of the era.
• The mosque is a significant historical site and is considered an important example of the cultural and architectural synthesis that occurred during the Slave Dynasty.

Additional Information

• Lodhi Dynasty
• The Lodhi Dynasty was the last dynasty of the Delhi Sultanate and existed between 1451 and 1526.
• It was founded by Bahlul Khan Lodhi and is known for its contributions to Indo-Islamic architecture, including the Lodhi Gardens in Delhi.
• Tughlaq Dynasty
• The Tughlaq Dynasty ruled from 1320 to 1414 and is known for its architectural innovations, such as the construction of Tughlaqabad Fort by Ghiyasuddin Tughlaq.
• The dynasty also focused on urban planning and created several fortified cities.
• Khilji Dynasty
• The Khilji Dynasty ruled from 1290 to 1320 and was known for its military conquests under rulers like Alauddin Khilji.
• The dynasty contributed to the development of Indo-Islamic architecture, including the construction of the Alai Darwaza at the Qutub Complex.

Shortcut Trick

Total interest percentage for 3 years = 3% × 3 = 9%.

Total Amount = 100% + 9% = 109% of the Principal.

Amount = 109% × 1380 = 1.09 × 1380 = ₹1504.2.

∴ The correct answer is ₹1504.2.

Alternate Method

Given: Principal (P) = ₹1380, Rate (R) = 3% per annum, Time (T) = 3 years.

Formula Used: Simple Interest (SI) = (P × R × T) ÷ 100 | Amount (A) = P + SI

⇒ Simple Interest = (1380 × 3 × 3) ÷ 100

⇒ Simple Interest = (1380 × 9) ÷ 100 = 12420 ÷ 100 = ₹124.2

⇒ Final Amount = Principal + Simple Interest

⇒ Final Amount = 1380 + 124.2 = ₹1504.2

∴ The correct answer is ₹1504.2.

Additional Information

Simple Interest Characteristics

In Simple Interest, the Principal remains constant throughout the Time period, and the Interest earned each year is always the same.

Amount Formula

The Total Amount (A) can also be calculated using the direct formula: A = P[1 + (R × T) ÷ 100].

Effective Rate

The effective rate of interest for the entire duration in SI is simply the product of the annual rate and the number of years.

The Correct answer is Sir Edward Maclagan.

Key Points

• Sir Edward Maclagan was an important figure in the history of cooperative movements in India.
• He headed the 1915 Committee, which was formed to examine the cooperative movement in India.
• The committee was tasked with studying the functioning and impact of cooperative societies and their role in the development of rural areas.
• The findings of the committee emphasized the importance of cooperatives as a tool for economic and social upliftment in the country.
• It laid the foundation for further reforms and development in the cooperative sector, including the introduction of the Cooperative Societies Act.
• The committee recommended measures to improve the efficiency and expand the reach of cooperative societies in India.
• Cooperative movements were seen as vital for addressing issues like rural credit shortages and promoting self-reliance among farmers and rural communities.

Additional Information

• Lord Curzon
• Lord Curzon was a British statesman who served as the Viceroy of India from 1899 to 1905.
• He is known for his controversial decision to partition Bengal in 1905, which led to widespread protests and the eventual reversal of the partition in 1911.
• He played a key role in the establishment of the Archaeological Survey of India to preserve historical monuments.
• Lord Irwin
• Lord Irwin, also known as Edward Wood, served as the Viceroy of India from 1926 to 1931.
• He is notable for signing the Gandhi-Irwin Pact in 1931, which marked a crucial moment in India’s struggle for independence.
• His tenure was marked by the Civil Disobedience Movement led by Mahatma Gandhi.
• Sir John Simon
• Sir John Simon was a British politician and head of the Simon Commission, which arrived in India in 1928.
• The commission was tasked with reviewing the constitutional reforms in India but faced widespread opposition due to the absence of Indian representation.
• The protests against the Simon Commission were a significant event in India’s freedom struggle, leading to the demand for Purna Swaraj (Complete Independence).

Decoding signs:

Required resultant: 200

So, checking each option one by one:

Option 1) 64 Q 16 P 60 R 32 S 8 ⇒ 64 × 16 ÷ 60 + 32 − 8

⇒ 64 × 16 ÷ 60 + 32 − 8

⇒ 64 × 0.27 + 32 − 8

⇒ 17.28 + 32 − 8

⇒ 49.28 − 8

⇒ 41.28

Option 2) 64 R 16 Q 32 S 60 P 8 ⇒ 64 + 16 × 32 − 60 ÷ 8

⇒ 64 + 16 × 32 − 60 ÷ 8

⇒ 64 + 16 × 32 − 7.5

⇒ 64 + 512 − 7.5

⇒ 576 − 7.5

⇒ 568.5

Option 3) 64 S 16 R 60 P 32 Q 8 ⇒ 64 − 16 + 60 ÷ 32 × 8

⇒ 64 − 16 + 60 ÷ 32 × 8

⇒ 64 − 16 + 1.875 × 8

⇒ 64 + 15 − 16

⇒ 79 − 16

⇒ 63

Option 4) 64 P 16 S 60 R 32 Q 8 ⇒ 64 ÷ 16 − 60 + 32 × 8

⇒ 64 ÷ 16 − 60 + 32 × 8

⇒ 4 − 60 + 32 × 8

⇒ 4 + 256 − 60

⇒ 260 − 60

⇒ 200

Hence, "Option 4" is the correct answer.

The correct answer is Pune.

Key Points

• Pune is located on the leeward side of the Western Ghats, which causes it to experience a rain-shadow region.
• A rain-shadow region occurs when mountains obstruct moist winds, leading to heavy rainfall on the windward side and dry conditions on the leeward side.
• The Western Ghats block the southwest monsoon winds, preventing much of the rain from reaching Pune.
• Pune receives an average annual rainfall of approximately 700 mm, which is relatively low compared to areas on the windward side of the Western Ghats.
• This geographical feature makes Pune's climate semi-arid, with hot summers and moderate winters.
• Despite being in a rain-shadow region, Pune is a major city in Maharashtra known for its educational institutions, IT industry, and cultural heritage.

Additional Information

• Shillong
• Shillong is located in Meghalaya, which is part of the northeastern region of India.
• It is situated on the windward side of the Khasi Hills, which causes it to receive heavy rainfall during the monsoon season.
• The nearby Cherrapunji and Mawsynram regions are among the wettest places on Earth.
• Cochin
• Cochin (Kochi) is located in the state of Kerala, on the windward side of the Western Ghats.
• It receives abundant rainfall due to the southwest monsoon winds.
• The city is known for its backwaters, port, and spice trade.
• Goa
• Goa is situated on the western coast of India, facing the Arabian Sea.
• It receives significant rainfall during the southwest monsoon season.
• Goa is famous for its beaches, tourism, and Portuguese heritage.

Given Table:

According to the given condition:

Given: # 8 9 $

Here, no rules applies here.

→ coded as Z 

8 → coded as B

9 → coded as Y 

$ → coded as U

So, # 8 9 $ → Coded as ZBYU

Hence, "Option 3" is the correct answer.

Shortcut Trick

Relative Speed = 99 + 72 = 171 km/hr = 171 × (5/18) = 47.5 m/s.

Total Length (A + B) = 47.5 × 46 = 2185 m.

Length Ratio A : B = 1 : 1.5 = 2 : 3 ⇒ 5 units = 2185 m ⇒ 1 unit = 437 m.

Length of Train B = 3 × 437 = 1311 m.

Speed of B = 72 × (5/18) = 20 m/s. Bridge Crossing: 20 × 82 = 1640 m.

Bridge Length = 1640 − 1311 = 329 m.

∴ The correct answer is 329 m.

Alternate Method

Given: Speed A = 99 km/hr, Speed B = 72 km/hr, Time = 46 s, Length B = 1.5 × Length A.

Formula Used: Distance = Speed × Time; Relative Speed (Opposite) = S₁ + S₂.

⇒ Relative Speed = (99 + 72) × (5/18) = 171 × (5/18) = 47.5 m/s.

⇒ Total Distance = L_A + L_B = 47.5 × 46 = 2185 m.

⇒ Since L_B = 1.5 L_A, then L_A + 1.5 L_A = 2185 ⇒ 2.5 L_A = 2185.

⇒ L_A = 2185 ÷ 2.5 = 874 m.

⇒ L_B = 1.5 × 874 = 1311 m.

⇒ Speed of Train B in m/s = 72 × (5/18) = 20 m/s.

⇒ Distance covered in 82 s = Speed B × Time = 20 × 82 = 1640 m.

⇒ Bridge Length = Total Distance − L_B = 1640 − 1311 = 329 m.

∴ The correct answer is 329 m.

Additional Information

Relative Speed Concepts

When moving in the opposite direction, speeds are added (S₁ + S₂). In the same direction, speeds are subtracted (|S₁ − S₂|).

Crossing Distance

When a train crosses another train or a bridge, the total distance covered is the sum of their lengths (L₁ + L₂).

Unit Conversion

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

The Correct answer is Provision for Indian representation in the Imperial Legislative Council.

Key Points

• The Indian Councils Act of 1892 was a crucial step by the British government to address some of the political demands of Indians during the late 19th century.
• This Act introduced the concept of Indian representation in the legislative councils, although the representation was limited and indirect.
• The Act allowed for a limited number of non-official Indian members to be nominated to the councils, both provincial and imperial, thereby marking the beginning of Indian participation in the legislative process.
• The Act permitted discussion of the budget and allowed members to ask questions on various matters, which was a significant development towards a participative legislative system.
• Despite its limitations, this Act was a precursor to further reforms, such as those introduced in the Indian Councils Act of 1909 (Morley-Minto reforms).
• This was an attempt by the British administration to appease the emerging Indian political class and defuse growing dissatisfaction with colonial rule.
• However, the Act did not introduce direct elections; members were nominated or indirectly elected by certain groups, such as landlords, merchants, and local bodies.

Additional Information

• Granting full self-governance to Indian provinces
• Full self-governance was not a part of the Indian Councils Act of 1892. The demand for self-governance gained momentum during the later stages of the Indian freedom movement, especially with the introduction of acts like the Government of India Act 1935.
• This Act only expanded representation but did not address the question of self-governance in Indian provinces.
• Establishment of a separate electorate for Muslims
• The concept of separate electorates for Muslims was introduced later in the Indian Councils Act of 1909 (Morley-Minto reforms) to accommodate communal representation.
• This was not a feature of the 1892 Act.
• Introduction of direct elections for legislative councils
• The Act of 1892 did not introduce direct elections. Members were chosen through nomination or indirect election methods.
• Direct elections were introduced much later, particularly in the Government of India Act 1919 (Montagu-Chelmsford reforms).

Shortcut Trick

For half-yearly compounding, the rate becomes half and the number of periods doubles.

Rate (r) = 18% ÷ 2 = 9% per half-year | Time (n) = 1 × 2 = 2 periods.

Net effective interest rate for 2 periods = 9 + 9 + (9 × 9)/100 = 18.81%.

Total Amount = 100% (Principal) + 18.81% (Interest) = 118.81% of Principal.

Amount = 60,000 × 1.1881 = ₹71,286.

∴ The correct answer is ₹71,286.

Alternate Method

Given:

Principal (P) = ₹60,000

Annual Rate (R) = 18% per annum

Time (T) = 1 year

Formula Used:

Amount (A) = P(1 + r/100)ⁿ

Calculations:

⇒ r = 18 ÷ 2 = 9% (Rate for 6 months)

⇒ n = 1 × 2 = 2 (Two half-year periods in 1 year)

⇒ A = 60,000 × (1 + 9/100)²

⇒ A = 60,000 × (109/100) × (109/100)

⇒ A = 6 × 109 × 109

⇒ A = 6 × 11881

⇒ A = ₹71,286

∴ The correct answer is ₹71,286.

Additional Information

Effective Rate of Interest

For two successive cycles of r%, the net percentage change is given by (x + y + xy/100)%. Here, 9 + 9 + (9×9)/100 = 18.81%.

Compounding Frequencies

For Quarterly compounding, Rate = R/4 and n = 4T. For Monthly compounding, Rate = R/12 and n = 12T.

Difference between CI and SI

For 2 years (or 2 cycles), the difference between Compound Interest and Simple Interest is P(r/100)².

Shortcut Trick

The angle formed by the angle bisectors of two adjacent angles in a quadrilateral is always equal to half the sum of the other two interior angles.

∠DOC = (∠A + ∠B) ÷ 2

∠DOC = (53° + 46°) ÷ 2 = 99° ÷ 2 = 49.5°

∴ The correct answer is 49.5°.

Alternate Method

Given:

• In quadrilateral ABCD, ∠A = 53° and ∠B = 46°.

• OD and OC are the angle bisectors of ∠D and ∠C respectively, meeting at point O.

Formula Used:

• Sum of all interior angles of a quadrilateral = 360°

• Sum of all interior angles of a triangle = 180°

Calculations:

In quadrilateral ABCD:

⇒ ∠A + ∠B + ∠C + ∠D = 360°

⇒ 53° + 46° + ∠C + ∠D = 360°

⇒ 99° + ∠C + ∠D = 360°

⇒ ∠C + ∠D = 360° − 99°

⇒ ∠C + ∠D = 261°

Since OD and OC are the angle bisectors of ∠D and ∠C respectively:

⇒ ∠ODC = ∠D ÷ 2

⇒ ∠OCD = ∠C ÷ 2

In triangle DOC:

⇒ ∠DOC + ∠ODC + ∠OCD = 180°

⇒ ∠DOC + (∠D ÷ 2) + (∠C ÷ 2) = 180°

⇒ ∠DOC + (∠C + ∠D) ÷ 2 = 180°

⇒ ∠DOC + 261° ÷ 2 = 180°

⇒ ∠DOC + 130.5° = 180°

⇒ ∠DOC = 180° − 130.5°

⇒ ∠DOC = 49.5°

Option Evaluation:

• Option (1) - 46.5°: Incorrect, as the calculated value of ∠DOC is 49.5°.

• Option (2) - 49.5°: Correct, as it matches the calculated value of ∠DOC.

• Option (3) - 60.5°: Incorrect, as the calculated value of ∠DOC is 49.5°.

• Option (4) - 44.5°: Incorrect, as the calculated value of ∠DOC is 49.5°.

∴ The correct answer is 49.5°.

Additional Information

Angle Bisector Theorem in Quadrilaterals

For any quadrilateral ABCD, the angle between the bisectors of two adjacent angles (say ∠C and ∠D) is equal to half the sum of the remaining two angles: ∠DOC = (∠A + ∠B) ÷ 2.

Opposite Angle Bisectors in Quadrilaterals

If the bisectors of opposite angles (say ∠A and ∠C) of a quadrilateral ABCD meet at a point, the angle between them is equal to half the difference of the other two opposite angles: θ = |∠B − ∠D| ÷ 2.

Sum of Interior Angles of a Polygon

The sum of the interior angles of any n-sided polygon is given by the formula: (n − 2) × 180°. For a quadrilateral (n = 4), the sum is always 360°.

Shortcut Trick

In a continued proportion a : b :: b : c, the formula is c = b² ÷ a.

Given values: a = 7.4 and b = 3.7.

x = (3.7 × 3.7) ÷ 7.4

x = 3.7 ÷ 2 = 1.85

∴ The correct answer is 1.85.

Alternate Method

Given:

Proportion: 7.4 : 3.7 :: 3.7 : x

Formula Used:

Product of extremes = Product of means

For a : b :: c : d ⇒ a × d = b × c

Calculations:

⇒ 7.4 × x = 3.7 × 3.7

⇒ x = (3.7 × 3.7) ÷ 7.4

⇒ x = (3.7 × 3.7) ÷ (2 × 3.7)

⇒ x = 3.7 ÷ 2

⇒ x = 1.85

∴ The correct answer is 1.85.

Additional Information

Third Proportional

When three numbers a, b, and c are in continued proportion (a:b = b:c), c is called the third proportional to a and b, where c = b²/a.

Mean Proportional

The mean proportional between two numbers a and c is b, such that b = √(a × c).

Fourth Proportional

In a proportion a : b :: c : d, d is the fourth proportional and is calculated as d = (b × c) / a.

Shortcut Trick

Salary is always 100%.

Savings = 45% → Expenditure = 100% − 45% = 55%.

Expenditure = 55% of ₹2,580 = 0.55 × 2580.

Expenditure = ₹1,419.

∴ The correct answer is ₹1,419.

Alternate Method

Given:

Total monthly Salary = ₹2,580

Savings percentage = 45%

Formula Used:

Expenditure = Salary − Savings

Calculations:

⇒ Savings amount = 45% of 2580

⇒ Savings = (45 ÷ 100) × 2580 = 0.45 × 2580 = ₹1,161

⇒ Expenditure = Total Salary − Savings

⇒ Expenditure = 2580 − 1161

⇒ Expenditure = ₹1,419

∴ The correct answer is ₹1,419.

Additional Information

Percentage Change

New Value = Original Value × (100 ± Change%)/100. Use − for decrease (expenditure after savings).

Base Change Rule

When calculating parts of a whole, ensure the base (Total Salary) remains constant for both percentages.

Successive Percentage

If spending is from the 'remaining' amount, use the formula: Final = Initial × (1 − r₁/100) × (1 − r₂/100).

Shortcut Trick

Arrange the 11 observations in ascending order:

11, 12, 38, 38, 49, 53, 55, 60, 70, 93, 98

Since the number of terms (n = 11) is odd, the median is the middle-most term:

Median = ((11 + 1) ÷ 2)^th term = 6^th term = 53

∴ The correct answer is 53.

Alternate Method

Given:

Observations: 93, 38, 12, 55, 70, 98, 60, 49, 53, 11, 38

Total number of observations (n) = 11

Formula Used:

When the number of observations (n) is odd:

Median = ((n + 1) ÷ 2)^th observation

Calculations:

Arrange the given data in ascending order:

⇒ 11, 12, 38, 38, 49, 53, 55, 60, 70, 93, 98

Count the number of observations:

⇒ n = 11 (which is an odd number)

Apply the median formula for odd n:

⇒ Median = ((11 + 1) ÷ 2)^th term

⇒ Median = (12 ÷ 2)^th term

⇒ Median = 6^th term

Looking at the sorted list, the 6^th term is 53.

Let's explain why other options are incorrect:

⇒ Option (1) 60 is the 8^th term, which is incorrect.

⇒ Option (2) 55 is the 7^th term, which is incorrect.

⇒ Option (4) 49 is the 5^th term, which is incorrect.

∴ The correct answer is 53.

Additional Information

Median for Even Number of Observations

If n is even, the median is the average of the (n ÷ 2)^th and ((n ÷ 2) + 1)^th observations: Median = [(n/2)^th term + (n/2 + 1)^th term] ÷ 2.

Mean, Median, and Mode Relationship

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

Properties of Median

The median is not affected by extremely large or small values (outliers), making it a better measure of central tendency than the mean for skewed data.

Shortcut Trick

Average Speed = Total Distance ÷ Total Time

Total Distance = 204 + 424 + 366 = 994 km

Total Time = (204 ÷ 68) + (424 ÷ 53) + (366 ÷ 61) = 3 + 8 + 6 = 17 hours

Average Speed = 994 ÷ 17 ≈ 58.47 km/hr

∴ The correct answer is 58.47 km/hr.

Alternate Method

Given:

D₁ = 204 km, S₁ = 68 km/hr

D₂ = 424 km, S₂ = 53 km/hr

D₃ = 366 km, S₃ = 61 km/hr

Formula Used:

Time = Distance ÷ Speed

Average Speed = (D₁ + D₂ + D₃) ÷ (T₁ + T₂ + T₃)

Calculations:

⇒ T₁ = 204 ÷ 68 = 3 hours

⇒ T₂ = 424 ÷ 53 = 8 hours

⇒ T₃ = 366 ÷ 61 = 6 hours

⇒ Total Time = 3 + 8 + 6 = 17 hours

⇒ Total Distance = 204 + 424 + 366 = 994 km

⇒ Average Speed = 994 ÷ 17

⇒ Average Speed = 58.4705... ≈ 58.47 km/hr

∴ The correct answer is 58.47 km/hr.

Additional Information

Average Speed for Equal Distances

If two equal distances are covered at speeds x and y, the average speed is (2xy) ÷ (x + y).

Relative Speed

Relative speed is the sum of speeds if moving in opposite directions (S₁ + S₂) and the difference if moving in the same direction (S₁ − S₂).

Conversion Factor

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

Given series: (Left) 2 6 % 2 6 4 € 7 * 9 $ 3 € 6 1 2 @ 8 % € 9 2 (Right)

According to the question, such symbols which are immediately preceded by a number and also immediately followed by a symbol:

Required condition: Number - Symbol - Symbol

(Left) 2 6 % 2 6 4 € 7 * 9 $ 3 € 6 1 2 @ 8 % € 9 2 (Right)

Thus, there is one such symbols which are immediately preceded by a number and also immediately followed by a symbol.

Hence, "Option 3" is the correct answer.

Given:

Mr. P starts from Point C and drives 5 km towards the west.

He then takes a left turn, drives 6 km, turns left and drives 8 km.

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

He then takes left turn and drives 12 km.

He takes a final left turn drives 7 km and stops at Point P. 

​

​

Thus, Mr. P should drive 4 km in the south direction in order to reach Point C again.

Hence, "Option 2" is the correct answer.

The logic followed here is.

Hence, the correct answer is "Option 4"..

The logic followed here is:

Hence, "Option 3" is the correct answer.

Shortcut Trick

Successive discount multiplier = (1 − d₁) × (1 − d₂) × (1 − d₃)

Net multiplier = (1 − 0.29) × (1 − 0.28) × (1 − 0.13) = 0.71 × 0.72 × 0.87

Net multiplier = 0.5112 × 0.87 = 0.444744

Single equivalent discount = (1 − 0.444744) × 100 = 55.5256%

Rounding up to two decimal places, we get 55.53%.

∴ The correct answer is 55.53%.

Alternate Method

Given → Discounts are 29%, 28%, and 13%. Formulas: Successive discount for two = a + b − (a × b) ÷ 100

⇒ First two discounts: 29 + 28 − (29 × 28) ÷ 100 = 57 − 8.12 = 48.88% ⇒ Combine with third: 48.88 + 13 − (48.88 × 13) ÷ 100 ⇒ 61.88 − 6.3544 = 55.5256% ⇒ Rounding to two decimal places = 55.53%

∴ The correct answer is 55.53%.

Additional Information

Successive Discounts

When multiple discounts are applied one after another, the net discount is less than the sum of individual percentages because each subsequent discount is calculated on the reduced price.

Rounding Rules

When rounding to two decimal places, if the third decimal is 5 or greater, the second decimal digit is incremented by 1.

The Correct answer is The Court permitted the petitioner to approach online platforms and search engines to mask their identities.

Key Points

• The Delhi High Court ruling in November 2024 dealt with the 'Right to Be Forgotten', a concept gaining traction globally to allow individuals to have their personal data removed from public platforms under certain conditions.
• In this case, the Court recognized the petitioner’s right to request that their identity be masked on online platforms and search engines, ensuring that their personal information is not readily accessible to the public.
• This decision emphasizes the protection of the right to privacy, which has been upheld as a fundamental right under Article 21 of the Indian Constitution.
• The judgement allowed individuals to exercise control over their digital footprint, particularly in sensitive cases like matrimonial disputes or acquittals in legal proceedings.
• The ruling aligns with the broader global discourse on balancing the right to privacy with the public's right to information.
• The Court's decision sets a precedent for addressing privacy concerns in the digital age, especially in light of India's evolving data protection framework.

Additional Information

• Right to Be Forgotten
• The 'Right to Be Forgotten' allows individuals to request the removal of their personal data from the internet under certain conditions, particularly when the data is no longer relevant or serves no legitimate purpose.
• This right has been recognized in countries like the European Union under the General Data Protection Regulation (GDPR).
• In India, this concept is still evolving, and its integration into laws like the Data Protection Bill is under discussion.
• Key points from the other options:
• Option 1: The Court did not reject the applicability of the 'Right to Be Forgotten' in cases of acquittal or quashed criminal proceedings; rather, it focused on balancing privacy with public interest.
• Option 2: While privacy is crucial, the Court did not specifically state that it cannot override public interest in matrimonial cases; instead, it permitted identity masking based on circumstances.
• Option 4: The Court did not mandate that the names of the couple in matrimonial disputes must remain public; instead, it allowed for masking to protect privacy.

The logic followed here is.

Hence, the correct answer is "Option 2"..

The Correct answer is 10%.

Key Points

• The 103rd Amendment Act, 2019 introduced a provision for reservation of 10% for the Economically Weaker Sections (EWS) of the general category in government jobs and educational institutions.
• This amendment added Clause (6) to Article 15 and Article 16 of the Indian Constitution to enable this provision.
• The reservation is aimed at providing social and economic justice to individuals who belong to the general category but face financial hardships.
• The criteria for EWS reservation include individuals whose family income is below ₹8 lakh per annum, among other asset-related conditions.
• This is the first reservation provision in India based solely on economic criteria, rather than caste, tribe, or backward class categories.
• The cap of 10% was decided to ensure that the overall reservation in India does not exceed the 50% ceiling imposed by the Supreme Court in the Indra Sawhney judgment (1992).
• The amendment is widely regarded as a significant step toward addressing the needs of economically disadvantaged sections of society while balancing constitutional provisions.

Additional Information

• Article 15(6)
• Article 15(6) allows the state to make special provisions for the advancement of Economically Weaker Sections (EWS) in matters of education.
• This includes reservation in educational institutions, both aided and unaided, except for minority institutions.
• Article 16(6)
• Article 16(6) empowers the state to provide reservation to the Economically Weaker Sections in matters of employment.
• This ensures equal opportunity in public employment for individuals from economically weaker backgrounds.
• Indra Sawhney Judgment
• The Indra Sawhney case (1992) established the 50% ceiling for reservations in India to maintain the principle of equality.
• It also clarified the concept of social and educational backwardness as a basis for reservation.

The Correct answer is Pt. Madan Mohan Malviya.

Key Points

• The Poona Pact was an agreement signed on September 24, 1932, between Mahatma Gandhi and Dr. B.R. Ambedkar.
• This agreement was related to the issue of separate electorates for the depressed classes (Scheduled Castes).
• It was signed at Yerwada Central Jail, Pune, where Gandhi was imprisoned.
• Since Gandhi was in jail, the pact was signed on his behalf by Pt. Madan Mohan Malviya, a prominent leader of the Indian National Congress.
• Dr. B.R. Ambedkar signed the pact on behalf of the depressed classes.
• The Poona Pact resulted in a compromise: instead of a separate electorate, the depressed classes were given reserved seats in the general electorate.
• It was a significant event in India's freedom struggle as it addressed the issue of political representation for marginalized communities.
• The pact also marked a step towards social justice and equality within the Indian society.

Additional Information

• Jawaharlal Nehru
• Jawaharlal Nehru was an eminent leader of the Indian National Congress and later became the first Prime Minister of India.
• He played a key role in the freedom movement but was not directly involved in the Poona Pact negotiations.
• Nehru is well-known for his contributions to the Non-Aligned Movement and his vision for a modern, secular India.
• Sardar Vallabhbhai Patel
• Sardar Vallabhbhai Patel is known as the Iron Man of India for his efforts in the integration of princely states into independent India.
• While he was a prominent leader in the freedom struggle, he was not a signatory or mediator in the Poona Pact.
• Patel is also remembered for his role in the Bardoli Satyagraha.
• Dr. Rajendra Prasad
• Dr. Rajendra Prasad was a leader of the Indian National Congress and later became the first President of India.
• He was active in the freedom movement and contributed to the Champaran Satyagraha.
• However, he was not directly involved in the Poona Pact.

The logic followed here is:

Option 1) WQ-BI

Option 2) UO-ZG

Option 3) JD-OW

Option 4) BV-GN

Thus, out of all "JD-OW" is the odd one out.

Hence, "Option 3" is the correct answer.

According to the given information,

Thus, 'W' is coded as '6'.

Hence, "Option 2" is the correct answer.

Given:

Simplify: 25 ÷ { 7 × ((3)/(5) of (5)/(9)) }

Formula used:

"of" means multiplication.

Calculation:

Simplify the inner brackets: ((3)/(5) of (5)/(9))

⇒ ((3)/(5) × (5)/(9))

⇒ (3 × 5) / (5 × 9)

⇒ 15 / 45

⇒ 1 / 3

Now, substitute back: 25 ÷ { 7 × (1/3) }

⇒ 25 ÷ (7 × 1/3)

⇒ 25 ÷ (7/3)

⇒ 25 × (3/7)

⇒ (25 × 3) / 7

⇒ 75 / 7

∴ The correct answer is option (2).

Shortcut Trick

Total Work (LCM of 24, 28) = 168 units.

Efficiency: A = 7, B = 6.

2-day work cycle (B then A) = 6 + 7 = 13 units.

In 12 cycles (24 days), work done = 12 × 13 = 156 units. Remaining = 12 units.

Day 25 (B's turn): B does 6 units. Remaining = 6 units. Day 26: A takes 6/7 days.

∴ The correct answer is 25 6/7 days.

Alternate Method

Given: Time taken by A = 24 days, B = 28 days. Working alternately starting with B.

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

⇒ Total efficiency in a 2-day cycle (B + A) = 6 + 7 = 13 units.

⇒ Number of complete cycles = 168 ÷ 13 = 12 cycles with a remainder.

⇒ Work completed in 12 cycles (24 days) = 12 × 13 = 156 units.

⇒ Remaining work = 168 − 156 = 12 units.

⇒ On 25^th day, B works and completes 6 units. Remaining = 12 − 6 = 6 units.

⇒ On 26^th day, A works. Time taken by A = Remaining work ÷ Efficiency = 6 ÷ 7 days.

⇒ Total time = 24 + 1 + 6/7 = 25 6/7 days.

∴ The correct answer is 25 6/7 days.

Additional Information

Alternate Day Work

In alternate day problems, identify the unit cycle (usually 2 days) and calculate work per cycle. The starting person significantly affects the remainder calculation.

Time and Work Relation

Work is always considered as 1 unit or the LCM of given days to simplify calculations. Efficiency is inversely proportional to time taken.

The Correct answer is maritime trade.

Key Points

• Lothal was one of the most important cities of the Indus Valley Civilization and is located in present-day Gujarat, India.
• The city was a prominent center for maritime trade due to its strategically constructed dockyard, which is considered one of the oldest in the world.
• The dockyard at Lothal was connected to the Sarashwati River (now dried up) and had access to the sea, facilitating trade routes with Mesopotamia, Egypt, and other regions.
• Lothal’s people are credited for their advanced knowledge of engineering and hydrology, which allowed them to construct a dockyard with a proper drainage system.
• Excavations have revealed evidence of bead-making factories, which produced goods like ornaments, semi-precious stones, and seals, highlighting their role in trade.
• Artifacts such as weights, seals, and tools found at Lothal indicate the city’s involvement in a system of standardized trade practices during that era.
• Lothal is also significant for its urban planning, featuring a well-organized grid layout, advanced drainage systems, and warehouses for storing goods for trade.
• The city played a key role in connecting the Indus Valley Civilization with other ancient civilizations, contributing to the exchange of goods, culture, and ideas.

Additional Information

• Military base
• There is no evidence to suggest that Lothal served as a military base.
• The Indus Valley Civilization is known for its peaceful existence and lack of military artifacts, unlike other ancient civilizations.
• Copper mining
• Copper was an important resource during the Indus Valley Civilization; however, copper mining activities were concentrated in regions like Khetri in Rajasthan.
• Lothal was primarily known for its dockyard and trade, not for mining activities.
• Spiritual rituals
• While the Indus Valley Civilization had advanced religious practices, Lothal does not stand out as a significant center for spiritual rituals.
• The city is more renowned for its trade and urban planning than its religious contributions.

Shortcut Trick

Let the HCF be x. Then the numbers are 8x, 2x, and 1x.

The LCM of ratios (8, 2, 1) is 8.

Therefore, LCM of numbers = 8 × x = 7552.

Solving for x: x = 7552 ÷ 8 = 944.

∴ The correct answer is 944.

Alternate Method

Given: Ratio of numbers = 8 : 2 : 1 and LCM = 7552.

Formula Used: LCM of numbers = (LCM of ratio parts) × HCF.

⇒ Let the numbers be 8k, 2k, and k, where k is the HCF.

⇒ LCM(8k, 2k, k) = k × LCM(8, 2, 1)

⇒ LCM(8, 2, 1) = 8

⇒ 8k = 7552

⇒ k = 7552 ÷ 8

⇒ k = 944

∴ The correct answer is 944.

Additional Information

LCM and HCF Relation

For two numbers a and b, the product of the numbers is equal to the product of their LCM and HCF: a × b = LCM × HCF.

HCF of Fractions

HCF of fractions = (HCF of Numerators) ÷ (LCM of Denominators).

LCM of Fractions

LCM of fractions = (LCM of Numerators) ÷ (HCF of Denominators).

Shortcut Trick

Volume of hemisphere = (2/3)πr³

Substitute radius (r) = 24 cm directly into the formula.

Volume = (2/3) × π × 24 × 24 × 24 = 2 × π × 8 × 24 × 24

Volume = 16 × 576 × π = 9216π

∴ The correct answer is 9216π cm³.

Alternate Method

Given:

Radius (r) of the hemispherical cap = 24 cm

Formula Used:

Volume of a hemisphere = (2/3)πr³

Calculations:

⇒ Volume = (2/3) × π × (24)³

⇒ Volume = (2/3) × π × 13824

⇒ Volume = 2 × π × 4608

⇒ Volume = 9216π

∴ The correct answer is 9216π cm³.

Additional Information

Total Surface Area of Hemisphere

The total surface area includes the curved surface and the flat base area: TSA = 3πr².

Curved Surface Area of Hemisphere

The area of the outer curved part only: CSA = 2πr².

Volume of a Sphere

A hemisphere is exactly half of a full sphere: Volume of Sphere = (4/3)πr³.

The Correct answer is Southwest to Northwest.

Key Points

• The Himalayan ranges in Arunachal Pradesh are oriented in the Southwest to Northwest direction.
• This region is characterized by the Eastern Himalayas, which include some of the most rugged and remote terrains in India.
• The orientation of the ranges is influenced by the and the collision of the Indian Plate with the Eurasian Plate.
• In Arunachal Pradesh, the Himalayas consist of ranges such as the Siang, Mishmi, and Patkai Hills, which follow this southwest-to-northwest alignment.
• The natural orientation plays a crucial role in defining the climatic conditions, river systems, and vegetation of the region.
• It is also important for the local biodiversity, as the Eastern Himalayas are known for their rich flora and fauna.
• The region is part of the Indo-Burma biodiversity hotspot, which is globally recognized for its ecological significance.
• Key rivers such as the Brahmaputra and its tributaries originate or pass through these ranges, further highlighting their geographical importance.

Additional Information

• North to South Orientation
• In the context of Indian geography, the North to South orientation is not characteristic of the Himalayan ranges but can be seen in smaller regional features or mountain ranges.
• Examples include certain ranges of the Western Ghats or mountain systems with localized alignments.
• Northwest to Southeast Orientation
• This orientation is typical for the general alignment of the Himalayas in their western parts.
• Ranges such as the Pir Panjal and parts of the Shivalik Hills follow this alignment.
• However, this does not apply to the Himalayan ranges in Arunachal Pradesh.
• East to West Orientation
• The East to West orientation is generally seen in the Trans-Himalayan ranges and certain geographical features outside the Indian subcontinent.
• In India, this alignment is rare for the Himalayas and is more characteristic of other mountain systems.

Shortcut Trick

Use the direct relation: Sum of Squares = n × (Variance + Mean²).

Given n = 100, Mean = 50, and Standard Deviation = 3.

Variance = 3² = 9.

Sum of Squares = 100 × (9 + 50²) = 100 × (9 + 2500) = 2,50,900.

∴ The correct answer is 2,50,900.

Alternate Method

Given:

Number of terms (n) = 100

Mean (μ) = 50

Standard Deviation (σ) = 3

Formula Used:

Variance (σ²) = (∑x² / n) − (μ)²

Calculations:

⇒ 3² = (∑x² / 100) − 50²

⇒ 9 = (∑x² / 100) − 2500

⇒ 9 + 2500 = ∑x² / 100

⇒ 2509 = ∑x² / 100

⇒ ∑x² = 2509 × 100

⇒ ∑x² = 2,50,900

∴ The correct answer is 2,50,900.

Additional Information

Variance and Standard Deviation

The Correct answer is The substrate concentration at which the reaction rate is half of Vmax.

Key Points

• The Michaelis-Menten constant (Km) is a crucial parameter in enzyme kinetics, often used to describe the efficiency of an enzyme in catalyzing reactions.
• Km is defined as the substrate concentration at which the enzyme-catalyzed reaction rate is half of Vmax (maximum reaction rate).
• This constant reflects the enzyme's affinity for its substrate. A low Km value indicates a high affinity, meaning the enzyme works efficiently even at low substrate concentrations.
• Conversely, a high Km value suggests a lower affinity, requiring higher substrate concentrations for effective catalysis.
• The Michaelis-Menten equation, v = (Vmax[S]) / (Km + [S]), relates the reaction rate (v) to substrate concentration ([S]), Vmax, and Km.
• The concept is widely applied in biochemistry and molecular biology to study enzyme behavior and design inhibitors for therapeutic purposes.
• This parameter is particularly relevant for understanding enzyme function in different physiological and pathological contexts.

Additional Information

• The enzyme concentration required for half-maximal catalysis
• The term refers to the amount of enzyme needed for half-maximal reaction but is not related to the definition of Km. Km depends on substrate concentration, not enzyme concentration.
• The maximum reaction rate (Vmax)
• Vmax is the highest reaction rate achieved when the enzyme is saturated with substrate. While Km is tied to Vmax, it does not describe the reaction rate itself.
• The inhibitor concentration that reduces enzyme activity by 50%
• This concept is related to IC50 (Inhibitory Concentration 50), which is different from Km. IC50 is used to measure inhibitor potency rather than substrate affinity.

The logic followed here is:

MP 14 is related to LS −1

And,

NK 5 is related to MN −10

Similarly,

SW −1 is related to

Hence, "Option 2" is the correct answer.

The logic followed here is:

Given:

5 - 6 - 10 - 20

5 + 1 = 6

6 + 4 = 10

10 × 2 = 20

And,

12 - 13 - 17 - 34

12 + 1 = 13

13 + 4 = 17

17 × 2 = 34

So, checking for each option one by one:

Option 1) 17 - 18 - 22 - 44

17 + 1 = 18

18 + 4 = 22

22 × 2 = 44

Option 2) 15 - 16 - 20 - 30

15 + 1 = 16

16 + 4 = 20

20 × 2 = 40 ≠ 30

Option 3) 23 - 24 - 28 - 54

23 + 1 = 24

24 + 4 = 28

28 × 2 = 56 ≠ 54

Option 4) 7 - 8 - 12 - 26

7 + 1 = 8

8 + 4 = 12

12 × 2 = 24 ≠ 26

Hence, "Option 1" is the correct answer.

Shortcut Trick

Net filling rate = (A × B) ÷ (B − A) where A is filling time and B is emptying time.

Time taken = (14 × 18) ÷ (18 − 14)

Time taken = (14 × 18) ÷ 4 = 252 ÷ 4

Time taken = 63 hours.

∴ The correct answer is 63 hours.

Alternate Method

Given: Filling tap time = 14 hours, Emptying tap time = 18 hours.

⇒ Net efficiency of both taps = 9 − 7 = 2 units/hour

⇒ Total work to fill the tank = 126 units

⇒ Time taken = Total Work ÷ Net Efficiency

⇒ Time taken = 126 ÷ 2

⇒ Time taken = 63 hours

∴ The correct answer is 63 hours.

Additional Information

Pipes and Cisterns Concept

Filling taps have positive efficiency, while emptying taps (leakage) have negative efficiency.

Net Work Formula

If pipe A fills in 'x' hours and pipe B empties in 'y' hours (where y > x), time to fill is xy/(y − x).

LCM Method

Total capacity is assumed as the LCM of individual times to simplify unit-based calculations.

Shortcut Trick

Ratio of Girls : Boys = 1 : 5.

Given 1 unit = 201 (Number of girls).

Number of boys = 5 units = 5 × 201 = 1005.

∴ The correct answer is 1005.

Alternate Method

Given:

Ratio of Girls to Boys = 1 : 5

Number of Girls = 201

Formula Used:

Value of one part = (Given Quantity) ÷ (Corresponding Ratio Part)

Required Quantity = (Value of one part) × (Required Ratio Part)

Calculations:

⇒ Ratio of Girls (G) : Boys (B) = 1 : 5

⇒ Let Girls = 1x and Boys = 5x

⇒ x = 201

⇒ Number of Boys = 5x

⇒ Number of Boys = 5 × 201

⇒ Number of Boys = 1005

∴ The correct answer is 1005.

Additional Information

Ratio & Proportion

A ratio compares two quantities. If a : b = x : y, then a/b = x/y.

Total Participants

To find the total number of students, add the units (1 + 5 = 6 units) and multiply by the value of one unit (6 × 201 = 1206).

Unitary Method

This method involves finding the value of a single unit first and then multiplying to find the required value.

The Correct answer is Article 15.

Key Points

• Article 15 of the Constitution of India prohibits the state from discriminating against any citizen on grounds of religion, race, caste, sex, or place of birth.
• The second clause of Article 15(2) specifically prohibits discrimination in accessing shops, public restaurants, hotels, and places of public entertainment, as well as the use of wells, tanks, bathing ghats, roads, and places of public resort maintained wholly or partly by State funds.
• This article aims to ensure equality and abolish all forms of social discrimination that restrict access to public amenities.
• It is part of the Fundamental Rights under the Constitution, emphasizing equality and safeguarding the rights of marginalized groups.
• The provision ensures the promotion of an inclusive society, fostering harmony and equal opportunity for all citizens of India.
• It reflects the core values of justice, equality, and fraternity enshrined in the Preamble of the Constitution.
• This article plays a crucial role in reducing the practices of untouchability and other forms of discrimination in Indian society.

Additional Information

• Article 18
• Article 18 deals with the abolition of titles, except for academic and military distinctions.
• It prohibits the state from conferring titles and prevents Indian citizens from accepting titles from a foreign state.
• This article ensures the principle of equality and eliminates any form of aristocracy.
• Article 17
• Article 17 abolishes untouchability and forbids its practice in any form.
• It is a significant provision aimed at eradicating caste-based discrimination in Indian society.
• Any act of untouchability is an offense punishable under law.
• Article 16
• Article 16 guarantees equality of opportunity in matters of public employment.
• It prohibits discrimination in public employment on the grounds of religion, race, caste, sex, descent, place of birth, or residence.
• The article, however, allows for reservation policies for socially and educationally backward classes, Scheduled Castes, and Scheduled Tribes.

Given:

Town G is to the south of Town H.

Town I is to the east of Town H.

Town J is to the west of Town I.

Town K is to the north of Town J.

Town G is to the south-east of Town K.

​

​

Thus, Town H is to the east of Town J.

Hence, "Option 1" is the correct answer.

The logic followed here is:

​

Hence, "Option 4" is the correct answer.

The Correct answer is Vindhyan Plateau

Key Points

• The Vindhyan Plateau is not a part of the physiographic subdivisions of the Northern Plains of India.
• The Northern Plains are primarily divided into regions based on the deposition of alluvial soil brought by rivers such as the Ganga, Brahmaputra, and Indus.
• The Vindhyan Plateau is part of the Peninsular Plateau, which is a distinct physiographic region of India.
• It is characterized by rugged terrain, hard rocks, and plateaus, unlike the fertile alluvial plains of the Northern Plains.
• The Vindhyan Plateau lies in central India and is bounded by the Vindhya mountain range.
• This region is composed predominantly of sedimentary rocks, and it does not feature the characteristics associated with the Northern Plains.
• The physiographic divisions of the Northern Plains include Bhangar, Khadar, Tarai Tract, and floodplains, all of which are alluvial regions formed by river systems.

Additional Information

• Bhangar
• Bhangar refers to the older alluvium deposits found in the Northern Plains of India.
• It is characterized by a slightly elevated terrain compared to the Khadar regions.
• Bhangar soils are less fertile as they contain calcareous deposits called 'Kankar'.
• Tarai Tract
• The Tarai Tract is a marshy region located at the foothills of the Himalayas.
• This region is formed due to the percolation of rivers as they enter the plains, leading to waterlogged soil.
• The Tarai is known for its rich biodiversity and is home to several national parks, such as Jim Corbett National Park.
• Khadar
• Khadar refers to the newer alluvium deposits found in the floodplains of rivers in the Northern Plains.
• It is highly fertile due to the continuous deposition of fresh alluvium during floods.
• Khadar regions are preferred for agricultural activities.

The logic followed here is:

Option 1) QWR

Option 2) NTO

Option 3) LRN

Option 4) SYT

Thus, out of all "LRN" is the odd one out.

Hence, "Option 3" is the correct answer.

The Correct answer is Serious.

Key Points

• The Global Hunger Index (GHI) is a tool designed to comprehensively measure and track hunger at global, regional, and national levels.
• India was categorized as "Serious" in the Global Hunger Index (GHI) 2024, indicating significant challenges related to hunger and malnutrition.
• The GHI score is calculated based on four key indicators: undernourishment, child stunting, child wasting, and child mortality.
• This categorization highlights that a significant portion of India's population still faces issues related to food insecurity and malnutrition.
• The Global Hunger Index is published annually by Concern Worldwide and Welthungerhilfe.
• India's position in the "Serious" category underlines the need for focused interventions, like improving nutrition programs, food distribution systems, and agricultural reforms.
• Despite economic growth, the persistence of hunger is attributed to factors such as poverty, inadequate healthcare, and lack of education.
• India's performance in the GHI affects its global image and emphasizes the importance of achieving Sustainable Development Goal (SDG) 2: Zero Hunger.

Additional Information

• Alarming
• The "Alarming" category in the Global Hunger Index represents extremely severe levels of hunger and malnutrition in a country.
• Countries in this category face critical challenges with widespread undernourishment and high rates of child mortality.
• Examples of countries that have been categorized as "Alarming" in the past include some nations in sub-Saharan Africa.
• Moderate
• The "Moderate" category indicates a relatively lower level of hunger and malnutrition compared to "Serious" and "Alarming" categories.
• Countries in this category have made progress in addressing issues such as food security and child nutrition.
• Examples of countries in this category are often middle-income nations with ongoing efforts to reduce hunger.
• Low
• The "Low" category reflects minimal levels of hunger and malnutrition, indicating a well-functioning food system and effective nutrition policies.
• Most developed countries fall under this category, such as those in Western Europe and North America.
• These nations typically enjoy high levels of economic development and social infrastructure.

The Correct answer is Tamil Nadu.

Key Points

• Tamil Nadu is unique among Indian states as it receives rainfall from both the Southwest Monsoon and the Northeast Monsoon.
• The state receives the majority of its rainfall during the Northeast Monsoon (October to December), which is also known as the Retreating Monsoon.
• During the Southwest Monsoon (June to September), Tamil Nadu receives rainfall primarily in the western parts of the state due to the Western Ghats acting as an orographic barrier.
• The Northeast Monsoon is vital for Tamil Nadu as it contributes to about 48% of the total annual rainfall in the state.
• The geographical location of Tamil Nadu, being adjacent to the Bay of Bengal, plays a crucial role in attracting cyclonic systems and heavy rainfall during the Northeast Monsoon.
• Major cities like Chennai and the Cauvery Delta region rely heavily on the Northeast Monsoon for their water requirements.
• This dual monsoon pattern is critical for agriculture, water resources, and livelihood in Tamil Nadu.

Additional Information

• Bihar
• Bihar receives most of its rainfall during the Southwest Monsoon (June to September).
• The state does not benefit significantly from the Northeast Monsoon, as its geographical location lies far from the influence of retreating monsoon winds.
• Kosi River, often termed the “Sorrow of Bihar,” causes severe flooding during the monsoon season.
• Maharashtra
• Maharashtra receives rainfall predominantly during the Southwest Monsoon (June to September).
• The state is home to the Western Ghats, which experience heavy orographic rainfall during this period.
• Regions such as Konkan and Western Maharashtra are particularly known for their heavy monsoon rains.
• Gujarat
• Gujarat receives most of its rainfall from the Southwest Monsoon, particularly during the months of June to September.
• The state is located in a semi-arid region, and the rainfall is unevenly distributed, with Saurashtra receiving less precipitation compared to other parts.
• The Narmada River and projects like the Sardar Sarovar Dam play a significant role in water management for the state.

The Correct answer is Starts the slide show from the beginning.

Key Points

• Pressing F5 in MS PowerPoint 2019 starts the Slide Show from the very first slide.
• The Slide Show feature is used to present a sequence of slides to an audience in a full-screen mode.
• This shortcut is widely used during presentations to instantly begin the slideshow without navigating through menus.
• The feature is especially helpful for teachers, corporate professionals, and students to deliver organized and visually appealing content.
• When the F5 key is pressed, PowerPoint transitions into presentation mode, displaying slides as designed.
• The function ensures that the presentation starts from slide one, making it ideal for formal and structured demonstrations.
• This shortcut is part of the keyboard shortcuts available in Microsoft Office applications to enhance user productivity.

Additional Information

• Opens the 'Print' dialog box
• This action is performed by pressing Ctrl + P in MS PowerPoint.
• The Print dialog box allows users to configure printing options such as number of copies, printer selection, and layout settings.
• Inserts a new slide
• To insert a new slide, the shortcut key is Ctrl + M.
• This function is used to add slides during the editing phase of a presentation.
• Saves the presentation
• Pressing Ctrl + S saves the presentation in PowerPoint.
• Saving ensures that no data is lost and allows users to keep their work updated.

The Correct answer is Mandrata.

Key Points

• Mandrata is not one of the primary tones used in Vedic chanting.
• The three primary tones in Vedic chanting are Udatta (high tone), Anudaatta (low tone), and Svarita (middle tone).
• These tones are used to maintain the intonation and rhythm of the chants, which is crucial for preserving the accuracy and sanctity of the Vedic texts.
• Vedic chanting is a highly sophisticated oral tradition that requires precise pronunciation and tonal modulation.
• The intonation system ensures the transmission of Vedic knowledge in its original form without distortion.
• The term Mandrata does not refer to any recognized tonal pattern or intonation system in Vedic literature. Instead, it may have been introduced erroneously or as a distractor in the options.

Additional Information

• Udatta
• Udatta is the high tone used in Vedic chanting.
• It plays a critical role in maintaining the melodic structure of the chants.
• This tone is characterized by its sharp and elevated pitch, which provides emphasis to specific syllables.
• Anudaatta
• Anudaatta refers to the low tone in Vedic chanting.
• This tone is used to create a contrast with Udatta and helps establish a balanced tonal pattern.
• Anudaatta is generally and is not emphasized in the chanting process.
• Svarita
• Svarita is the middle tone in Vedic chanting.
• It is produced by a slight elevation following the low tone of Anudaatta.
• This tone serves as a transition between the high and low tones, ensuring the fluidity of the chant.

The Correct answer is Annamalai Range, Cardamom Hills, Palani Hills.

Key Points

• Anaimudi is the highest peak in South India, with an elevation of 2,695 meters (8,842 feet) above sea level.
• It is located in the Western Ghats mountain range in the state of Kerala, India.
• The peak lies at the tri-junction of three major hill ranges: Annamalai Range, Cardamom Hills, and Palani Hills.
• The name "Anaimudi" translates to "Elephant's Forehead" in Tamil and Malayalam, reflecting the shape of the peak.
• The region surrounding Anaimudi is home to the Eravikulam National Park, which is known for its rich biodiversity, including the Nilgiri Tahr, an endangered species of mountain goat.
• Anaimudi is a significant destination for trekking enthusiasts and offers breathtaking views of the lush greenery and tea plantations of the Western Ghats.
• The peak is also an important part of the UNESCO World Heritage-listed Western Ghats, recognized for its ecological and cultural significance.

Additional Information

• Nilgiri Hills, Western Ghats, Eastern Ghats
• The Nilgiri Hills are part of the Western Ghats, located in Tamil Nadu, Kerala, and Karnataka. However, Anaimudi is not situated at the tri-junction of these ranges.
• The Eastern Ghats are a discontinuous range of mountains along the eastern coast of India, distinct from the Western Ghats.
• Rajmahal Hills, Garo Hills, Khasi Hills
• The Rajmahal Hills are located in Jharkhand, and the Garo Hills and Khasi Hills are in Meghalaya in northeastern India.
• These hills are not related to the location of Anaimudi or the Western Ghats.
• Mahadeo Hills, Maikala Range, Rajpipla Hills
• The Mahadeo Hills are located in Madhya Pradesh, while the Maikala Range is in Chhattisgarh, and the Rajpipla Hills are in Gujarat.
• These ranges are not part of the Western Ghats or associated with Anaimudi.

Given number: 6193425

According to the question, 

So, the number of digits that appeared more than once in the new number thus formed are → 8 and 4  = Two

Hence, "Option 3" is the correct answer.

The Correct answer is Article 38.

Key Points

• Article 38 of the Indian Constitution is a part of the Directive Principles of State Policy (DPSP).
• This article directs the State to secure a social order for the promotion of the welfare of the people by striving to minimize inequalities in income, status, facilities, and opportunities.
• The provision under this article is aimed at creating a just and equitable society.
• It emphasizes the need for reducing inequalities among individuals and groups in all spheres of life, including economic, social, and political aspects.
• Article 38(1) directs the State to promote the welfare of the people by securing and protecting a social order in which justice (social, economic, and political) is accessible to all.
• Article 38(2) further instructs the State to strive to reduce inequalities not only among individuals but also among groups of people residing in different areas or engaged in different vocations.
• The DPSPs, including Article 38, are non-justiciable, meaning they cannot be enforced by the courts, but they act as guiding principles for governance and policymaking.
• The objective of Article 38 aligns with the vision of creating a welfare state, a fundamental goal of the Indian Constitution.

Additional Information

• Article 40
• Article 40 focuses on the organization of village panchayats.
• It directs the State to take steps to organize village panchayats and endow them with such powers and authority as may be necessary to enable them to function as units of self-government.
• This article is significant for promoting grassroots democracy and decentralized governance in India.
• Article 37
• Article 37 highlights that the Directive Principles of State Policy (DPSP) are fundamental in the governance of the country and it shall be the duty of the State to apply these principles in making laws.
• However, the DPSPs, including Article 37, are non-enforceable by any court, unlike fundamental rights.
• Article 39
• Article 39 directs the State to ensure that certain principles are followed for the betterment of society, such as equal pay for equal work, distribution of resources to subserve the common good, protection of children, and prevention of exploitation.
• This article is crucial for achieving socio-economic justice in India.