The correct answer is Article 23.

Key Points

• Article 23 of the Indian Constitution explicitly prohibits human trafficking, forced labor, and other forms of exploitation.
• This provision applies to both citizens and non-citizens, ensuring universal protection against exploitation.
• Under Article 23, acts such as begar (compulsory labor without payment) are outlawed, emphasizing dignity and equality.
• Article 23 is enforceable by law, and violations can lead to punitive actions under relevant legislations such as the Immoral Traffic (Prevention) Act, 1956.
• This article is a part of the Fundamental Rights section, which guarantees civil liberties to all individuals against state and private exploitation.

Additional Information

• Human Trafficking:
• Refers to the illegal trade of humans for exploitation such as forced labor, sexual slavery, or commercial sexual exploitation.
• Globally recognized as a serious crime and violation of human rights under international laws such as the Palermo Protocol.
• Immoral Traffic (Prevention) Act, 1956:
• A key legislation in India aimed at preventing and combating human trafficking.
• Provides measures for rescue, rehabilitation, and prosecution of offenders involved in trafficking.
• Article 24:
• Prohibits the employment of children below the age of 14 years in hazardous occupations such as factories and mines.
• Complements Article 23 by addressing exploitation specific to child labor.
• Fundamental Rights:
• Article 23 is a part of the Fundamental Rights enshrined in Part III of the Constitution.
• These rights are enforceable by the judiciary and protect against exploitation and discrimination.

The logic followed here is:

Thus, the Missing number is 115.

Hence, the correct answer is "Option 2".

The correct answer is ₹2.72 lakh crore.

Key Points

• The Ministry of Road Transport and Highways (MoRTH) in India had an estimated capital expenditure of ₹2.72 lakh crore for the financial year 2024-25.
• This allocation aimed to accelerate the construction of national highways and improve road infrastructure across the country.
• The increased budget allocation was part of the Indian government's focus on enhancing connectivity and supporting economic growth.
• The capital expenditure for MoRTH has been steadily increasing in recent years, reflecting the government's commitment to infrastructure development.
• This funding supports projects such as the Bharatmala Pariyojana, aimed at developing economic corridors and expressways.

Additional Information

• Bharatmala Pariyojana:
• A flagship program launched by the Indian government to develop highways and economic corridors across the country.
• It aims to improve freight movement, reduce travel time, and enhance overall connectivity.
• The program includes the construction of expressways, bridges, and bypasses to boost infrastructure.
• National Infrastructure Pipeline (NIP):
• The NIP is a government initiative aimed at providing world-class infrastructure across India.
• It includes projects in sectors like transportation, energy, water, and communication.
• Road infrastructure plays a significant role in the NIP, with substantial funding allocated to MoRTH projects.
• Gati Shakti Master Plan:
• Launched by the Indian government to integrate and coordinate infrastructure projects for seamless connectivity.
• This initiative focuses on the synergy between road, rail, air, and waterways for effective logistics management.
• Public-Private Partnerships (PPP) in Road Infrastructure:
• India extensively uses PPP models for road construction and maintenance to ensure efficient project execution.
• PPP models like Build-Operate-Transfer (BOT) and Hybrid Annuity Model (HAM) are widely adopted.

Given:

47 + (49)/(7) + 65 - 27

Calculations:

47 + (49 ÷ 7) + 65 - 27

⇒ 47 + 7 + 65 - 27

⇒ 54 + 65 - 27

⇒ 119 - 27

⇒ 92

∴ The correct answer is option (4).

Shortcut Trick

First three even natural numbers (B) = 2 + 4 + 6 = 12.

Third proportional C = B² ÷ A = 12² ÷ 57.

C = 144 ÷ 57 ≈ 2.5263...

∴ The correct answer is 2.53.

Alternate Method

Given:

First number (A) = 57

Second number (B) = Sum of first three even natural numbers

Third proportional = C

Calculations:

⇒ B = 2 + 4 + 6 = 12

⇒ For third proportional: A/B = B/C

⇒ 57/12 = 12/C

⇒ C = (12 × 12) ÷ 57

⇒ C = 144 ÷ 57

⇒ C = 2.526315...

⇒ C ≈ 2.53 (Rounded off to two decimal places)

∴ The correct answer is 2.53.

Additional Information

Third Proportional

If three quantities a, b, and c are in continued proportion (a:b = b:c), then c is called the third proportional, calculated as c = b²/a.

Mean Proportional

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

Sum of First n Even Numbers

The sum of the first n even natural numbers is given by the formula n(n + 1).

The logic followed in this pattern involves a consistent alphabetical shift for the letters and an arithmetic operation for the numbers:​

For 'UB 15' related to 'SF 11':

For 'IO 8' related to 'GS 4':

Applying the same logic to 'EL 3':

Thus, EL 3 is related to CP -1.

Hence, the correct answer is "Option 3".

The correct answer is Voyage to New Horizons of Maritime Partnership.

Key Points

• The theme of the 8th Indian Ocean Conference was Voyage to New Horizons of Maritime Partnership.
• The event focused on fostering collaboration among Indian Ocean Region (IOR) nations to ensure maritime security, economic growth, and sustainable development.
• It emphasized the importance of strengthening maritime partnerships for regional stability and global peace.
• The Indian Ocean Conference serves as a key platform for dialogue on geopolitical and economic challenges in the Indian Ocean Region.
• The conference brought together policymakers, academics, and industry leaders from across the globe to address pressing maritime issues.

Additional Information

• Indian Ocean Region (IOR)
• The Indian Ocean Region is a strategically significant area encompassing 38 countries bordering the Indian Ocean.
• It is vital for global trade, with nearly half of the world's container traffic passing through it.
• The region plays a crucial role in energy security, as it connects major oil-producing nations to energy-consuming markets.
• Maritime Security
• Maritime security refers to measures taken to protect seas and oceans from threats like piracy, terrorism, and illegal fishing.
• It ensures safe navigation, trade, and sustainable use of marine resources.
• Blue Economy
• The Blue Economy involves the sustainable use of ocean resources for economic growth, improved livelihoods, and ocean ecosystem health.
• Key sectors include fisheries, aquaculture, maritime transport, renewable energy, and tourism.
• Indian Ocean Conference
• The Indian Ocean Conference was first held in 2016 and has become a significant forum for discussing regional challenges.
• The conference aims to enhance cooperation among Indian Ocean states and stakeholders.

Given interchange rules:

• ‘+’ and ‘−’ are interchanged.
• ‘×’ and ‘÷’ are interchanged.

The given equation is:

127 ÷ 5 + 707 × 7 − 38 = ?

Replace the operators with their corresponding new meanings:

127 × 5 − 707 ÷ 7 + 38 = ?

Now, we solve the equation following the BODMAS rule:

= 127 × 5 − 707 ÷ 7 + 38

= 635 − 101 + 38

= 534 + 38

= 572

Hence, the correct answer is "Option 3".

The shaded part shows that the plumbers are there who are also hairdressers and judges.

 

Thus, the plumbers are there who are also hairdressers and judges is "19".

Hence, the correct answer is "Option 1".

The given code language is:

Thus, 'food' is coded as 'uv'.

Hence, the correct answer is "Option 4".

Shortcut Trick

Use the relation between Marked Price (MP) and Cost Price (CP): MP/CP = (100 + Profit%)/(100 − Discount%).

Given: MP is 31% above CP, so MP/CP = 131/100.

Profit% = 9%. Let Discount% be D.

131/100 = (100 + 9)/(100 − D) ⇒ 131/100 = 109/(100 − D).

100 − D = (109 × 100) ÷ 131 ⇒ 100 − D ≈ 83.206.

D = 100 − 83.206 = 16.79%.

∴ The correct answer is 16.79%.

Alternate Method

Given: Marked Price (MP) = ₹744, MP = 131% of CP, Profit = 9%. Formulas: CP = MP ÷ (1 + Markup%), SP = CP × (1 + Profit%), Discount% = (MP − SP) ÷ MP × 100.

⇒ Cost Price (CP) = 744 ÷ 1.31 ≈ 567.9389

⇒ Selling Price (SP) = CP × 1.09 ≈ 567.9389 × 1.09 ≈ 619.0534

⇒ Discount Amount = MP − SP = 744 − 619.0534 = 124.9466

⇒ Discount % = (124.9466 ÷ 744) × 100 ≈ 16.7938%

∴ The correct answer is 16.79%.

Additional Information

Marked Price and Discount

The Marked Price is the price listed on the label. Discount is always calculated on the Marked Price: SP = MP − (Discount% of MP).

Markup Percentage

Markup is the extra amount added to the Cost Price to reach the Marked Price. Formula: Markup% = [(MP − CP) ÷ CP] × 100.

The correct answer is Eastern Coastal Plain.

Key Points

• The Utkal Plains are located along the eastern coast of India, forming part of the larger Eastern Coastal Plain.
• The region lies primarily in the state of Odisha and is bordered by the Bay of Bengal to the east.
• The Utkal Plains are characterized by fertile alluvial soil, making them suitable for agriculture, particularly rice cultivation.
• This region is known for its major rivers, such as the Mahanadi, Brahmani, and Baitarani, which contribute to the area's fertility.
• Coastal features like beaches, dunes, and deltas are prominent in the Utkal Plains, shaping its unique geographical and ecological profile.

Additional Information

• Eastern Coastal Plain:
• The Eastern Coastal Plain stretches from the suburbs of West Bengal to Tamil Nadu, covering states like Odisha, Andhra Pradesh, and parts of Puducherry.
• It is broader and more fertile compared to the Western Coastal Plain, with prominent deltas like the Ganga-Brahmaputra, Mahanadi, Godavari, Krishna, and Kaveri.
• The plain is known for its rich biodiversity, including mangroves, estuaries, and lagoons such as the Chilika Lake in Odisha.
• Utkal Plains' Significance:
• The region is rich in minerals like bauxite and iron ore, fostering industrial development in Odisha.
• It is home to cultural landmarks such as the famous Jagannath Temple in Puri and the Sun Temple in Konark.
• Coastal Plains of India:
• India's coastal plains are divided into the Eastern Coastal Plain and the Western Coastal Plain.
• The Eastern Coastal Plain is wider, while the Western Coastal Plain is narrower and interrupted by the Western Ghats.
• Rivers of Odisha:
• Major rivers such as the Mahanadi, Brahmani, and Subarnarekha support agriculture and irrigation in Odisha.
• The Mahanadi River forms a vast delta before emptying into the Bay of Bengal.

Given series:

9 8 3 1 4 6 # 6 4 6 * % & $ @ 9 1 % 1 % # £

Condition to be checked:

Number → Number → Symbol

9 8 3 1 4 6 # 6 4 6 * % & $ @ 9 1 % 1 % # £

There are three such numbers in the above arrangement (4 6 #, 4 6 *,  9 1 %).

Hence, the correct answer is "Option 2".

The correct answer is Gandhara.

Key Points

• The Takht-i-Bahi inscription is linked to the ancient region of Gandhara, which was located in the present-day areas of northern Pakistan and eastern Afghanistan.
• Takht-i-Bahi is a Buddhist monastic complex known for its historical and archaeological significance, recognized as a UNESCO World Heritage Site in 1980.
• The inscription and site date back to the Kushan period, reflecting the flourishing of Buddhism in Gandhara during this era.
• Gandhara was a key center for the dissemination of Buddhist art, culture, and teachings, heavily influenced by Greek and Hellenistic styles due to Alexander the Great's incursions into the region.
• Takht-i-Bahi remains one of the most well-preserved monastic complexes from the Gandhara period, providing valuable insights into ancient Buddhist practices and architecture.

Additional Information

• Gandhara Art
• Gandhara art is known for its fusion of Indian and Hellenistic influences, creating unique representations of Buddhist iconography.
• It played a significant role in the development of Buddhist sculpture, particularly the depiction of the Buddha in human form.
• The art is characterized by intricate carvings, reliefs, and statues made from stone, stucco, and clay.
• Kushan Empire
• The Kushan Empire ruled over Gandhara during the 1st-3rd centuries CE, promoting Buddhism and trade along the Silk Road.
• Kushan rulers, such as Kanishka, were instrumental in spreading Buddhism to Central Asia and China.
• UNESCO World Heritage Status
• Takht-i-Bahi was declared a UNESCO World Heritage Site in 1980 due to its historical, cultural, and architectural importance.
• The site includes stupas, monastic cells, meditation halls, and assembly areas, showcasing the monastic lifestyle of ancient Buddhist practitioners.
• Buddhist Monastic Practices
• Buddhist monasteries like Takht-i-Bahi served as centers for religious education, meditation, and community welfare.
• Monks followed strict routines of study and meditation while adhering to the teachings of the Buddha.
• Such sites were funded by local rulers, merchants, and pilgrims who supported the spread of Buddhism.

The correct answer is Undavalli caves.

Key Points

• The "Reclining Statue of Lord Vishnu" is located in the Undavalli caves, situated in the Guntur district of Andhra Pradesh, India.
• This statue is a prominent example of ancient Indian rock-cut architecture, carved out of a single block of granite.
• The statue depicts Lord Vishnu in a reclining posture, also known as Anantasayana, resting on the serpent Adishesha.
• The Undavalli caves date back to the 4th-5th century CE and were originally associated with Buddhist monks before being adapted for Hindu worship.
• The caves are classified as monolithic rock-cut architecture and are considered a significant heritage site in South India.

Additional Information

• Undavalli Caves:
• The caves are a fine example of Gupta period architecture, which reflects the transition from Buddhism to Hinduism in ancient India.
• They are multi-storied caves, with the largest one containing the iconic statue of Lord Vishnu in a reclining posture.
• The caves were initially built as Buddhist monasteries and later converted into Hindu temples.
• The site is under the protection of the Archaeological Survey of India (ASI).
• Reclining Vishnu (Anantasayana):
• The posture symbolizes Lord Vishnu resting on the serpent Adishesha, representing cosmic balance and preservation.
• It is a recurring theme in Hindu temple sculptures, signifying the sustainer of the universe.
• Rock-Cut Architecture:
• This architectural style involves carving temples, monasteries, or sculptures directly out of natural rock formations.
• Famous examples in India include the Ajanta caves, Ellora caves, and Elephanta caves.
• Other Important Caves in India:
• Ajanta Caves: Known for Buddhist frescoes and paintings.
• Ellora Caves: Famous for Hindu, Jain, and Buddhist rock-cut temples, including the Kailasa temple.
• Elephanta Caves: Located near Mumbai, showcasing Hindu Shaivite sculptures.

Shortcut Trick

Ratio of Investment (X : Y : Z) = 45 : 37 : 71.

Total ratio units = 45 + 37 + 71 = 153 units.

Difference between Y and Z = 71 − 37 = 34 units.

Given, 153 units = ₹2,790 ⇒ 1 unit = 2,790 ÷ 153 = ₹18.235 (approx) — Wait, checking 2790 ÷ 153: 153 × 10 = 1530; 2790 ÷ 153 = 18.235 is incorrect, let's re-calculate: 153 × 20 = 3060. 2790 ÷ 153 ≈ 18.23. Let's use unitary method: (2790 ÷ 153) × 34 = ₹620.

∴ The correct answer is ₹620.

Alternate Method

Given → Investment Ratio X:Y:Z = 45:37:71 | Total Profit = ₹2,790 | Time period is same. Formulas: Profit Share ∝ Investment × Time | Share = (Individual Ratio ÷ Total Ratio) × Total Profit.

⇒ Sum of ratios = 45 + 37 + 71 = 153. ⇒ Value of 1 unit = 2,790 ÷ 153. ⇒ 153 × 1 = 153; 2790 − 1530 = 1260. 153 × 18.235... (Recalculating: 2790 × 34 ÷ 153). ⇒ 2790 and 153 are both divisible by 9: 153 ÷ 9 = 17; 2790 ÷ 9 = 310. ⇒ Difference = (310 ÷ 17) × 34. ⇒ Difference = 310 × (34 ÷ 17) = 310 × 2 = ₹620.

∴ The correct answer is ₹620.

Additional Information

Partnership Basics

When the time period of investment is the same for all partners, the Profit is distributed directly in the ratio of their Investments.

Variable Time Period

If time periods differ, Profit Ratio = (Capital₁ × Time₁) : (Capital₂ × Time₂).

The given code language is:

Thus, 'E' is coded as '2'.

Hence, the correct answer is "Option 3".

Shortcut Trick

Given the average of 8 numbers is 124.

Relationship: Least number = (1/16) × Total Sum.

Since Total Sum = Average × Count, we have:

Least number = (124 × 8) ÷ 16 = 124 ÷ 2 = 62.

∴ The correct answer is 62.

Alternate Method

Given:

Average of the set = 124

Total count of numbers (n) = 8

Formula Used:

Sum of all numbers = Average × Total numbers

Calculations:

⇒ Sum of the eight numbers = 124 × 8

⇒ Sum = 992

⇒ According to the question, Least number = (1/16) × Sum

⇒ Least number = 992 ÷ 16

⇒ Least number = 62

∴ The correct answer is 62.

Additional Information

Arithmetic Mean Formula

The average (Arithmetic Mean) of 'n' observations x₁, x₂, ..., x_n is given by (Σx_i) ÷ n.

Sum Property

If you know the average and the number of items, the total sum is always Average × Count.

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).

Shortcut Trick

For two quadratic equations to have both roots common, the ratio of their corresponding coefficients must be equal.

Compare coefficients: 2/4 = −5/−(k+1) = 3/6

Simplify the ratios: 1/2 = 5/(k+1)

Cross-multiply: k + 1 = 10 ⇒ k = 9

∴ The correct answer is 9.

Alternate Method

Given:

Equation 1: 2x² − 5x + 3 = 0

Equation 2: 4x² − (k+1)x + 6 = 0

Formula Used:

For equations a₁x² + b₁x + c₁ = 0 and a₂x² + b₂x + c₂ = 0 to have both roots common, the condition is:

a₁/a₂ = b₁/b₂ = c₁/c₂

Calculations:

Identify the coefficients from both equations:

⇒ a₁ = 2, b₁ = −5, c₁ = 3

⇒ a₂ = 4, b₂ = −(k+1), c₂ = 6

Applying the common root condition:

⇒ 2/4 = −5 / (−(k+1)) = 3/6

⇒ 1/2 = 5 / (k+1)

⇒ k + 1 = 5 × 2

⇒ k + 1 = 10

⇒ k = 10 − 1

⇒ k = 9

∴ The correct answer is 9.

Additional Information

Condition for One Common Root

If two quadratic equations have only one root in common, the condition is (c₁a₂ − c₂a₁)² = (a₁b₂ − a₂b₁)(b₁c₂ − b₂c₁).

Nature of Roots

The discriminant D = b² − 4ac determines the nature: D > 0 (real/distinct), D = 0 (real/equal), D < 0 (imaginary/complex).

Sum and Product of Roots

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

Given:

: KSM :: OWQ : %

Option 1) # = LTM, % = NVP

For # (LTM) to KSM

For OWQ to % (NVP)

 

Since the pattern for LTM to KSM (-1, -1, 0) is not the same as the pattern for OWQ to NVP (-1, -1, -1), Option 1 is incorrect.

Option 2) # = LTN, % = NVP

For # (LTN) to KSM

 

For OWQ to % (NVP)

 

Since the pattern for LTN to KSM (-1, -1, -1) is the same as the pattern for OWQ to NVP (-1, -1, -1), Option 2 is correct.

Option 3) # = LTN, % = NUP

For # (LTN) to KSM

 

For OWQ to % (NUP)

 

Since the pattern for LTN to KSM (-1, -1, -1) is not the same as the pattern for OWQ to NUP (-1, -2, -1), Option 3 is incorrect.

Option 4) # = LTN, % = NVO

For # (LTN) to KSM

 

For OWQ to % (NVO)

 

Since the pattern for LTN to KSM (-1, -1, -1) is not the same as the pattern for OWQ to NVO (-1, -1, -2), Option 4 is incorrect.

Hence, the correct answer is "Option 2".

The correct answer is Manjira.

Key Points

• Manjira is a pair of small hand cymbals, commonly used in Indian devotional and folk music.
• Manjira is classified as an Idiophone instrument, which produces sound primarily by the vibration of the instrument itself, without the use of strings or membranes.
• Unlike Avanaddha Vadya (membranophones), Manjira does not have a stretched membrane that is struck to produce sound.
• Avanaddha Vadya refers to percussion instruments like Dhol, Tabla, and Damru, which use a tightly stretched membrane to create sound when struck or played.
• Manjira is not categorized as an Avanaddha Vadya because it lacks the defining characteristic of a stretched membrane.

Additional Information

• Avanaddha Vadya:
• These are percussion instruments that produce sound by striking a stretched membrane.
• Examples include Tabla, Dhol, Damru, Mridangam, and Pakhawaj.
• They are an integral part of Indian classical and folk music.
• Idiophones:
• Instruments that produce sound by vibrating themselves, without the use of strings or membranes.
• Examples include Manjira, Ghungroo, and Jal Tarang.
• They are primarily used in folk and devotional music in India.
• Membranophones vs. Idiophones:
• Membranophones (like Tabla) use a stretched membrane for sound production, while Idiophones (like Manjira) rely on the material of the instrument itself.
• These classifications are part of the Hornbostel-Sachs system of musical instrument categorization.
• Manjira in Indian Music:
• Manjira is often used in bhajans, kirtans, and traditional folk dances.
• Its bright, metallic sound complements vocals and other instruments in devotional settings.

The correct answer is Lord Macaulay.

Key Points

• The first Law Commission in India was established in 1834 under the Charter Act of 1833.
• Lord Thomas Babington Macaulay was appointed as the Chairman of the First Law Commission.
• The Commission was tasked with codifying Indian laws and making them uniform across the country.
• One of its significant achievements was the drafting of the Indian Penal Code (IPC), which was later enacted in 1860.
• The work done by the Law Commission under Macaulay laid the foundation for the modernization of the Indian legal system.

Additional Information

• Charter Act of 1833:
• This Act was a landmark legislation by the British Parliament that centralized legislative authority in India.
• It marked the beginning of law codification in India and led to the formation of the First Law Commission.
• The Act also abolished the East India Company's monopoly on trade.
• Indian Penal Code (IPC):
• The IPC was drafted by the First Law Commission under Lord Macaulay's leadership.
• It serves as the primary criminal code for India, covering offenses and their punishments.
• Enacted in 1860, it has undergone several amendments but remains a cornerstone of Indian criminal law.
• Law Commission of India:
• It is an executive body established by the Government of India to recommend legal reforms.
• The Commission was first formed during British rule and continues to function in post-independence India.
• It is reconstituted every few years to study specific legal issues and suggest amendments or new laws.
• Lord Macaulay's Contribution:
• Besides legal reforms, Macaulay is known for his role in introducing English education in India.
• His famous "Minute on Education" argued for the promotion of English as the medium of instruction.
• He played a critical role in shaping the administrative and legal landscape during British rule in India.

The correct answer is Art.

Key Points

• Arijit Singh, one of India's most acclaimed playback singers, was awarded the Padma Shri in 2025 for his contributions to the field of Art.
• The Padma Shri is the fourth-highest civilian award in India, granted for distinguished contributions across various fields such as art, literature, sports, and social work.
• Arijit Singh is renowned for his soulful voice and versatility in singing, contributing significantly to Indian music and Bollywood soundtracks.
• His popular songs include "Tum Hi Ho," "Channa Mereya," and "Ae Dil Hai Mushkil," which have earned him widespread recognition and numerous awards.
• The recognition underscores his role in elevating Indian music on both national and international platforms.

Additional Information

• Padma Awards:
• Instituted in 1954, the Padma Awards are among the highest civilian honors in India.
• They are categorized into three levels: Padma Vibhushan (highest), Padma Bhushan, and Padma Shri.
• Awarded in various disciplines such as art, literature, science, social work, and public affairs.
• The awards are announced annually on Republic Day (January 26).
• Contributions to Art:
• Art encompasses various forms like music, dance, painting, sculpture, and cinema.
• Artists play a vital role in preserving cultural heritage and fostering creativity.
• Recognition through awards like the Padma Shri encourages individuals to excel in their artistic pursuits.
• Arijit Singh's Impact:
• Arijit Singh's music resonates with diverse audiences due to its emotional depth and technical brilliance.
• He has received numerous awards including Filmfare Awards and IIFA Awards for Best Playback Singer.
• His work spans various genres, from romantic ballads to upbeat tracks, showcasing his versatility.
• Bollywood Music Industry:
• Bollywood music is integral to Indian cinema, often driving its popularity and success.
• Playback singers like Arijit Singh play a pivotal role in shaping the musical landscape of films.
• The industry has produced globally recognized talent, contributing to India's soft power.

Given- E P T F U

Rule No. (1): This condition does not apply because the last letter (U) is a vowel, not a consonant.

Rule No. (2): This condition does not apply because the 2nd letter (P) is a consonant, not a vowel.

Rule No. (3): This condition applies because the 3rd letter (T) is a consonant and the 4th letter (F) is also a consonant. So, both will be coded as the code for the 3rd letter (T).

Rule No. (4): This condition does not apply because the 2nd letter (P) is a consonant, not a vowel.

Based on the applicable rule (3), the 3rd and 4th elements will be coded as the code for the 3rd letter.

The code for E is @.

The code for P is 9.

The code for T is $.

So, T will be coded as $.

The code for F is 7.

But, due to rule (3), F will also be coded as $ (the code for T).

The code for U is %.

Thus, 'E P T F U' is coded as → @ 9 $$ %.

Hence, the correct answer is "Option 1".

Shortcut Trick

Length of chord AB = 2 × √(Radius² − Distance²)

⇒ AB = 2 × √(6² − 4.5²)

⇒ AB = 2 × √(36 − 20.25)

⇒ AB = 2 × √15.75 = 2 × √(63/4)

⇒ AB = 2 × (3√7 / 2) = 3√7 cm

∴ The correct answer is 3√7 cm.

Alternate Method

Given: Radius (OA) = 6 cm, Shortest distance (OM) = 4.5 cm.

Formula Used: In a right-angled triangle, Hypotenuse² = Base² + Perpendicular².

In right-angled triangle OMA, where M is the midpoint of chord AB:

⇒ OA² = OM² + AM²

⇒ 6² = 4.5² + AM²

⇒ 36 = 20.25 + AM²

⇒ AM² = 36 − 20.25 = 15.75

⇒ AM = √15.75 = √(63/4) = 3√7 / 2 cm

Since the perpendicular from the centre bisects the chord:

⇒ AB = 2 × AM

⇒ AB = 2 × (3√7 / 2) = 3√7 cm

∴ The correct answer is 3√7 cm.

Additional Information

Perpendicular Bisector Property

The perpendicular drawn from the centre of a circle to a chord always bisects the chord into two equal parts.

Pythagorean Relation in Circles

For any circle, the radius (r), the distance from the centre (d), and the chord length (L) are related by: r² = d² + (L/2)².

Shortest Distance

The shortest distance between a point (centre) and a line (chord) is always the perpendicular distance.

The correct answer is uphold the supremacy of the Constitution.

Key Points

• Judicial review is a mechanism to ensure that laws and executive actions comply with the provisions of the Constitution, thereby upholding its supremacy.
• It empowers the judiciary to invalidate laws or actions by the legislature and executive if they violate constitutional principles.
• The concept of judicial review is derived from the principle of the separation of powers and checks and balances in governance.
• Judicial review safeguards fundamental rights and ensures accountability of the government to constitutional norms.
• This principle is integral to democratic governance and prevents arbitrary use of power by any branch of the government.

Additional Information

• Judicial Review:
• The term refers to the authority of the courts to examine the constitutionality of legislative acts and executive decisions.
• Judicial review originated in the United States through the landmark case Marbury v. Madison (1803).
• In India, judicial review is an essential feature of the Constitution under Articles 13, 32, and 226.
• It is a part of the basic structure doctrine established by the Supreme Court in the Keshavananda Bharati case (1973).
• Supremacy of the Constitution:
• The Constitution is the highest legal authority in India, and all laws and actions must conform to it.
• Article 141 ensures that judgments of the Supreme Court are binding on all courts in India.
• The concept reinforces the rule of law and prevents autocratic governance.
• Separation of Powers:
• It is a governance principle dividing powers among the legislature, executive, and judiciary.
• Judicial review acts as a check on the legislature and executive to maintain balance.
• Fundamental Rights:
• Judicial review ensures protection against violations of fundamental rights enshrined under Part III of the Constitution.
• Examples include the right to equality, freedom of speech, and protection against discrimination.

The correct answer is Control Panel.

Key Points

• The Control Panel in Windows OS is a centralized interface for managing system settings and configurations, including date and time changes.
• To change the system date and time, users can navigate to Control Panel > Date and Time > Change Date and Time.
• The Date and Time settings allow users to adjust the system clock, time zone, and synchronization settings with internet time servers.
• Control Panel has been a core feature in Windows OS since its early versions, providing access to hardware, software, and user account management tools.
• In newer Windows versions (e.g., Windows 10/11), date and time settings can also be accessed through the Settings app, but Control Panel remains a legacy tool for advanced configurations.

Additional Information

• Device Manager:
• This tool is used to manage hardware devices connected to the system.
• It allows users to update drivers, disable/enable devices, and troubleshoot hardware issues.
• File Explorer:
• A file management tool used to browse, organize, and manage files and folders on the system.
• It does not provide access to system settings like date and time.
• Task Manager:
• Primarily used for monitoring system performance, managing running processes, and controlling startup programs.
• It does not offer options to modify system settings like date and time.
• Settings App:
• Introduced in Windows 8 and improved in Windows 10/11, it provides a modern interface for managing system configurations.
• It includes a section for Date and Time settings, offering a streamlined alternative to the legacy Control Panel.

Given: I, J, K, L, M, N and R are sitting around a circular table facing the centre of the table.

K sits fourth to the right of L,  N is an immediate neighbour of R and I. Only two people sit between M and I when counted from the left of M.

 J sits third to the left of R. N is an immediate neighbour of R and I. 

Thus, Only 4 people between K and N when counted from the left of N.

Hence, the correct answer is "Option 2".

Given:

Town C is to the east of Town D.

Town E is to the north of Town C.

Town F is to the south of Town E.

Town G is to the west of Town F.

Town D is to the north-east of Town G

Thus, the position of Town C with respect to Town F is North.

Hence, the correct answer is "Option 4".

Given:

Jon's rank from the top = 24th.

Jon's rank from the bottom = 16th.

Total persons = (Rank from Top) + (Rank from Bottom) - 1

Total students = 24 + 16 - 1

= 40 - 1

= 39

Thus, there are 39 students in the class.

Hence, the correct answer is "Option 3".

Shortcut Trick

Area of Regular Hexagon = 6 × (Area of equilateral triangle)

Area = 1.5 × √3 × side²

Area = 1.5 × √3 × (16√2)² = 1.5 × √3 × 512

Area = 768√3 cm²

∴ The correct answer is 768√3 cm².

Alternate Method

Given: Side (a) of regular hexagon = 16√2 cm

Formula Used: Area = [3√3 ÷ 2] × a²

⇒ Area = [3√3 ÷ 2] × (16√2)²

⇒ Area = [3√3 ÷ 2] × (256 × 2)

⇒ Area = [3√3 ÷ 2] × 512

⇒ Area = 3√3 × 256

⇒ Area = 768√3 cm²

∴ The correct answer is 768√3 cm².

Additional Information

Properties of Regular Hexagon

A regular hexagon consists of 6 equilateral triangles. All internal angles are 120° and the sum of interior angles is 720°.

Perimeter of Hexagon

The perimeter of a regular hexagon with side a is given by the formula P = 6a.

Inradius and Circumradius

Circumradius (R) = a and Inradius (r) = (√3 ÷ 2) × a.

Shortcut Trick

Savings = 50% → Expenditure = 100% − 50% = 50%.

Since Savings = Expenditure, then 50% = ₹320.

Total Income (100%) = 320 × 2 = ₹640.

∴ The correct answer is ₹640.

Alternate Method

Given:

Savings Percentage = 50%

Expenditure = ₹320

Formula Used:

Income = Expenditure + Savings

Calculations:

⇒ Let the Total Income be x.

⇒ Savings = 50% of x = 0.5x

⇒ Expenditure = Income − Savings

⇒ 320 = x − 0.5x

⇒ 0.5x = 320

⇒ x = 320 ÷ 0.5

⇒ x = 640

∴ The correct answer is ₹640.

Additional Information

Percentage Change

Income change can be calculated using the formula: % Change = (New Value − Old Value) ÷ Old Value × 100.

Base Value Concept

In income problems, the Total Income is always considered as the base (100%) for calculations of savings and expenditure.

Successive Percentage

If income increases by a% and then b%, effective increase = (a + b + ab/100)%.

Shortcut Trick

Total distance = 2 × [(Downstream Speed × Upstream Speed) ÷ (Downstream Speed + Upstream Speed)] × Total Time

Total distance = 2 × [(41 × 20.5) ÷ (41 + 20.5)] × 13

Total distance = 2 × [(41 × 20.5) ÷ 61.5] × 13 = 2 × (41 ÷ 3) × 13

Total distance = 1066/3 km

∴ The correct answer is 1066/3 km.

Alternate Method

Given:

Downstream Speed (u) = 41 km/hr

Upstream Speed (v) = 20.5 km/hr

Total Time (T) = 13 hours

Formula Used:

Time = Distance ÷ Speed

Total Distance = 2 × One-way Distance (D)

Calculations:

⇒ Total Time = (D ÷ u) + (D ÷ v)

⇒ 13 = (D ÷ 41) + (D ÷ 20.5)

⇒ 13 = (D + 2D) ÷ 41

⇒ 13 = 3D ÷ 41

⇒ 3D = 13 × 41 = 533

⇒ D = 533/3 km

⇒ Total distance travelled = 2 × D = 2 × (533/3)

⇒ Total distance = 1066/3 km

∴ The correct answer is 1066/3 km.

Additional Information

Speed of Boat and Stream

Speed of boat in still water (x) = (Downstream + Upstream) ÷ 2. Speed of stream (y) = (Downstream − Upstream) ÷ 2.

Average Speed for Round Trip

Average Speed = (2 × u × v) ÷ (u + v). Total Distance = Average Speed × Total Time.

Relative Speed in Water

Downstream speed = Speed of boat + Speed of current. Upstream speed = Speed of boat − Speed of current.

The logic followed here is.

Option (1) 'PS - NQ':

Option (2) 'KN - IL':

Option (3) 'EH - CF':

Option (4) 'GJ - FK':

Hence, the correct answer is "Option 4" .

The logic followed here is:

Logic: 3rd number = 2nd number - 1st number.

For, (43, 48, 5)

⇒ 48 - 43 = 5.

For, (49, 70, 21)

⇒ 70 - 49 = 21.

Option 1) (20, 34, 14)

⇒ 34 - 20 = 14.

Here, logic followed.

Option 2) (45, 52, 4)

⇒ 52 - 45 = 7 ≠ 4.

Here, logic not followed.

Option 3) (48, 71, 20)

⇒ 71 - 48 = 23 ≠ 20.

Here, logic not followed.

Option 4) (36, 52, 13)

⇒ 52 - 36 = 16 ≠ 13.

Here, logic not followed.

Hence, the correct answer is "Option 1".

The correct answer is Textile and Apparel.

Key Points

• The textile and apparel industry is the second-largest sector in India in terms of job creation, after agriculture.
• Cluster development is a widely used strategy in this sector to promote competitiveness and regional specialization.
• The Indian textile and apparel industry contributes significantly to the GDP, export earnings, and employment generation.
• India is one of the world's largest producers of textiles and garments, with a strong presence in cotton, silk, and jute production.
• The industry is highly labor-intensive, employing over 45 million people directly and around 60 million indirectly.

Additional Information

• Cluster Development
• Cluster development involves grouping enterprises within a specific geographic location to promote shared resources, collaboration, and innovation.
• It enhances productivity, competitiveness, and economies of scale for small and medium enterprises (SMEs).
• This approach is particularly effective in labor-intensive industries like textiles and apparel.
• Contribution to Exports
• The textile and apparel industry accounts for approximately 12% of India’s total export earnings.
• India is a leading exporter of cotton textiles, garments, and home furnishings globally.
• Government Initiatives
• Programs like Integrated Textile Parks and Technology Upgradation Fund Scheme (TUFS) aim to support the industry.
• The National Technical Textiles Mission was launched to enhance the use of technical textiles in India.
• Employment Generation
• The textile sector is a major source of employment, providing jobs to millions, particularly women in rural areas.
• It plays a critical role in poverty alleviation and rural development in India.

Given: P, Q, R, S, T, U and V are sitting around a circular table facing the centre.

R sits third to the left of Q. P sits second to the left of T.

Both U and P are immediate neighbours of Q. V is not an immediate neighbour of R. 

Thus,  Only 3 people sit between T and U when counted from the left of T

Hence, the correct answer is "option 2".

The correct answer is The concentration of neurotransmitter and the number of receptors in the postsynaptic membrane.

Key Points

• The synaptic transmission is critically dependent on the concentration of neurotransmitters released by the presynaptic neuron into the synaptic cleft.
• The number and sensitivity of receptors on the postsynaptic membrane determine how effectively the neurotransmitter can bind and initiate a response.
• Neurotransmitter availability is regulated by mechanisms such as reuptake, enzymatic degradation, and diffusion, which directly influence synaptic effectiveness.
• Higher receptor density on the postsynaptic membrane enhances signal transmission, while receptor downregulation can reduce synaptic efficiency.
• Synaptic plasticity, including changes in receptor number and neurotransmitter concentration, is fundamental to learning and memory processes.

Additional Information

• Neurotransmitter:
• Neurotransmitters are chemical messengers released by neurons to transmit signals across a synapse to another neuron, muscle cell, or gland cell.
• Examples include dopamine, serotonin, acetylcholine, and glutamate.
• They can be excitatory (promote action potential) or inhibitory (reduce action potential).
• Postsynaptic Receptors:
• Receptors on the postsynaptic membrane can be ionotropic (directly linked to ion channels) or metabotropic (indirectly linked through second messengers).
• The binding of neurotransmitters to these receptors initiates various cellular responses.
• Synaptic Plasticity:
• Synaptic plasticity refers to the ability of synapses to strengthen or weaken over time, based on activity levels.
• It plays a crucial role in learning, memory, and adaptive neural responses.
• Reuptake and Enzymatic Degradation:
• Reuptake involves the removal of neurotransmitters from the synaptic cleft by transporter proteins.
• Enzymatic degradation breaks down neurotransmitters to terminate their activity in the synaptic cleft.

The correct answer is Copper.

Key Points

• According to the NITI Aayog's 'Trade Watch – Quarterly (July-September [Q2] FY25)' report, copper entered India’s top ten imports due to increased infrastructure demand.
• Copper is widely used in construction, electrical wiring, and industrial applications, making it critical for infrastructure projects.
• The global demand for copper has surged due to its use in renewable energy systems, such as solar panels and wind turbines, aligning with India's green energy goals.
• India's domestic copper production has declined in recent years, prompting higher imports to meet growing infrastructure needs.
• The report highlights that India's focus on urbanization and industrial expansion has contributed to the increased demand for copper imports.

Additional Information

• Copper and Infrastructure Development
• Copper is a highly conductive metal used extensively in electrical systems, including power transmission and distribution.
• It is a preferred material for plumbing, roofing, and cladding in construction projects.
• The rising demand for energy-efficient solutions has further increased copper usage in electric vehicles (EVs) and renewable energy projects.
• India's Copper Industry
• India has witnessed a decline in domestic copper production since the closure of Sterlite Copper's smelter in 2018, leading to increased reliance on imports.
• Major copper-consuming industries in India include power, construction, and transportation.
• India imports copper from countries like Chile, Japan, and China to meet domestic requirements.
• Global Copper Demand Trends
• The global push towards decarbonization and renewable energy has significantly increased copper demand.
• Electric vehicles use approximately four times more copper than traditional vehicles, further driving demand.
• Copper is essential for developing smart grids and advanced infrastructure systems worldwide.
• Trade and Economic Implications
• Increased imports of copper may widen India’s trade deficit in the short term.
• Strategic investments in domestic copper production and recycling could reduce dependency on imports.
• The rise in infrastructure projects is expected to boost economic growth despite higher import costs.

The correct answer is Legislative Council.

Key Points

• In 1892, during the Allahabad Session of the Indian National Congress, a resolution was passed demanding increased representation of Indians in the Legislative Council.
• The resolution was part of the early phase of the Congress, which focused on constitutional reforms and political representation.
• The demands aimed at ensuring that Indians had a voice in the governance of the country under British rule.
• This resolution marked a significant step in the gradual evolution of the Indian National Congress's political objectives.
• Such demands eventually laid the groundwork for subsequent reforms like the Indian Councils Act of 1892, which allowed limited Indian participation in the legislative process.

Additional Information

• Indian Councils Act of 1892
• The Indian Councils Act of 1892 was an important legislative reform introduced by the British government.
• It expanded the powers of Legislative Councils, allowing members to ask questions on the budget and other public matters.
• While the Act was limited in scope, it was a small step toward involving Indians in governance.
• Indian National Congress (INC)
• The INC was founded in 1885 by Allan Octavian Hume, Dadabhai Naoroji, and Dinshaw Wacha.
• In its early years, the Congress focused on moderate demands, such as representation in councils and administrative reforms.
• Allahabad Session of 1892
• This session reflected the growing demand for political rights among Indians.
• It highlighted the role of the Congress in articulating constitutional demands during the pre-Gandhian era.
• Viceroy’s Legislative Council
• Under British rule, the Viceroy's Legislative Council was the primary legislative body.
• Indians were initially excluded but were gradually allowed limited participation following persistent demands.

Shortcut Trick

Let the pipes be A, B and C (waste pipe).

Total Work (LCM of 35, 15, 42) = 210 units.

Efficiency: A = 6, B = 14, A + B − C = 5.

Efficiency of Waste Pipe C = (6 + 14) − 5 = 15 units/min.

Time taken by C to empty = 210 ÷ 15 = 14 min.

∴ The correct answer is 14 min.

Alternate Method

⇒ Let efficiency of emptying pipe be C.

⇒ Total efficiency = Efficiency of A + Efficiency of B − Efficiency of C

⇒ 5 = 6 + 14 − C

⇒ 5 = 20 − C

⇒ C = 20 − 5 = 15 units/min

⇒ Time taken by pipe C to empty the cistern = Total Work ÷ Efficiency of C

⇒ Time = 210 ÷ 15 = 14 min

∴ The correct answer is 14 min.

Additional Information

Net Efficiency Concept

For a cistern with inlet and outlet pipes, Net efficiency = ∑(Inlet efficiencies) − ∑(Outlet efficiencies). If net efficiency is positive, the tank fills; if negative, the tank empties.

Time and Work Relation

Time taken to complete a task is inversely proportional to efficiency: Time = Total Work ÷ Efficiency. In pipes and cisterns, capacity of the tank acts as the Total Work.

The correct answer is Inland waterways.

Key Points

• Inland waterways are the most energy-efficient mode of transport in India in terms of energy consumption per tonne-km.
• This mode of transport consumes significantly less fuel compared to roadways, railways, and airways, making it environmentally friendly and cost-effective.
• India has a vast network of rivers and canals that are utilized for inland waterway transport, with major waterways designated under the National Waterways Act, 2016.
• Waterways are particularly suitable for transporting heavy goods such as coal, iron ore, and cement, which are not time-sensitive.
• The Inland Waterways Authority of India (IWAI) is responsible for developing and regulating inland waterways in the country.

Additional Information

• Energy Efficiency in Transport:
• Energy consumption per tonne-km is a critical metric for evaluating the efficiency of transport systems.
• Inland waterways use less fuel per tonne-km compared to roadways and railways, making them the most efficient mode of transport.
• National Waterways:
• India has five major National Waterways (NW1 to NW5) under active development for cargo and passenger transport.
• NW1 (Ganga River) and NW2 (Brahmaputra River) are the most prominent waterways.
• Challenges of Inland Waterways:
• Infrastructure development, dredging, and maintaining navigable depth are key challenges.
• Seasonal variations in water levels can impact operations.
• Advantages of Inland Waterways:
• Reduces road congestion and air pollution.
• Lower operating costs make it ideal for bulk goods transport.
• Promotes sustainable and eco-friendly logistics solutions.

The logic followed here is:

Thus, 'OMJ' will be the next in the series.

Hence, the correct answer is "Option 3".

The correct answer is Chennai.

Key Points

• Chennai, located on the southeastern coast of India, receives significant rainfall during the retreating monsoon season (October to December).
• The retreating monsoon (also known as the Northeast Monsoon) is characterized by winds blowing from the northeast direction, bringing rainfall to Tamil Nadu and adjoining areas.
• Unlike most parts of India, which receive rainfall during the Southwest Monsoon (June to September), Tamil Nadu, particularly Chennai, relies heavily on the retreating monsoon for its annual rainfall.
• Chennai experiences cyclonic activity in the Bay of Bengal during this period, contributing to intense and sudden rainfall events.
• Nearly 48% of Tamil Nadu's annual rainfall is attributed to the retreating monsoon, with Chennai being a significant beneficiary.

Additional Information

• Southwest vs. Northeast Monsoon:
• The Southwest Monsoon (June-September) brings rainfall to most parts of India, while the Northeast Monsoon (October-December) predominantly affects Tamil Nadu, coastal Andhra Pradesh, and parts of Kerala and Karnataka.
• The Southwest Monsoon is driven by southwesterly winds, whereas the Northeast Monsoon is powered by northeasterly winds.
• Role of Bay of Bengal:
• The Bay of Bengal plays a critical role during the retreating monsoon, as cyclonic storms often form here, intensifying rainfall along the southeastern coast of India.
• Chennai frequently experiences heavy downpours due to depressions or cyclones originating in the Bay of Bengal.
• Climate of Tamil Nadu:
• Tamil Nadu has a tropical climate, and the retreating monsoon is vital for agriculture, water resources, and drinking water supply in the region.
• The state's dependency on the Northeast Monsoon makes it unique compared to other Indian states.
• Terminology:
• Retreating Monsoon: The period when monsoon winds retreat southward, starting from northern India and moving towards the Bay of Bengal.
• Northeast Monsoon: Another term for the retreating monsoon, specifically referring to the rainfall caused by northeasterly winds.

The correct answer is 01%.

Key Points

• According to the IMF's April 2025 Global Financial Stability Report, global stock returns declined on average by 01% during major geopolitical risk events.
• Major geopolitical risk events often trigger uncertainty in financial markets, leading to a decline in investor confidence.
• This 01% decline is an average value, indicating the general sensitivity of global stock markets to geopolitical events.
• Such declines are often short-term, but they highlight the interconnectedness of global financial markets with geopolitical stability.
• The report emphasizes the need for robust risk management strategies to mitigate the impact of such events on financial stability.

Additional Information

• Geopolitical Risk:
• Geopolitical risk refers to the uncertainty or instability caused by political events, conflicts, or policy changes that impact global markets.
• Examples of geopolitical events include wars, trade disputes, sanctions, and political upheavals.
• IMF Global Financial Stability Report:
• This biannual report assesses the stability of global financial markets and highlights key risks and vulnerabilities.
• It provides insights into macroeconomic policies, financial market developments, and emerging trends.
• Impact of Geopolitical Risks on Markets:
• Geopolitical risks can lead to fluctuations in stock markets, currency values, and commodity prices.
• They often affect investor sentiment, leading to reduced capital flows and increased market volatility.
• Risk Mitigation Strategies:
• To counter the effects of geopolitical risks, investors and policymakers use strategies such as diversification, hedging, and regulatory reforms.
• Central banks and governments often intervene to stabilize markets during periods of heightened geopolitical risks.

The correct answer is Pressing Ctrl + N.

Key Points

• Pressing Ctrl + N in MS PowerPoint creates a new presentation, not a new slide within an existing presentation.
• To add a new slide in MS PowerPoint, you can use Ctrl + M, which is a shortcut specifically for creating new slides.
• The 'New Slide' option located under the Home tab on the ribbon allows users to add a new slide to the presentation.
• Right-clicking within the slide sorter pane and selecting 'New Slide' is a valid method to add new slides.
• Ctrl + N is often confused with commands for adding slides but is exclusively intended for creating a brand new presentation file.

Additional Information

• Slide Shortcuts in MS PowerPoint:
• Ctrl + M: Adds a new slide to the current presentation.
• Ctrl + D: Duplicates the currently selected slide.
• Ctrl + Shift + Up/Down: Moves slides within the slide sorter pane.
• Understanding Ctrl + N:
• Function: Used to create a new presentation in MS PowerPoint, not a new slide.
• It is also applicable in other Microsoft Office applications, such as Word and Excel, to create new documents or workbooks.
• Slide Sorter Pane:
• Located on the left side of the PowerPoint interface, it displays a thumbnail view of all slides.
• Allows users to rearrange slides, delete slides, or add new slides by right-clicking.
• Ribbon Interface:
• The ribbon is the toolbar at the top of MS PowerPoint containing tabs such as Home, Insert, Design, etc.
• The 'New Slide' option under the Home tab is one of the most commonly used methods to add slides.

The correct answer is Creating convection currents.

Key Points

• The Himalayas act as a natural barrier that blocks the cold winds from Central Asia, preventing extreme cold conditions in northern India during winters.
• They obstruct the southwest monsoon winds, forcing them to shed moisture, which results in heavy rainfall in the Indian subcontinent.
• The Himalayan peaks contribute to snowfall in northern India, especially in regions like Himachal Pradesh, Jammu & Kashmir, and Uttarakhand.
• While the Himalayas influence wind movement and precipitation, they do not directly create convection currents, which are primarily a result of temperature differentials between the Earth's surface and the atmosphere.

Additional Information

• Himalayas' Role in Climate:
• The Himalayas influence India's climate by forming a barrier that blocks cold winds and traps warm air.
• They play a significant role in the monsoon system by obstructing monsoon winds and causing orographic rainfall.
• Convection Currents:
• These are vertical movements of air or fluids caused by temperature differences.
• They are a key mechanism in atmospheric and oceanic circulations but are not directly tied to the Himalayas' role in India's climate.
• Orographic Rainfall:
• This occurs when moist air ascends a mountain range, cools, and condenses, leading to rainfall.
• The Himalayas play a crucial role in causing orographic rainfall during the southwest monsoon season.
• Natural Climate Barrier:
• The Himalayas protect the Indian subcontinent from the cold Siberian winds, maintaining a relatively warmer climate in northern India.

Shortcut Trick

In a 30°−60°−90° triangle, the ratio of sides opposite to the angles is 1 : √3 : 2.

Side opposite to 60° (Height) → √3 units = 171 m.

Side opposite to 90° (Hypotenuse/Distance to top) → 2 units.

Value of 1 unit = 171/√3 = 57√3 m.

Value of 2 units = 2 × 57√3 = 114√3 m.

∴ The correct answer is 114√3 m.

Alternate Method

Given:

Height of hill (AB) = 171 m

Angle of elevation (θ) = 60°

Formula used: sin θ = Perpendicular / Hypotenuse

⇒ sin 60° = Height / Distance to top

⇒ √3 / 2 = 171 / d

⇒ d = (171 × 2) / √3

⇒ d = 342 / √3

⇒ d = (342 × √3) / 3

⇒ d = 114√3 m

∴ The correct answer is 114√3 m.

Additional Information

Trigonometric Ratios

For a right-angled triangle, sin θ = P/H, cos θ = B/H, and tan θ = P/B. These are essential for finding heights and distances.

Standard Values

Important values: sin 60° = √3/2, cos 60° = 1/2, and tan 60° = √3.

Angle of Elevation vs Depression

The Angle of Elevation is measured upwards from the horizontal, while the Angle of Depression is measured downwards. Numerically, they are equal due to alternate interior angles.

Shortcut Trick

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

Rotation about 56 cm side ⇒ Height (h) = 56 cm and Radius (r) = 42 cm.

Slant height (l) is the hypotenuse = 70 cm.

Total Surface Area = πr(l + r) = π × 42 × (70 + 42) = π × 42 × 112 = 4704π cm².

∴ The correct answer is 4704π cm².

Alternate Method

Given: sides of right triangle = 56 cm, 42 cm, 70 cm. Rotated about the 56 cm side.

Formula Used: Total Surface Area (TSA) of Cone = πr² + πrl = πr(r + l)

⇒ Radius (r) of the cone = 42 cm

⇒ Slant Height (l) of the cone = 70 cm

⇒ Total Surface Area = π × 42 × (42 + 70)

⇒ Total Surface Area = π × 42 × 112

⇒ Total Surface Area = 4704π cm²

∴ The correct answer is 4704π cm².

Additional Information

Slant Height of Cone

The relationship between slant height (l), radius (r), and height (h) is given by l² = r² + h².

Curved Surface Area

The area of the curved surface of a cone is πrl, where r is the radius and l is the slant height.

Volume of Cone

The volume of a cone is (1/3)πr²h, which is exactly one-third of the volume of a cylinder with the same base and height.

Shortcut Trick

Rate of increase = 25% = 1/4. Population ratio (Previous Year : Current Year) = 4 : 5.

Population 3 years ago = 1,60,000 × (4/5)³ = 1,60,000 × 64/125 = 81,920.

Population 2 years ago = 81,920 × (5/4) = 1,02,400.

Difference = 1,02,400 − 81,920 = 20,480.

∴ The correct answer is 20,480.

Alternate Method

Given: Current Population (P) = 1,60,000, Rate (R) = 25%, Time (n) = 3 years.

Formula: P_ago = P / (1 + R/100)ⁿ

⇒ Population 3 years ago = 1,60,000 / (1 + 25/100)³

⇒ 1,60,000 / (5/4)³ = 1,60,000 × (64/125) = 1280 × 64 = 81,920

⇒ Population 2 years ago = 1,60,000 / (1 + 25/100)²

⇒ 1,60,000 / (5/4)² = 1,60,000 × (16/25) = 6400 × 16 = 1,02,400

⇒ Required Difference = 1,02,400 − 81,920 = 20,480

∴ The correct answer is 20,480.

Additional Information

Population Growth Formula

For constant growth, Future Population = P × (1 + R/100)ⁿ, where P is the current value.

Successive Percentage Change

The net change for two years with rates R₁ and R₂ is (R₁ + R₂ + R₁R₂/100)%.

Depreciation Rule

If the value decreases, use the formula Value = P × (1 − R/100)ⁿ.

Shortcut Trick

Total interest percentage for 12 months = 6% × 12 = 72%

Simple Interest = 72% of Principal

SI = 72% of 900 = 72 × 9 = 648

∴ The correct answer is ₹648.

Alternate Method

Given:

Principal (P) = ₹900

Rate of interest (R) = 6% per month

Time period (T) = 12 months

Formula Used:

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

Calculations:

⇒ SI = (900 × 6 × 12) ÷ 100

⇒ SI = 9 × 6 × 12

⇒ SI = 54 × 12

⇒ SI = 648

∴ The correct answer is ₹648.

Additional Information

Total Amount Formula

The total Amount (A) after the interest period is the sum of the Principal and the Simple Interest: A = P + SI.

Unit Consistency Rule

Always ensure that the Rate (R) and Time (T) are in the same unit (e.g., both monthly or both annual) before applying the formula.

Simple Interest vs Compound Interest

In Simple Interest, interest is calculated only on the initial principal, whereas in Compound Interest, interest is calculated on the principal plus the accumulated interest of previous periods.

The correct answer is Jan Aushadhi Diwas.

Key Points

• Jan Aushadhi Diwas is celebrated annually on March 7th to create awareness and promote the use of generic medicines.
• The initiative is part of the Pradhan Mantri Bhartiya Janaushadhi Pariyojana (PMBJP), a government scheme launched to provide affordable and quality medicines to all citizens.
• Generic medicines, which are distributed through Jan Aushadhi Kendras, are 50% to 90% cheaper than branded medicines, ensuring affordability for the general public.
• Jan Aushadhi Kendras serve as a crucial step towards accessible healthcare by offering medicines at reduced costs, benefiting especially the economically weaker sections.
• In March 2025, Jan Aushadhi Diwas was celebrated to emphasize the role of generic medicines in reducing healthcare costs and improving accessibility across India.

Additional Information

• Generic Medicines:
• Generic medicines are drugs that are chemically identical to branded drugs but are sold under their chemical name rather than a brand name.
• They are approved by the regulatory authorities for their efficacy, safety, and quality.
• Generic medicines help reduce the financial burden of healthcare on the population.
• Pradhan Mantri Bhartiya Janaushadhi Pariyojana (PMBJP):
• Launched in 2008 and revamped under the leadership of PM Narendra Modi, PMBJP aims to provide affordable medicines through a network of Jan Aushadhi Kendras.
• These Kendras are functional across the country, with over 9,000 outlets as of 2023.
• The program ensures the availability of quality medicines certified by the Bureau of Pharma PSUs of India (BPPI).
• Health Impact:
• Jan Aushadhi Kendras play a critical role in improving healthcare access for low-income and rural communities.
• They contribute towards reducing the financial stress related to medical expenses, enabling better health outcomes.
• Awareness Campaigns:
• Events like Jan Aushadhi Diwas are used to spread information about generic medicines and their benefits.
• These campaigns aim to break misconceptions about the efficacy of generic drugs and encourage public trust.

The correct answer is Option 3: Both Statement 1 and Statement 2.

Key Points

• Statement 1 is correct: The First Five-Year Plan (1951-1956) was based on the Harrod-Domar growth model and emphasised agricultural development to address food shortages and achieve food security.
• The plan focused on agriculture, irrigation, and land reforms to rebuild the agrarian economy after independence.
• Statement 2 is correct: The Second Five-Year Plan (1956-1961), also known as the Mahalanobis Plan, prioritised industrialisation, particularly heavy industries, to build the foundation for long-term economic growth.
• The Mahalanobis Model advocated increasing the share of investment in industries producing capital goods, with a focus on public sector enterprises.
• Both plans played a crucial role in shaping India’s economic development trajectory during its early years of independence.

Additional Information

• Harrod-Domar Model: This economic model emphasises the relationship between savings, investment, and economic growth. It was chosen for the First Five-Year Plan to address India’s immediate post-independence challenges, like food shortages and inflation.
• Mahalanobis Model: Named after economist P.C. Mahalanobis, this model guided the Second Five-Year Plan. It prioritised capital goods industries to create a base for self-reliant economic growth.
• Five-Year Plans: India adopted the concept of centralised economic planning inspired by the Soviet Union. The Planning Commission was established in 1950 to oversee the formulation and implementation of these plans.
• Public Sector Focus: The Second Five-Year Plan emphasised public sector enterprises to achieve industrialisation, reduce dependency on imports, and create infrastructure for long-term growth.
• Transition to NITI Aayog: The Planning Commission was replaced by NITI Aayog in 2015. The five-year planning framework was discontinued, and a more decentralised approach to planning was adopted.

The correct answer is Longitudinal.

Key Points

• Sound waves in air are longitudinal waves, where the particles of the medium move in the same direction as the wave propagation.
• In a longitudinal wave, particles oscillate back and forth along the direction of energy transfer, resulting in compressions (high-pressure regions) and rarefactions (low-pressure regions).
• Sound cannot propagate through a vacuum as it requires a material medium like air, water, or solid for the transmission of vibrations.
• Examples of longitudinal waves include sound waves, seismic P-waves, and pressure waves in fluids.
• The speed of sound in air depends on temperature, pressure, and humidity, with an average speed of approximately 343 m/s at 20°C.

Additional Information

• Longitudinal Waves
• These waves consist of compressions and rarefactions, with energy transfer occurring parallel to particle motion.
• The wavelength in a longitudinal wave is the distance between two consecutive compressions or rarefactions.
• Transverse Waves
• In transverse waves, particles of the medium oscillate perpendicular to the direction of wave propagation.
• Examples include electromagnetic waves (e.g., light) and water surface waves.
• Sound Wave Properties
• Frequency: Determines the pitch of the sound and is measured in Hertz (Hz).
• Amplitude: Relates to the loudness or intensity of the sound.
• Speed: Depends on the medium's density and elasticity.
• Electromagnetic Waves
• Unlike sound waves, electromagnetic waves (e.g., light, radio waves) do not require a medium for propagation and can travel through a vacuum.

Given Expression: M – N + O ÷ P × Q

M – N: M is the brother of N.

N + O: N is the mother of O.

O ÷ P: O is the father of P.

P × Q: P is the wife of Q.

According to the given information Family Tree Representation:

Therefore, M is Wife's father's mother's brother of Q.

Hence, the correct answer is "Option 1"

The correct answer is CHESS (Centre for High Energy Systems and Sciences).

Key Points

• CHESS (Centre for High Energy Systems and Sciences) is a premier DRDO lab responsible for research in high-energy systems, including advanced laser systems.
• In April 2025, CHESS successfully conducted a test of a laser weapon, marking a significant advancement in India's directed energy weapon (DEW) capabilities.
• This laser weapon test is part of India's efforts to develop indigenous DEWs for use in air defense, counter-drone systems, and other strategic applications.
• CHESS has been working on developing laser systems capable of targeting and neutralizing threats with high precision and minimal collateral damage.
• The success of this test showcases India's growing capabilities in futuristic defense technologies, aligning with the "Atmanirbhar Bharat" (self-reliant India) initiative.

Additional Information

• Directed Energy Weapons (DEWs):
• DEWs use focused energy in the form of lasers, microwaves, or particle beams to damage or neutralize enemy targets.
• They provide advantages such as precision targeting, reduced collateral damage, and cost-effectiveness compared to traditional munitions.
• DEWs can be used for applications such as missile defense, counter-drone systems, and disabling electronic systems.
• DRDO (Defence Research and Development Organisation):
• DRDO is India's premier defense R&D agency, under the Ministry of Defence, established in 1958.
• It is tasked with developing cutting-edge technologies for the Indian Armed Forces.
• DRDO's research spans multiple domains, including missiles, radars, electronic warfare, and advanced weapon systems.
• CHESS (Centre for High Energy Systems and Sciences):
• Located in Hyderabad, CHESS is a DRDO lab specializing in high-energy systems and directed energy weapons.
• It collaborates with other DRDO labs and academic institutions to develop advanced technologies for the Indian military.
• India's Laser Weapon Program:
• India has been investing in laser weapons for applications such as missile defense, counter-drone operations, and air defense.
• CHESS and other DRDO labs are actively working on developing high-power lasers to address emerging security threats.

Given: E, X, P, A, N, and D live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it, number 2 and so on, till the topmost floor is numbered 6.

1. Only one person lives above D.

2. Only A lives below P.

3. X lives on a floor above D.

 

4. E lives on an even numbered floor.

The last remaining person is N, and the only remaining floor is 3. So N lives on Floor 3.

 

N lives on Floor 3.

Therefore, Two people live below N.

Hence, the correct answer is "Option 1".

Given: M, N, O, P, Y and Z live on six different floors of the same building. 

1. O lives on an even numbered floor but not on floor number 4.

2. Only two people live between O and Z.

• Case 1: O lives on Floor 2.
• Case 2: O lives on Floor 6.

3. Y lives on an odd numbered floor but not on the lowermost floor.

4. P lives immediately below Y.

This means Y and P form a consecutive block [Y, P].

Case 1 for O:

If O is on Floor 2 and Z is on Floor 5.

Now, place Y and P. Y must be on an odd floor (3 or 5), not 1. Floor 5 is taken by Z. If Y is on Floor 3, then P would be on Floor 2. However, O is already on Floor 2. This creates a contradiction. Therefore, Case 1 (O on Floor 2) is not possible.

Case 2 for O:

If O is on Floor 6 and Z is on Floor 3..

 

5. Only two people live between Y and M.

The only remaining person is N, and the only remaining floor is 1. So N lives on Floor 1.

N lives on Floor 1 and P lives on Floor 4.

Therefore, Two people live between N and P.

Hence, the correct answer is "Option 1".

Given:

x = 12^0.36

y = 12^0.64

x^z = y⁴

Formula used:

Exponent rules: a^m × aⁿ = a^m+n

Calculation:

Substitute x and y into the equation:

⇒ (12^0.36)^z = (12^0.64)⁴

⇒ 12^0.36z = 12^{4 × 0.64}

⇒ 12^0.36z = 12^2.56

Since bases are equal, equate exponents:

⇒ 0.36z = 2.56

⇒ z = 2.56 ÷ 0.36

⇒ z ≈ 7.11

∴ The correct answer is option (3).

Shortcut Trick

Assume an assumed mean of 60 and calculate deviations.

Net deviation = +9 + 0 − 21 − 2 − 5 − 29 + 24 + 4 + 20 = 0.

Actual Mean = Assumed Mean + (Net Deviation ÷ Total Observations).

Mean = 60 + (0 ÷ 9) = 60.

∴ The correct answer is 60.

Alternate Method

Given observations: 69, 60, 39, 58, 55, 31, 84, 64, 80

Number of observations (n): 9

Formula Used: Arithmetic Mean (μ) = (Sum of all observations) ÷ (Total number of observations)

⇒ Sum (Σx) = 69 + 60 + 39 + 58 + 55 + 31 + 84 + 64 + 80

⇒ Sum (Σx) = 540

⇒ Mean = 540 ÷ 9

⇒ Mean = 60

∴ The correct answer is 60.

Additional Information

Properties of Arithmetic Mean

The sum of deviations of items from their arithmetic mean is always zero, i.e., Σ(x_i − μ) = 0.

Effect of Change in Origin

If a constant value 'k' is added to or subtracted from every observation, the mean will also be increased or decreased by 'k'.

Weighted Arithmetic Mean

When observations have varying levels of importance, the Weighted Mean is calculated as Σw_ix_i ÷ Σw_i, where w represents the weight.

The correct answer is The text retains its original formatting from the source..

Key Points

• Keep Source Formatting is one of the paste options available in MS-PowerPoint 2019 to retain the original look of the copied text.
• When text is pasted using this option, it preserves the font style, size, color, and other formatting from the source document.
• This feature is useful when the copied text has specific formatting that needs to remain unchanged on the destination slide.
• The pasted text does not adopt the theme fonts or colors of the destination slide but retains its original formatting.
• Users can access this option by right-clicking on the slide and selecting "Paste Options," followed by "Keep Source Formatting."

Additional Information

• Paste Options in MS-PowerPoint:
• Keep Source Formatting: Retains the original formatting of the text from the source.
• Use Destination Theme: Adopts the theme fonts and colors of the destination slide.
• Picture: Converts the copied text into an image.
• Text Only: Pastes the text without any formatting.
• Theme Fonts and Colors:
• These are predefined fonts and colors associated with the slide's design.
• Using the destination theme ensures uniformity across all slides in a presentation.
• Automatic Text Adjustment:
• MS-PowerPoint can automatically resize text to fit within placeholders.
• This feature is called "AutoFit" and can be enabled or disabled as needed.
• Clipboard Functionality:
• The clipboard temporarily stores copied text or objects for pasting.
• In MS-PowerPoint, users can access advanced clipboard options for formatting control.

Shortcut Trick

Identify that Selling Price 1 (SP₁) represents 70% of Cost Price (CP).

Required Selling Price 2 (SP₂) must represent 115% of CP.

Ratio of SP₁ to SP₂ = 70 : 115 = 14 : 23.

Given 14 units =  ₹112, then 1 unit =  ₹8.

Therefore, 23 units = 23 × 8 =  ₹184.

∴ The correct answer is  ₹184.

Alternate Method

Given → SP₁ =  ₹112, Loss% = 30%, Desired Gain% = 15%. Formulas: CP = SP × 100 ÷ (100 − Loss%) | SP = CP × (100 + Gain%) ÷ 100.

⇒ CP = 112 × 100 ÷ (100 − 30) = 112 × 100 ÷ 70 =  ₹160. ⇒ New SP = 160 × (100 + 15) ÷ 100 = 160 × 115 ÷ 100. ⇒ New SP = 16 × 11.5 =  ₹184.

∴ The correct answer is  ₹184.

Additional Information

Cost Price and Profit/Loss

Cost Price is always considered as 100% in percentage-based calculations unless specified otherwise.

Relation between SPs

When CP is constant, SP₁ ÷ (100 − L₁%) = SP₂ ÷ (100 + G₂%).

BODMAS Rule:

According to the question, the letters are interchanged with mathematical operators as follows:

 

1) 84 C 12 D 76 A 36 B 4

Equation: 84 + 12 − 76 ÷ 36 × 4

⇒ 84 + 12 − 76 ÷ 36 × 4

⇒ 84 + 12 − 2.11 × 4

⇒ 84 + 12 − 8.44

⇒ 96 − 8.44

⇒ 87.56 ≠ 75 (Incorrect)

2) 84 B 12 C 76 D 36 A 4

Equation: 84 × 12 + 76 − 36 ÷ 4

⇒ 84 × 12 + 76 − 36 ÷ 4

⇒ 1008 + 76 − 36 ÷ 4

⇒ 1008 + 76 − 9

⇒ 1084 − 9

⇒ 1075 ≠ 75 (Incorrect)

3) 84 A 12 D 76 C 36 B 4

Equation: 84 ÷ 12 − 76 + 36 × 4

⇒ 84 ÷ 12 − 76 + 36 × 4

⇒ 7 − 76 + 36 × 4

⇒ 7 − 76 + 144

⇒ −69 + 144

⇒ 75 = 75 (Correct)

4) 84 D 12 A 76 B 36 C 4

Equation: 84 − 12 ÷ 76 × 36 + 4

⇒ 84 − 12 ÷ 76 × 36 + 4

⇒ 84 − 0.16 × 36 + 4

⇒ 84 − 5.76 + 4

⇒ 78.24 + 4

⇒ 82.24 ≠ 75 (Incorrect)

Hence, the correct answer is "Option 3".

Shortcut Trick

Area of rectangular field = 11 × 14 = 154 m².

Area of circular field = πr² = 154.

Since 154 is a standard value for a circle with radius (r) = 7 m.

Circumference = 2πr = 2 × (22/7) × 7 = 44 m.

∴ The correct answer is 44 m.

Alternate Method

Given: Length (l) = 14 m, Breadth (b) = 11 m, Area of Circle = Area of Rectangle.

Formula Used: Area of rectangle = l × b; Area of circle = πr²; Circumference = 2πr.

⇒ Area of rectangular field = 14 × 11 = 154 m²

⇒ Area of circular field = πr² = 154

⇒ (22/7) × r² = 154

⇒ r² = (154 × 7) ÷ 22

⇒ r² = 7 × 7 ⇒ r = 7 m

⇒ Circumference = 2 × (22/7) × 7

⇒ Circumference = 44 m

∴ The correct answer is 44 m.

Additional Information

Area and Circumference of Circle

Area = πr² and Circumference = 2πr, where r is the radius of the circle.

Rectangular Area

Area of a rectangle is the product of its length and breadth (L × B).

Standard Circle Values

For r = 7, Area = 154 and Circumference = 44. For r = 14, Area = 616 and Circumference = 88.

The correct answer is Delhi.

Key Points

• In May 2025, the Delhi Cabinet approved ₹3.21 crore to conduct five cloud-seeding trials aimed at combating air pollution.
• The initiative focuses on artificial rain creation through cloud-seeding technology to mitigate pollution levels in the capital city.
• Cloud-seeding involves dispersing substances like silver iodide or sodium chloride into the atmosphere to enhance precipitation.
• This is part of Delhi's broader efforts to address the severe air pollution issues the region faces, especially during winter months.
• The trials are being conducted in collaboration with expert agencies and scientists to ensure effective implementation and monitoring.

Additional Information

• Cloud-Seeding Technology:
• It is a weather modification technique that aims to enhance rainfall by dispersing substances into the clouds.
• Commonly used agents include silver iodide, potassium iodide, and dry ice.
• It is widely used in regions facing droughts or high pollution levels to improve air quality and water availability.
• Air Pollution in Delhi:
• Delhi is one of the most polluted cities globally, with PM2.5 and PM10 levels often exceeding safe limits.
• Major contributors include vehicular emissions, industrial activities, and stubble burning in neighboring states.
• Air pollution peaks during winter due to temperature inversion and reduced wind speeds.
• Health Impacts of Air Pollution:
• Prolonged exposure to high pollution levels can lead to respiratory issues, cardiovascular diseases, and reduced life expectancy.
• Children and the elderly are particularly vulnerable to air pollution-related health risks.
• Improving air quality has direct benefits for public health and economic productivity.
• Government Measures to Combat Pollution:
• Delhi has implemented measures like the Odd-Even vehicle scheme, expansion of public transport, and promotion of electric vehicles.
• Installation of smog towers and air purifiers in high-pollution zones has been prioritized.
• Collaborative efforts with neighboring states to manage stubble burning are ongoing.

Given:

Expression: 139 - 15 × (11 + 4) + 52

Calculation:

139 - 15 × (11 + 4) + 52

⇒ 139 - 15 × 15 + 52

⇒ 139 - 225 + 52

⇒ (139 + 52) - 225

⇒ 191 - 225

⇒ -34

∴ The correct answer is option (1).

Shortcut Trick

Total efficiency of A + B + C = (1/7) + (1/9) = 16/63 units per day.

Given Efficiency of A = Efficiency of (B + C).

∴ Efficiency of A = (1/2) × (16/63) = 8/63.

Efficiency of B = Efficiency of (A + B) − Efficiency of A = (1/7) − (8/63) = (9 − 8)/63 = 1/63.

∴ The correct answer is 63 days.

Alternate Method

Given: Time taken by (A + B) = 7 days, Time taken by C = 9 days.

⇒ Combined Efficiency of A + B + C = 9 + 7 = 16 units/day.

⇒ Since A = B + C, then A + (B + C) = A + A = 2A.

⇒ 2 × Efficiency of A = 16 ⇒ Efficiency of A = 8 units/day.

⇒ Efficiency of B = Efficiency of (A + B) − Efficiency of A = 9 − 8 = 1 unit/day.

⇒ Time taken by B alone = Total Work ÷ Efficiency of B = 63 ÷ 1 = 63 days.

∴ The correct answer is 63 days.

Additional Information

Work and Efficiency Relation

Efficiency is inversely proportional to time. Total Work = Efficiency × Time.

LCM Method

To find Total Work, take the LCM of the individual days taken by the workers to complete the work.

Combined Work Formula

If two people work together with efficiencies E₁ and E₂, their combined time T = Total Work ÷ (E₁ + E₂).

The logic followed here is:

 

Thus, the missing number 176.

Hence, the correct answer is "Option 2".

The correct answer is Dr. Jitendra Singh.

Key Points

• Dr. Jitendra Singh, a renowned diabetologist and an active researcher in diabetes, was awarded the prestigious Lifetime Achievement Award for research in Diabetes in July 2024.
• The award recognizes his significant contributions to the field of diabetes management, treatment, and prevention strategies over the years.
• Dr. Jitendra Singh has authored numerous research papers and publications on the subject, providing valuable insights into diabetes care.
• He has also played a pivotal role in promoting awareness about diabetes and its complications in India.
• This recognition highlights his lifelong dedication to improving the lives of individuals affected by diabetes through both clinical practice and research.

Additional Information

• Diabetes Overview:
• Diabetes is a chronic condition characterized by high blood sugar levels due to the body's inability to produce or effectively use insulin.
• There are three main types of diabetes: Type 1, Type 2, and gestational diabetes.
• Type 2 diabetes is the most common form, often linked to lifestyle factors such as diet and physical activity.
• Impact of Diabetes in India:
• India is considered the diabetes capital of the world, with over 77 million people diagnosed with diabetes as of 2023.
• The rising prevalence of diabetes has been attributed to urbanization, sedentary lifestyles, and unhealthy dietary habits.
• Importance of Research in Diabetes:
• Research plays a critical role in developing new treatments, understanding genetic predispositions, and creating effective prevention strategies.
• Advancements in diabetes research have led to innovations such as insulin analogs, continuous glucose monitoring systems, and artificial pancreas technology.
• Government Initiatives in India:
• Programs like the National Programme for Prevention and Control of Cancer, Diabetes, Cardiovascular Diseases, and Stroke (NPCDCS) aim to combat diabetes and related disorders.
• Awareness campaigns and free screening initiatives are regularly conducted to educate the public and promote early diagnosis.

The correct answer is Read-Only Mode.

Key Points

• Read-Only Mode in MS Excel allows users to open and view a workbook while restricting editing and modifications.
• This feature is useful for sharing sensitive data that needs to be protected from unauthorized changes.
• To enable Read-Only Mode, you can save the workbook and select the "Tools > General Options" in the Save As dialog box, then set a password for editing.
• Users can view the file without entering the password, but they cannot make changes unless they have the editing password.
• Read-Only Mode ensures data integrity and helps prevent accidental or intentional modifications.

Additional Information

• Protected View:
• Files opened from potentially unsafe locations (e.g., email attachments) are opened in Protected View to prevent malicious content from affecting your system.
• Protected View allows viewing but blocks editing until explicitly enabled by the user.
• Workbook Password Protection:
• Excel allows users to set passwords to restrict access to the workbook or worksheet.
• Passwords can be set for opening and/or editing the file.
• Track Changes Feature:
• Excel provides the "Track Changes" feature to monitor modifications made to a workbook collaboratively.
• It helps identify who made edits and what changes were made.
• Freeze Panes:
• This feature is used to lock specific rows or columns while scrolling through a worksheet.
• It enhances visibility but does not provide security or restrict editing.

The correct answer is Ctrl + P.

Key Points

• Ctrl + P is the universal shortcut used to open the Print dialog box in most Microsoft Office applications, including MS Excel 365.
• Using this shortcut allows users to configure printing settings such as selecting the printer, adjusting page orientation, and specifying print ranges.
• It is a time-saving alternative to navigating through the "File" menu to access the print feature.
• This shortcut is also consistent across different versions of MS Excel, making it easy for users to remember and use.
• In addition to Ctrl + P, Excel also provides options to customize printing through the "Page Layout" tab for advanced settings.

Additional Information

• Keyboard Shortcuts in Excel
• Keyboard shortcuts are combinations of keys that perform a specific function, saving time and enhancing productivity.
• Examples include Ctrl + S (Save), Ctrl + N (New Workbook), and Ctrl + O (Open).
• Using shortcuts reduces dependency on the mouse and accelerates workflow in Excel.
• Print Features in Excel
• The Print dialog box in Excel allows users to select specific sheets, ranges, or the entire workbook for printing.
• Advanced options include "Print Selection," "Print Area," and "Fit to Page" for customized outputs.
• The "Print Preview" option helps users ensure proper formatting before finalizing the print.
• Page Layout and Printing
• The "Page Layout" tab in Excel provides options to set margins, orientation (portrait/landscape), and scaling for printing.
• Headers and footers, gridlines, and print titles can also be configured here.
• Excel 365 Features
• MS Excel 365 is part of Microsoft 365 and offers cloud-based functionality for real-time collaboration.
• It includes various tools such as Power Query, advanced charting options, and AI-driven insights to enhance usability.
• Printing features in Excel 365 remain consistent with earlier versions but include enhanced compatibility with cloud printers.

BODMAS Rule:

According to the question, the signs are interchanged as follows:

Now, given the equation: 15 − 3 ÷ 5 + 18 × 6 = ?

After interchanging the specified signs, the new equation is:

15 × 3 + 5 − 18 ÷ 6 = ?

Perform operations according to BODMAS:

⇒ 15 × 3 + 5 − 18 ÷ 6

⇒ 45 + 5 − 18 ÷ 6

⇒ 45 + 5 − 3

⇒ 50 − 3

⇒ 47

Hence, the correct answer is "Option 3".

The logic followed here is:

For, GEAN - NAGE - GAEN

<br>

For, MAKE - EKMA - MKAE

Similarly,

FOWL - LWFO - FWOL 

Hence, the correct answer is "Option 1".

The correct answer is Papua New Guinea.

Key Points

• The 2026 Rugby League World Cup was initially awarded to France, but due to financial challenges, it was reallocated to new hosts.
• Australia and Papua New Guinea will co-host the rescheduled tournament in 2026.
• Papua New Guinea is one of the few countries where rugby league is the national sport and enjoys a massive following.
• The inclusion of Papua New Guinea as a co-host highlights its strong rugby league culture and the region's importance to the sport.
• The event will feature both men's and women's tournaments, promoting inclusivity and global participation in the sport.

Additional Information

• Rugby League World Cup:
• The Rugby League World Cup is an international tournament organized by the International Rugby League (IRL).
• The first Rugby League World Cup was held in 1954 in France, making it the oldest rugby world championship.
• The competition features national teams from around the world, with Australia traditionally being the dominant team.
• Papua New Guinea's Rugby League Culture:
• Rugby league is the national sport of Papua New Guinea, with deep cultural and social significance.
• The country has a professional rugby league team, the PNG Hunters, which competes in the Queensland Cup in Australia.
• 2026 Rugby League World Cup:
• The tournament will feature men's, women's, and wheelchair competitions.
• It aims to expand the global appeal of rugby league while emphasizing diversity and inclusivity.
• Hosting matches in both Australia and Papua New Guinea will help grow the sport's presence in the Asia-Pacific region.
• International Rugby League (IRL):
• The IRL is the global governing body for rugby league, responsible for organizing international tournaments.
• The IRL works to develop the sport globally, focusing on emerging markets and grassroots initiatives.

Given:

: LQT :: ZEH : %

Option 1) # = ODW, % = OIE

For # (ODW) to LQT

For ZEH to % (OIE)

Since the pattern for ODW to LQT (-3, +13, -3) is not the same as the pattern for ZEH to OIE (-11, +4, -3), Option 1 is incorrect.

Option 2) # = OTW, % = WBE

For # (OTW) to LQT

For ZEH to % (WBE)

Since the pattern for OTW to LQT (-3, -3, -3) is the same as the pattern for ZEH to WBE (-3, -3, -3), Option 2 is correct.

Option 3) # = LKO, % = WYE

For # (LKO) to LQT

For ZEH to % (WYE)

Since the pattern for LKO to LQT (0, +6, +5) is not the same as the pattern for ZEH to WYE (-3, +20, -3), Option 3 is incorrect.

Option 4) # = OHD, % = LDK

For # (OHD) to LQT

For ZEH to % (LDK)

Since the pattern for OHD to LQT (-3, +9, +16) is not the same as the pattern for ZEH to LDK (-14, -1, +3), Option 4 is incorrect.

Hence, the correct answer is "Option 2".

The correct answer is A multi-member National Commission.

Key Points

• The Sixty-fifth Amendment Act of 1990 established a multi-member National Commission for Scheduled Castes and Scheduled Tribes to ensure their welfare and development.
• This amendment replaced the single Special Officer for Scheduled Castes and Scheduled Tribes with a full-fledged National Commission.
• The commission was tasked with investigating and monitoring matters related to safeguards provided to Scheduled Castes and Scheduled Tribes under the Constitution.
• It also evaluates the progress of various schemes implemented for the upliftment of SC/ST communities.
• The commission submits annual reports to the President of India, who forwards them to Parliament for discussion and action.

Additional Information

• Scheduled Castes and Scheduled Tribes:
• These are historically disadvantaged communities recognized in the Indian Constitution for special measures to ensure their social, educational, and economic development.
• Scheduled Castes are communities traditionally subjected to social discrimination, while Scheduled Tribes represent indigenous groups living in remote areas.
• National Commission for Scheduled Castes:
• In 2004, the National Commission for SC/ST was bifurcated into two separate commissions: the National Commission for Scheduled Castes and the National Commission for Scheduled Tribes.
• The National Commission for Scheduled Castes focuses exclusively on issues related to Scheduled Castes.
• National Commission for Scheduled Tribes:
• The National Commission for Scheduled Tribes was established under Article 338A of the Indian Constitution.
• It monitors safeguards related to STs, advises on policies, and evaluates the development of tribal communities.
• Constitutional Safeguards for SC/ST:
• Article 46: Promotes educational and economic interests of SCs/STs.
• Article 17: Abolishes "untouchability" and forbids its practice.
• Article 15(4): Allows the state to make special provisions for SCs/STs in education.

Shortcut Trick

Relative speed in opposite direction = 32 + 28 = 60 km/hr = 60 × (5/18) = 50/3 m/s.

Total distance (L_A + L_B) = Speed × Time = (50/3) × 33 = 550 m.

Since L_B = 1.5 L_A, Total = 2.5 L_A = 550 ⇒ L_A = 220 m and L_B = 330 m.

Distance covered by B in 54s = (28 × 5/18) × 54 = 420 m.

Length of Bridge = Total Distance − L_B = 420 − 330 = 90 m.

∴ The correct answer is 90 m.

Alternate Method

Given: Speed_A = 32 km/hr, Speed_B = 28 km/hr, Time_crossing = 33 s, L_B = 1.5 L_A, Time_bridge = 54 s.

Formula: Relative Speed (Opposite) = S₁ + S₂ | Distance = Speed × Time

⇒ Relative Speed = (32 + 28) × 5/18 = 60 × 5/18 = 50/3 m/s

⇒ L_A + L_B = (50/3) × 33 = 550 m

⇒ L_A + 1.5 L_A = 550 ⇒ 2.5 L_A = 550 ⇒ L_A = 220 m

⇒ Length of Train B (L_B) = 1.5 × 220 = 330 m

⇒ Speed of Train B in m/s = 28 × 5/18 = 70/9 m/s

⇒ Total distance (Train B + Bridge) = (70/9) × 54 = 420 m

⇒ Length of Bridge = 420 − 330 = 90 m

∴ The correct answer is 90 m.

Additional Information

Relative Speed Concept

When two objects move in opposite directions, their relative speed is S₁ + S₂. In the same direction, it is |S₁ − S₂|.

Crossing Objects

When a train crosses a bridge or another train, 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 logic followed here is:

Thus, 'KRM' will be the next in the series.

Hence, the correct answer is "Option 3".

Given: 

Mr. Y starts from Point B and drives 4 km towards the south.

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

He then takes a left turn and drives 9 km. He takes a final left turn, drives 11 km and stops at Point A.

Thus, he drive 16 km towards the west  in order to reach Point B again.

Hence, the correct answer is "Option 4".

Shortcut Trick

If x + 1/x = k, then x³ + 1/x³ = k³ − 3k.

Given that k = 15.

Substituting the value: 15³ − 3 × 15

Value = 3375 − 45 = 3330.

∴ The correct answer is 3330.

Alternate Method

Given:

x + 1/x = 15

Formula Used:

Using the Algebraic Identity: (a + b)³ = a³ + b³ + 3ab(a + b)

Calculation:

⇒ Cube both sides of the given equation:

⇒ (x + 1/x)³ = 15³

⇒ x³ + (1/x)³ + 3 × x × (1/x) × (x + 1/x) = 3375

⇒ x³ + 1/x³ + 3(15) = 3375

⇒ x³ + 1/x³ + 45 = 3375

⇒ x³ + 1/x³ = 3375 − 45

⇒ x³ + 1/x³ = 3330

∴ The correct answer is 3330.

Additional Information

Square Identity

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

Negative Sign Identity

If x − 1/x = k, then the value of x³ − 1/x³ = k³ + 3k.

Higher Powers

To find x⁴ + 1/x⁴, first find x² + 1/x² = m, then use the formula m² − 2.