Shortcut Trick

Parallel lines ⇒ alternate interior angles equal

⇒ ∠MND = ∠AMN

⇒ Given ∠MND = 47°

⇒ ∠AMN = 47°

∴ Answer = 47°

Alternate Method

Given:

AB ∥ CD

PQ is a transversal

∠MND = 47°

Formula:

Alternate interior angles are equal when lines are parallel

Calculation:

⇒ ∠MND and ∠AMN are alternate interior angles

⇒ ∠AMN = ∠MND

⇒ ∠AMN = 47°

∴ Final Answer = 47°

Additional Information

Alternate Interior Angles: Equal when a transversal cuts parallel lines

Corresponding Angles: Same relative position ⇒ equal

Co-interior Angles: Sum = 180° on same side

Key Tip: Always locate angle position before applying rule

Shortcut Trick

Consecutive numbers ⇒ average = (first + last) ÷ 2

⇒ = (1 + 60) ÷ 2 = 61 ÷ 2

⇒ = 30.5

∴ Answer = 30.5

Alternate Method

Given:

Natural numbers from 1 to 60

Formula:

Average = (Sum of numbers) ÷ Total numbers

Sum of first n natural numbers = n(n + 1) ÷ 2

Calculation:

⇒ Sum = 60 × 61 ÷ 2 = 1830

⇒ Total numbers = 60

⇒ Average = 1830 ÷ 60 = 30.5

∴ Final Answer = 30.5

Additional Information

Consecutive Numbers: Average = (First + Last) ÷ 2

Sum Formula: n(n+1) ÷ 2

Key Insight: Middle value represents average

Tip: Use shortcut instead of full summation

The correct answer is James Princep.

Key Points

• James Princep was an English scholar, orientalist, and an officer in the Calcutta Mint of the East India Company.
• In the year 1837, he successfully deciphered the Brahmi and Kharosthi scripts, which were used in the earliest inscriptions and coins of ancient India.
• Through his research, he identified that the inscriptions referring to a king named Devanampiya Piyadasi (meaning "Beloved of the Gods" and "of Pleasant Gaze") were actually referring to the Mauryan Emperor Ashoka.
• This breakthrough allowed historians to correlate archaeological evidence with Buddhist chronicles like the Dipavamsa and Mahavamsa, establishing Ashoka as one of the greatest rulers in Indian history. Hence, the statement regarding James Princep is correct.
• The identification of these inscriptions provided a chronological framework for ancient Indian history, which was previously based largely on legends and myths.

Additional Information

• R C Majumdar:
• Ramesh Chandra Majumdar (1888–1980) was a prominent Indian historian known for his monumental work "The History and Culture of the Indian People".
• While he contributed extensively to the study of ancient India and Bengal, he was not the one who deciphered the Brahmi script.
• Romila Thapar:
• Romila Thapar is a world-renowned Indian historian whose primary focus is Ancient India.
• She is well-known for her book "Ashoka and the Decline of the Mauryas", published in 1961, which offers a socio-economic analysis of the Mauryan Empire.
• Her work interprets the Dhamma of Ashoka as a civic code rather than a religious doctrine.
• Susan Bayly:
• Susan Bayly is a professor of Historical Anthropology at the University of Cambridge.
• Her research focuses on caste, society, and colonialism in South Asia and Southeast Asia, particularly Vietnam.
• She is the author of "Caste, Society and Politics in India from the Eighteenth Century to the Modern Age".
• Brahmi Script:
• It is the ancestor of almost all modern Indian scripts and was used by Ashoka for his Rock Edicts and Pillar Edicts.
• The script was primarily written from left to right, and its decipherment opened the door to understanding Magadhi Prakrit.

Important Points

• Epigraphy: The study of inscriptions is known as epigraphy. The decipherment by James Princep is considered the most significant milestone in Indian epigraphy.
• Maski Inscription: Although James Princep linked Piyadasi to Ashoka, the final confirmation came in 1915 when an inscription was found at Maski in Karnataka that explicitly mentioned the name "Ashoka" alongside "Devanampiya".
• Asiatic Society: James Princep served as the founding editor of the Journal of the Asiatic Society of Bengal, which published his findings on Ashokan pillars located in Delhi and Allahabad.
• Kharosthi Script: Unlike Brahmi, Kharosthi was written from right to left and was used primarily in the Northwest regions of the Indian subcontinent, such as Gandhara (modern-day Pakistan and Afghanistan).

The correct answer is Criticized Hindu practices regarding widows.

Key Points

• Yamuna Paryatam, published in 1857, is widely regarded as the first novel in the Marathi language. It was written by Baba Padmanji, a prominent social reformer and convert to Christianity.
• The central theme of the novel is the plight of widows in contemporary Hindu society. It vividly describes the physical and mental suffering they endured, including the practice of shaving heads (tonsure) and social boycotts. Hence, the statement that it criticized Hindu practices regarding widows is correct.
• The narrative follows the journey of a young woman named Yamuna and her husband Vinayak as they travel and witness the miserable conditions of widows across various places. This journey serves as a medium for social commentary.
• Statement 1: The novel did not focus on adventure stories. While it involves travel, the primary objective was social reform rather than escapism or thrill-seeking adventure. Hence, this statement is incorrect.
• Statement 2: It did not focus on the political life of the Yamuna region. The title "Yamuna Paryatam" refers to the protagonist's name, Yamuna, and her "Paryatam" (travels), rather than the geography of the Yamuna River or political administration. Hence, this statement is incorrect.
• Statement 4: The novel did not praise Hindu customs; instead, it was a sharp critique of orthodox Brahminical traditions that oppressed women and denied them the right to remarry. Hence, this statement is incorrect.

Additional Information

• Baba Padmanji (1831-1906): He was a significant figure in the 19^th-century social reform movement in Maharashtra. He was born into a Kasari family but later embraced Christianity in 1854. His writings often reflected the interplay between Christian ethics and the need for Hindu social reform.
• Advocacy for Remarriage: One of the core messages of Yamuna Paryatam was the promotion of widow remarriage. At the end of the novel, the protagonist Yamuna, after becoming a widow herself, chooses to remarry and convert to Christianity, symbolizing a break from oppressive traditional bonds.
• Literary Significance: Before this work, Marathi literature largely consisted of poetry and religious texts. Yamuna Paryatam introduced the prose narrative form to the masses, paving the way for the development of the modern Marathi novel.
• Historical Context: The novel was written during a period of intense intellectual ferment in India, specifically in Bombay (Mumbai) and Poona (Pune), where reformers like Jyotirao Phule were also beginning to challenge caste and gender hierarchies.
• Impact on Women's Rights: By highlighting the domestic violence and emotional trauma faced by women, the book played a crucial role in bringing women's issues to the forefront of the public discourse in Western India.

Important Points

• Social Realism: The book is considered an early example of social realism in Indian literature. It did not shy away from depicting the harsh realities of the caste system and patriarchy.
• Language and Style: Baba Padmanji used a simple and direct style of Marathi, making the book accessible to the common person rather than just the learned Shastris or Pandits.
• Year of Publication: 1857 is a landmark year in Indian history due to the Great Revolt, and the publication of this novel in the same year highlights that social revolutions were occurring alongside political upheavals.
• Religious Influence: The novel also acted as a piece of Christian apologetics, suggesting that the liberation of women could be found through the adoption of Christian values, which was a common theme among 19^th-century converts.

The logic followed here is:

For, AOE → BQH

For, OST → PUW

Now, checking all options:

Option 1: DAF → FCH

Option 2: ADP → BGQ

Option 3: SHF → TJI

Option 4: LAJ → MDN

Hence, the correct answer is Option 3.

The logic followed here is:

So, 'ZYZ 41' will replace the question mark in the given series.

Hence, the correct answer is "Option 2".

The correct answer is Centralised bureaucracy guided by Arthashastra.

Key Points

• The Mauryan Empire, founded by Chandragupta Maurya in approximately 322 BCE, was characterized by a highly sophisticated and centralised bureaucracy. This system ensured that the central government had direct control over various aspects of the state, from revenue to security. Hence, statement 1 is correct.
• The administrative framework was heavily influenced by the Arthashastra, a classic treatise on statecraft, economic policy, and military strategy authored by Chanakya (also known as Kautilya or Vishnugupta), who was the Prime Minister and mentor to Chandragupta Maurya.
• The empire was divided into provinces, usually headed by a Kumara (prince) or a member of the royal family. Unlike later medieval systems, these provincial governors were appointed officials and not hereditary rulers, ensuring the King's authority remained absolute. Hence, statement 2 is incorrect.
• The Mauryan economy was largely state-controlled, and land revenue was the primary source of income. The feudal land grant system, where land was given to intermediaries in exchange for military service, was a feature that developed much later during the Gupta period and the early medieval era. Hence, statement 3 is incorrect.
• Revenue collection was a strictly secular and administrative function carried out by state officials like the Samaharta (Chief Collector). Religious institutions did not have the authority to collect state taxes; instead, they were often recipients of state patronage. Hence, statement 4 is incorrect.

Additional Information

• Structure of the Central Government:
• The King was the fountainhead of all authority, assisted by a council of ministers called the Mantriparishad.
• The bureaucracy was composed of a hierarchy of officials known as Amatyas (civil servants) and Adhyakshas (superintendents of various departments).
• There were nearly 27-30 departments managing diverse sectors like agriculture (Sita-adhyaksha), commerce (Panyadhyaksha), and weights and measures (Pautavadhyaksha).
• Municipal Administration:
• The Greek ambassador Megasthenes, in his work Indica, provides a detailed account of the administration of the capital city, Pataliputra.
• The city was managed by six committees of five members each, looking after industries, foreigners, births and deaths, trade, manufactured goods, and the collection of the tenth of the prices as tax.
• The Espionage System:
• A unique feature of the Mauryan state was its extensive network of spies, referred to as Gudha Purushas.
• Spies were categorized into Sanstha (stationary) and Sanchari (wandering), reporting directly to the King about the loyalty of officials and the pulse of the public.
• Military Strength:
• The Mauryan army was massive, consisting of infantry, cavalry, chariots, and elephants. Pliny and Megasthenes mention that Chandragupta Maurya maintained an army of 6,00,000 infantry, 30,000 cavalry, and 9,000 elephants.
• The military was administered by a board of 30 members divided into six committees of five members each.

Important Points

• Saptanga Theory: Kautilya described the state as having seven limbs (Saptanga): Swami (The King), Amatya (The Ministers), Janapada (The Territory/People), Durga (The Fortification), Kosha (The Treasury), Danda (The Army), and Mitra (The Ally).
• Diplomatic Relations: Chandragupta Maurya defeated the Greek general Seleucus Nicator in 305 BCE, leading to a treaty where the Mauryan Empire gained territories like Arachosia (Kandahar) and Gedrosia (Baluchistan).
• Public Welfare: Despite being highly centralized, the state focused on public works, including the construction of the Royal Road (precursor to the Grand Trunk Road) and irrigation projects like the Sudarshana Lake in Junagadh, Gujarat.

Shortcut Trick

⇒ Sum of digits = 4+4+5+A+0+2+0+8 = 23 + A

⇒ For divisibility by 3 ⇒ (23 + A) divisible by 3

⇒ 23 mod 3 = 2 ⇒ Need A mod 3 = 1

⇒ Possible A: 1, 4, 7 ⇒ max = 7

∴ Answer = 7

Alternate Method

Given:

Number = 445A0208

Formula Used:

A number is divisible by 3 if sum of digits is divisible by 3

Calculation:

⇒ Sum of known digits = 4 + 4 + 5 + 0 + 2 + 0 + 8 = 23

⇒ Total sum = 23 + A

⇒ Required: (23 + A) divisible by 3

⇒ Check largest A (0 to 9):

⇒ A = 9 ⇒ 32 (not divisible)

⇒ A = 8 ⇒ 31 (not divisible)

⇒ A = 7 ⇒ 30 (divisible)

∴ The correct answer is 7.

Additional Information

Divisibility Rule (3): Sum of digits divisible by 3

Digit Range: A can be 0 to 9

Modulo Trick: Work with remainders

Exam Tip: Check largest valid digit

The correct answer is Navigates to the next tab on the right.

Key Points

• In modern web browsers such as Google Chrome, Mozilla Firefox, Microsoft Edge, and Safari, the shortcut Ctrl + Tab is used for tab navigation.
• When a user has multiple tabs open, pressing Ctrl + Tab moves the focus to the next tab on the right side of the current active tab. Hence, the statement regarding navigating to the next tab on the right is correct.
• The action of launching a new tab is typically performed using the shortcut Ctrl + T in Windows/Linux. Hence, the statement regarding launching a new tab is incorrect.
• The action of removing or closing the selected tab is performed using Ctrl + W or Ctrl + F4. Hence, the statement regarding removing the selected tab is incorrect.
• To navigate to the previous tab on the left, the user must press Ctrl + Shift + Tab. Hence, the statement regarding navigating to the previous tab on the left is incorrect.
• This shortcut allows for efficient multitasking without the need for a mouse or trackpad, significantly increasing productivity for power users.

Additional Information

• Browser Tab Management:
• Ctrl + Shift + T: This is an essential command used to reopen the last closed tab. It is extremely useful if a tab was closed by accident.
• Ctrl + 1 through 8: Pressing Ctrl along with a numerical value from 1 to 8 will switch the focus to that specific tab number (counting from the left).
• Ctrl + 9: This shortcut immediately switches to the last tab opened in the window, regardless of how many tabs are active.
• Window and Navigation Shortcuts:
• Ctrl + N: Opens a new browser window.
• Ctrl + Shift + N: In Google Chrome, this opens a new Incognito window for private browsing. In Firefox, the equivalent is Ctrl + Shift + P for a Private Window.
• Ctrl + L or Alt + D: Moves the cursor focus directly to the Address Bar (Omnibox), allowing the user to type a new URL or search query immediately.
• Historical Context:
• Tabbed browsing was popularized in the early 2000s by browsers like Opera and Firefox, moving away from the single-window model of early Internet Explorer versions. The Ctrl + Tab convention was adopted to mirror the Alt + Tab function used by Windows to switch between applications.

Important Points

• Operating System Differences:
• On macOS, the Command (⌘) key is used instead of the Control (Ctrl) key for most functions. For example, Command + Option + Right Arrow or Control + Tab can be used to switch tabs in Safari on Mac.
• In some browsers like Firefox, the behavior of Ctrl + Tab can be customized in the settings to cycle through tabs in recently used order rather than purely sequential left-to-right order.
• Efficiency and Accessibility:
• Keyboard shortcuts are a vital part of web accessibility guidelines, ensuring that users with motor impairments who cannot use a mouse can still navigate the web effectively using a keyboard.
• In 2024, most browsers also support Vertical Tabs (notably Microsoft Edge), but the Ctrl + Tab shortcut remains the universal standard for cycling through the list.

Shortcut Trick

⇒ Final = 5P ⇒ Interest = 4P

⇒ SI = P × r × t / 100 ⇒ 4P = P × r × 12 / 100

⇒ r = (4 × 100) / 12 = 33.33%

∴ Answer = 33.33%

Alternate Method

Given:

Amount becomes 5 times in 12 years

Formula Used:

SI = (P × r × t) / 100

Amount = P + SI

Calculation:

⇒ Let principal = P

⇒ Amount = 5P

⇒ SI = 5P − P = 4P

⇒ Using SI formula:

⇒ 4P = (P × r × 12) / 100

⇒ Cancel P:

⇒ 4 = (r × 12) / 100

⇒ r = (4 × 100) / 12

⇒ r = 33.33%

∴ The correct answer is 33.33%.

Additional Information

Simple Interest: SI = (P × r × t)/100

Amount Relation: A = P + SI

Shortcut: Multiply factor − 1 gives interest multiple

Exam Tip: Cancel P early

Shortcut Trick

Check endpoints (max function minimum occurs at edges)

p = 0 ⇒ max{4, −4} = 4

p = 1 ⇒ max{3, −3} = 3

⇒ Minimum = 3

∴ Answer = 3

Alternate Method

Given:

Expression = max {p² − 2p + 4, −p² + 2p − 4}

Range: 0 ≤ p ≤ 1

Formula:

For minimum of max, compare both expressions

Calculation:

⇒ Let f = p² − 2p + 4

⇒ g = −p² + 2p − 4

⇒ Note: g = −f

⇒ So expression = max(f, −f) = |f|

⇒ f = (p − 1)² + 3 ≥ 3

⇒ Minimum at p = 1

⇒ Value = 3

∴ Final Answer = 3

Additional Information

Max Function: max(a, b) picks larger value

Symmetry: max(f, −f) = |f|

Quadratic Min: (x − a)² ≥ 0

Tip: Convert to modulus for speed

The logic followed here is:

Logic: Second number = (First number × 3) + (Third number − 2)

For, (40, 122, 4)

⇒ 40 × 3 = 120

⇒ 4 − 2 = 2

⇒ 120 + 2 = 122 

For, (30, 101, 13)

⇒ 30 × 3 = 90

⇒ 13 − 2 = 11

⇒ 90 + 11 = 101 

Now, checking the options using the same pattern:

Option 1) (2, 26, 17)

⇒ 2 × 3 = 6

⇒ 17 − 2 = 15

⇒ 6 + 15 = 21 ≠ 26 

Option 2) (10, 51, 18)

⇒ 10 × 3 = 30

⇒ 18 − 2 = 16

⇒ 30 + 16 = 46 ≠ 51 

Option 3) (37, 120, 11)

⇒ 37 × 3 = 111

⇒ 11 − 2 = 9

⇒ 111 + 9 = 120 

Option 4) (10, 50, 17)

⇒ 10 × 3 = 30

⇒ 17 − 2 = 15

⇒ 30 + 15 = 45 ≠ 50 

Hence, the correct answer is Option 3.

The correct answer is Puducherry.

Key Points

• Puducherry is one of the few Union Territories in India that possesses its own Legislative Assembly and a Council of Ministers headed by a Chief Minister.
• The 14^th Constitutional Amendment Act, 1962, led to the creation of Puducherry as a Union Territory and provided for the establishment of a legislature and council of ministers.
• According to Article 239A of the Constitution of India, Parliament has the power to create a local legislature or a Council of Ministers (or both) for certain Union Territories like Puducherry.
• The administrative structure of Puducherry is governed by The Government of Union Territories Act, 1963, which outlines the functions and powers of the Legislative Assembly.
• Other Union Territories like Dadra and Nagar Haveli, Daman and Diu, and Andaman and Nicobar Islands do not have their own Legislative Assemblies and are administered directly by the President through an Administrator.

Additional Information

• Delhi (National Capital Territory): It was provided with a Legislative Assembly and a Council of Ministers through the 69^th Constitutional Amendment Act, 1991, which inserted Article 239AA into the Constitution.
• Jammu and Kashmir: Under the Jammu and Kashmir Reorganisation Act, 2019, the erstwhile state was bifurcated into two Union Territories; Jammu and Kashmir was designed to have a Legislative Assembly, while Ladakh was created without one.
• Administration of UTs: Part VIII of the Constitution of India (Articles 239 to 241) deals with the administration of Union Territories. Every Union Territory is administered by the President acting through an Administrator or Lieutenant Governor appointed by him.
• Dadra and Nagar Haveli and Daman and Diu: These were merged into a single Union Territory on January 26, 2020, through the Dadra and Nagar Haveli and Daman and Diu (Merger of Union Territories) Act, 2019, to improve administrative efficiency.
• Andaman and Nicobar Islands: Established as a Union Territory in 1956, it is located in the Bay of Bengal and is administered by a Lieutenant Governor without a local legislature.

Important Points

• The Lieutenant Governor (LG) in Union Territories with legislatures (like Puducherry and Delhi) has specific discretionary powers that differ from the Governors of regular States.
• In Puducherry, the Legislative Assembly can make laws on subjects in the State List (List II) and the Concurrent List (List III) of the Seventh Schedule, except where it conflicts with Parliamentary laws.
• The total number of seats in the Puducherry Legislative Assembly is 33, which includes 30 elected members and 3 members nominated by the Central Government.
• Unlike States, the Union Territories are considered federal units that are under the direct control and supervision of the Union Government of India.

The logic followed here is:

Logic: Third number = (First number × Second number) − 5

For, (15, 7, 100)

⇒ 15 × 7 = 105

⇒ 105 − 5 = 100 

For, (25, 8, 195)

⇒ 25 × 8 = 200

⇒ 200 − 5 = 195 

Now, checking the options using the same pattern:

Option 1) (26, 4, 104)

⇒ 26 × 4 = 104

⇒ 104 − 5 = 99 ≠ 104 

Option 2) (18, 10, 185)

⇒ 18 × 10 = 180

⇒ 180 − 5 = 175 ≠ 185 

Option 3) (23, 6, 133)

⇒ 23 × 6 = 138

⇒ 138 − 5 = 133 

Option 4) (21, 11, 236)

⇒ 21 × 11 = 231

⇒ 231 − 5 = 226 ≠ 236 

Hence, the correct answer is Option 3.

The logic followed here is:

Given:

GLOW → 4628

WEAR → 3574

Thus, the code for W is 4.

Hence, the correct answer is Option 3.

The logic followed here is:

Logic: Each letter shifts by +1, +2, +3 respectively.

For, KPN → ?

⇒ K +1 → L

⇒ P +2 → R

⇒ N +3 → Q

⇒ KPN → LRQ

Now, apply reverse to find # from RWU:

⇒ R −1 → Q

⇒ W −2 → U

⇒ U −3 → R

⇒ # = QUR

Now, check options for matching pattern:

Option 1) SXV → RWU (−1, −2, −3) 

and JOM → KPN (+1, +2, +3) 

Here, pattern matches perfectly.

Hence, the correct answer is Option 1.

The correct answer is India entered the top 100 for the first time.

Key Points

• In the year 2025, India reached a significant landmark in its journey toward global sustainability by entering the top 100 countries in the UN Sustainable Development Goals (SDGs) rankings for the first time. This reflects a consistent improvement from its 109^th position recorded in 2024.
• The Sustainable Development Report, published annually by the Sustainable Development Solutions Network (SDSN), evaluates the progress of 193 UN Member States in achieving the 17 SDGs.
• The milestone was achieved due to India's proactive implementation of large-scale social welfare schemes that align with the 2030 Agenda. The improvement in the index score indicates that India has made substantial strides in reconciling economic growth with environmental and social objectives.
• Key sectors contributing to this rise include SDG 1 (No Poverty), SDG 6 (Clean Water and Sanitation), and SDG 11 (Sustainable Cities and Communities). The targeted delivery of services through digital public infrastructure has been a major catalyst in this achievement.
• While India achieved all SDGs is an incorrect statement as the target year is 2030 and no country has fully achieved them yet, India's entry into the top 100 marks a shift from being a "performer" to a "front runner" in various global categories.

Additional Information

• The 17 Sustainable Development Goals (SDGs):
• Adopted by the United Nations in 2015, these goals consist of 169 targets intended to be reached by 2030. They cover a wide spectrum of issues including poverty, hunger, health, education, gender equality, and climate action.
• NITI Aayog’s Role:
• In India, the NITI Aayog is the primary body responsible for the SDG India Index, which monitors the progress of States and Union Territories. It categorizes them into four groups based on their composite score: Aspirant (0–49), Performer (50–64), Front Runner (65–99), and Achiever (100).
• Global Rankings and SDSN:
• The Sustainable Development Solutions Network (SDSN) has been operating since 2012 under the auspices of the UN Secretary-General. The global ranking is influenced by the SDG Index Score, where Finland, Sweden, and Denmark have traditionally held the top spots.
• India's Major Interventions:
• Schemes such as the Jal Jeevan Mission (aiming for 100% tap water connectivity), Pradhan Mantri Awas Yojana (housing for all), and the Ayushman Bharat (world's largest health insurance scheme) have been instrumental in improving India's global standing.

Important Points

• Historical Context: In 2023 and 2024, India hovered around the 112^th to 109^th rank. The jump to the top 100 in 2025 signifies an accelerated pace of development and better data reporting mechanisms on international platforms.
• Challenges in Specific Goals: Despite the overall rank improvement, India still faces challenges in SDG 2 (Zero Hunger) and SDG 5 (Gender Equality). Addressing stunting and wasting among children remains a priority for the Ministry of Women and Child Development.
• SDG 13 (Climate Action): India is one of the few G20 nations on track to meet its Nationally Determined Contributions (NDCs) under the Paris Agreement, which significantly boosts its SDG Index performance compared to many developed countries.
• Data and Monitoring: The Ministry of Statistics and Programme Implementation (MoSPI) developed the National Indicator Framework (NIF), which consists of over 300 indicators to track SDG progress specifically within the Indian socio-economic context.

The logic followed here is:

Given:

Kinshuk starts from Point D and walks 5 km South.

She turns left → 9 km East.

She turns left → 5 km North.

She turns right → 2 km East.

So, Kinshuk is 11 km East from Point D.

Hence, the correct answer is Option 2.

The logic followed here is:

thus, "37" will replace the question mark in the given series.

Hence, the correct option is "Option 4"

Shortcut Trick

Assume CP = 100

⇒ MP = 250 (150% ↑)

⇒ Required SP = 160 (60% profit)

⇒ Discount = 250 − 160 = 90

⇒ Discount% = 90/250 × 100 = 36%

∴ Answer = 36%

Alternate Method

Given:

Marked price = 150% above CP

Profit = 60%

Formula:

MP = CP × (1 + 150/100)

SP = CP × (1 + 60/100)

Discount% = (MP − SP)/MP × 100

Calculation:

⇒ Let CP = 100

⇒ MP = 100 × 2.5 = 250

⇒ SP = 100 × 1.6 = 160

⇒ Discount = 250 − 160 = 90

⇒ Discount% = (90/250) × 100 = 36%

∴ Final Answer = 36%

Additional Information

Marked Price: MP = CP × (1 + markup%)

Selling Price: SP = CP × (1 + profit%)

Discount: MP − SP

Tip: Assume CP = 100 for faster solving

The correct answer is Drain of Wealth Theory.

Key Points

• Dadabhai Naoroji, popularly known as the "Grand Old Man of India", propounded the Drain of Wealth Theory in his seminal book "Poverty and Un-British Rule in India" published in 1901.
• The theory highlights the constant flow of wealth from India to England, for which India received no adequate economic or material return. This systematic drain was identified as the primary cause of poverty in India during the British colonial period.
• Dadabhai Naoroji was the first Indian to attempt the estimation of National Income. In 1867-68, he calculated the per capita income of Indians to be Rs. 20 per year, showcasing the extreme economic hardship under British administration.
• The Drain of Wealth was manifested through various channels such as Home Charges (expenditure incurred in England by the Secretary of State on behalf of India), interest on foreign debt, and salaries/pensions of British officials.
• His work provided a scientific and statistical foundation for economic nationalism in India, challenging the British claim that their rule was beneficial for the Indian economy.

Additional Information

• Subsidiary Alliance Theory:
• This was a non-intervention policy used by Lord Wellesley, the Governor-General of India from 1798 to 1805.
• Under this system, the ruler of an allying Indian State was compelled to accept the permanent stationing of a British force within his territory and pay a subsidy for its maintenance.
• The Nizam of Hyderabad was the first to enter into a Subsidiary Alliance with the British in 1798.
• Doctrine of Lapse Theory:
• This was an annexation policy followed by Lord Dalhousie, who served as the Governor-General from 1848 to 1856.
• According to this doctrine, any Princely State under the direct or indirect influence of the British would be annexed if the ruler died without a natural heir (adopted heirs were not recognized for the purpose of succession to the throne).
• Satara (1848), Sambalpur (1849), Jhansi (1853), and Nagpur (1854) were prominent states annexed under this policy.
• Two Nation Theory:
• This theory proposed that Hindus and Muslims were two distinct nations with different cultures, religions, and customs, and therefore could not live together in one country.
• While its roots are often traced back to Sir Syed Ahmed Khan, it was later championed by Muhammad Ali Jinnah and the Muslim League, leading to the Partition of India in 1947.

Important Points

• Dadabhai Naoroji was the first Indian to be elected as a Member of Parliament (MP) in the British House of Commons, representing the Finsbury Central constituency from 1892 to 1895.
• He played a crucial role in the formation of the Indian National Congress (INC) and served as its President three times: in 1886 (Calcutta), 1893 (Lahore), and 1906 (Calcutta).
• During the 1906 session of the INC, he was the leader who first used the word "Swaraj" (Self-rule) from the Congress platform as the ultimate goal for the Indian people.
• He founded the London Indian Society in 1865 and the East India Association in 1866 to put forward Indian viewpoints across to the British public and Parliament.

Given number: 5714623

Logic:

Add 1 to each odd digit

Subtract 2 from each even digit

Original number: 5 7 1 4 6 2 3

New number: 6 8 2 2 4 0 4

Now, second from left = 8

Second from right = 0

Sum = 8 + 0 = 8

Hence, the correct answer is Option 2.

The correct answer is Birth Anniversary of Mahatma Gandhi.

Key Points

• Prime Minister Narendra Modi launched the Dharti Aaba Janjatiya Gram Utkarsh Abhiyan (DAJGUA) on 2^nd October 2024. This date coincides with the 155^th Birth Anniversary of Mahatma Gandhi.
• The mega scheme was officially unveiled during a public program held in Hazaribagh, Jharkhand. The name "Dharti Aaba" is a tribute to the legendary tribal freedom fighter Birsa Munda, who is revered as the "Father of the Earth."
• The total financial outlay for this ambitious mission is Rs. 79,156 crore. Out of this, the Central Government will contribute Rs. 56,333 crore, while the State Governments will provide Rs. 22,823 crore.
• The mission is designed to transform the lives of tribal communities by covering 63,843 villages across 549 districts and 2,740 blocks in 30 States and Union Territories.
• It aims to benefit more than 5 crore tribal people, ensuring that the fruits of development reach the most remote Janjatiya areas of the country.

Additional Information

• Socio-Economic Goals: The DAJGUA focuses on 17 Central Ministries implementing 25 interventions to bridge gaps in social infrastructure, health, education, and livelihood.
• Infrastructure Development: Under the scheme, the government aims to provide Pucca houses to eligible households and ensure all-weather road connectivity to tribal habitations.
• Sustainable Livelihood: The mission promotes Forest Rights Act (FRA) beneficiary empowerment and provides vocational training and skill development to tribal youth to enhance their employment opportunities.
• Health and Nutrition: It includes provisions for improving maternal and child health, reducing anemia, and strengthening mobile medical units in hilly and difficult terrains.
• Educational Support: The scheme emphasizes the construction of Ashram Schools and hostels to increase the literacy rate and reduce dropout rates among tribal students.

Important Points

• Saturation Approach: Much like the PM-JANMAN (Pradhan Mantri Janjati Adivasi Nyaya Maha Abhiyan), this scheme follows a saturation model to ensure 100% coverage of government services in the targeted tribal villages.
• Energy and Connectivity: The mission includes the electrification of un-electrified households and the installation of mobile towers to provide 4G/5G digital connectivity in remote tribal regions.
• Water and Sanitation: Under the Jal Jeevan Mission, the abhiyan ensures piped water supply and individual household latrines for every tribal family.
• Tribal Culture: The launch in 2024 also serves as a precursor to the Janjatiya Gaurav Divas (celebrated on November 15), highlighting the government's commitment to preserving tribal heritage and culture.

Shortcut Trick

Highest frequency = 40 ⇒ Modal class = 65–75

l = 65, h = 10, f₁ = 40, f₀ = 30, f₂ = 34

Mode = l + [(f₁ − f₀)/(2f₁ − f₀ − f₂)] × h

= 65 + [(40−30)/(80−30−34)] × 10

= 65 + (10/16) × 10

= 65 + 6.25 = 71.25

∴ Answer = 71.25

Alternate Method

Given Table:

Step 1: Identify modal class

Highest frequency = 40 ⇒ Class = 65–75

Step 2: Values

l = 65

h = 10

f₁ = 40 (modal)

f₀ = 30 (previous)

f₂ = 34 (next)

Step 3: Formula

Mode = l + [(f₁ − f₀)/(2f₁ − f₀ − f₂)] × h

Step 4: Calculation

= 65 + [(40 − 30)/(2×40 − 30 − 34)] × 10

= 65 + (10/16) × 10

= 65 + 6.25

= 71.25

∴ Final Answer = 71.25

Additional Information

Modal Class: Class with highest frequency

Formula: Mode = l + [(f₁−f₀)/(2f₁−f₀−f₂)] × h

Tip: Always pick correct neighboring frequencies

Common Mistake: Wrong class selection

The logic followed here is:

For, GJHA → JNLD

For, KMEL → NQIO

Now, applying the same logic to NROT:

So, NROT → QVSW

Hence, the correct answer is Option 4.

Given Statements:

All kites are rabbits.

No kite is an eagle.

All eagles are pigs.

The least possible Venn diagram for the given statements is:

Conclusions:

I. No pig is a rabbit

No direct relation between pigs and rabbits is given

They may or may not overlap

⇒ False

II. Some pigs are kites

No kite is an eagle and all eagles are pigs

No direct relation between kites and pigs

⇒ False

So, neither conclusion I nor II follows.

Hence, the correct answer is Option 4.

The correct answer is Avalanche.

Key Points

• An Avalanche is a natural disaster characterized by the rapid mass movement of snow, ice, soil, and rock down a mountain slope. It occurs when the shear stress on the snowpack exceeds its shear strength.
• These events are most common in high-altitude mountainous regions such as the Himalayas in India, the Alps in Europe, and the Rockies in North America.
• The primary triggers for an Avalanche include heavy snowfall, wind-loading, rapid temperature rise, and seismic activity like earthquakes. Human activities, such as skiing, snowmobiling, or construction in hilly areas, can also trigger these slides.
• An Avalanche can reach speeds of up to 200 kilometers per hour (approx. 124 miles per hour), making it one of the most dangerous geophysical hazards for climbers, skiers, and mountain residents.
• The Avalanche involving snow and ice is distinct from other mass movements because it specifically relies on the thermal and structural properties of the snowpack layers.

Additional Information

• Types of Avalanches:
• Slab Avalanche: This is the most dangerous type, where a cohesive layer of snow breaks off and slides down. It is often triggered by a mechanical failure in a weak layer of the snowpack.
• Powder Snow Avalanche: These consist of a low-density cloud of suspended snow that behaves like a fluid, often moving at extreme velocities.
• Wet Snow Avalanche: These occur due to melting during the spring season or after rain-on-snow events, moving more slowly but with immense force.
• Prevention and Mitigation:
• In countries like Switzerland and Canada, snow fences and deflection dams are built to protect highways and railways.
• Controlled explosions are used by mountain safety teams to trigger small, harmless slides before the snow accumulation becomes critical.
• Afforestation (planting trees) on slopes acts as a natural barrier against small to medium-sized Avalanches.
• Impact and Data:
• Every year, hundreds of lives are lost globally due to Avalanches. In 2012, the Gayari Sector avalanche in Siachen resulted in the death of over 130 soldiers.
• The snow-ice mix in an avalanche can become as hard as concrete once it stops moving, making rescue operations extremely difficult.

Important Points

• Cyclone: This is a meteorological phenomenon characterized by low atmospheric pressure and strong winds rotating inward. It typically forms over warm ocean waters. Hence, this option is incorrect as it does not involve the downward movement of snow on mountains.
• Tsunami: This refers to a series of giant ocean waves caused by underwater disturbances such as tectonic shifts or submarine volcanic eruptions. It affects coastal regions. Hence, this option is incorrect.
• Landslide: A Landslide is a broad term for the downward movement of rock, debris, or earth. While similar to an avalanche, a landslide typically refers to soil-based movement, whereas the question specifically highlights snow and ice. Hence, while related to mass movement, it is not the most specific answer for snow.
• Geographic Distribution: In India, the Snow and Avalanche Study Establishment (SASE), a laboratory of DRDO, is responsible for monitoring and forecasting avalanches in the Himalayan region.

Given Statements:

All coppers are irons.

All irons are silvers.

All silvers are golds.

The least possible Venn diagram for the given statements is:

Conclusions:

I. Some golds are irons

Since all irons are inside golds, definitely some golds are irons

⇒ True

II. All silvers are coppers

Silvers are a bigger group and coppers are inside irons

So silvers cannot be inside coppers

⇒ False

So, only conclusion (I) follows.

Hence, the correct answer is Option 4.

Shortcut Trick

Observe: 4.23 = 4 + 0.23 and 0.69 = 3 × 0.23, 12.69 = 3 × (4.23)

Expression matches: (a − b)³ = a³ − 3a²b + 3ab² − b³

⇒ Numerator = (4.23 − 0.23)³ = 4³ = 64

Denominator = 0.4 × 0.4 × 4 = 0.64

⇒ Value = 64 ÷ 0.64 = 100

∴ Answer = 100

Alternate Method

Given:

[(4.23)³ − 0.69(4.23)² + 12.69(0.23)² − (0.23)³] / (0.4 × 0.4 × 4)

Step 1: Identify pattern

0.69 = 3 × 0.23

12.69 = 3 × 4.23

⇒ Expression = a³ − 3a²b + 3ab² − b³

⇒ = (a − b)³

Step 2: Substitute

a = 4.23, b = 0.23

⇒ Numerator = (4.23 − 0.23)³ = 4³ = 64

Step 3: Denominator

= 0.4 × 0.4 × 4 = 0.64

Step 4: Final

= 64 ÷ 0.64 = 100

∴ Final Answer = 100

Additional Information

Identity Used: (a − b)³

Key Idea: Match coefficients carefully

Tip: Convert decimals into relation form

Exam Trick: Spot cube identity quickly

The correct answer is Rio Earth Summit.

Key Points

• The Rio Earth Summit, officially known as the United Nations Conference on Environment and Development (UNCED), was held in Rio de Janeiro, Brazil, from 3 to 14 June 1992. Hence, this option is correct.
• This global event was a major milestone that popularized the concept of Sustainable Development, defined as development that meets the needs of the present without compromising the ability of future generations to meet their own needs.
• The summit resulted in several landmark documents, including Agenda 21 (a blueprint for sustainable development in the 21^st century), the Rio Declaration on Environment and Development, and the Statement of Forest Principles.
• It also led to the creation of vital international treaties, namely the United Nations Framework Convention on Climate Change (UNFCCC) and the Convention on Biological Diversity (CBD).
• The conference saw participation from 172 governments, with 108 attendance at the level of heads of state or government, making it one of the largest gatherings of world leaders at the time to address environmental issues.

Additional Information

• Montreal Protocol (1987):
• The Montreal Protocol on Substances that Deplete the Ozone Layer is an international treaty designed to protect the ozone layer.
• It was signed on 16 September 1987 and focuses on phasing out the production and consumption of ozone-depleting substances like chlorofluorocarbons (CFCs) and halons. Hence, this option is incorrect.
• Kyoto Protocol (1997):
• The Kyoto Protocol was adopted in Kyoto, Japan, on 11 December 1997 and entered into force in 2005.
• It was an extension of the 1992 UNFCCC that committed industrialized countries and economies in transition to limit and reduce greenhouse gas (GHG) emissions in accordance with agreed individual targets. Hence, this option is incorrect.
• Paris Agreement (2015):
• The Paris Agreement is a legally binding international treaty on climate change adopted by 196 parties at COP 21 in Paris on 12 December 2015.
• Its primary goal is to limit global warming to well below 2 degrees Celsius, preferably to 1.5 degrees Celsius, compared to pre-industrial levels. Hence, this option is incorrect.
• Definition of Sustainable Development:
• While the Rio Summit popularized the term, the formal definition was first introduced in the Brundtland Report (also titled Our Common Future) published in 1987 by the World Commission on Environment and Development (WCED).

Important Points

• Agenda 21: This is a comprehensive plan of action to be taken globally, nationally, and locally by organizations of the United Nations System, Governments, and Major Groups in every area in which human impacts on the environment.
• UNFCCC: Established during the 1992 summit, it serves as the parent treaty of the 2015 Paris Agreement and the 1997 Kyoto Protocol.
• Sustainable Development Goals (SDGs): Building on the momentum of the Rio Summit and subsequent meetings like Rio+20 (2012), the UN adopted the 17 Sustainable Development Goals in 2015 to be achieved by the year 2030.

The correct answer is Nrityanjali.

Key Points

• The online festival titled Nrityanjali was organized by the Films Division, under the Ministry of Information and Broadcasting, Government of India.
• The festival was held from September 23 to September 25, 2020, as a digital initiative to bring the heritage of Indian classical dance to the public during the COVID-19 pandemic.
• The primary objective of Nrityanjali was to showcase documentaries that chronicled the lives, struggles, and artistic excellence of legendary dance exponents who have shaped India’s cultural landscape.
• The festival featured biographical films on icons such as Rukmini Devi Arundale (Bharatanatyam), Pandit Birju Maharaj (Kathak), Kelucharan Mohapatra (Odissi), and Yamini Krishnamurthy (Bharatanatyam and Kuchipudi).
• It was streamed on the Films Division website and their official YouTube channel, making it accessible to a global audience for free.

Additional Information

• Indian Classical Dances:
• There are currently 8 classical dances recognized by the Sangeet Natak Akademi: Bharatanatyam (Tamil Nadu), Kathak (North India), Kathakali (Kerala), Kuchipudi (Andhra Pradesh), Odissi (Odisha), Manipuri (Manipur), Mohiniyattam (Kerala), and Sattriya (Assam).
• The Ministry of Culture sometimes includes Chhau in this list, making it 9.
• Exponents Mentioned in the Festival:
• Rukmini Devi Arundale: She was instrumental in the revival of Bharatanatyam from its original Sadir style and established the Kalakshetra Foundation in Chennai in 1936.
• Pandit Birju Maharaj: A doyen of the Lucknow Kalka-Bindadin Gharana of Kathak, he was a recipient of the Padma Vibhushan in 1986.
• Kelucharan Mohapatra: He is credited with the revival of Odissi in the 20^th century and was the first person from Odisha to receive the Padma Vibhushan in 2000.
• Films Division of India:
• Established in 1948, it is headquartered in Mumbai.
• It serves as the main government agency to produce and distribute documentaries and news magazines for public education and the preservation of Indian history.

Important Points

• Natya Utsav: This is a general term for drama or theater festivals. Many organizations like Sahitya Kala Parishad organize annual Natya Utsavs to promote stage plays.
• Nritya Mahotsav: This translates to "Dance Festival." Notable examples include the Khajuraho Dance Festival in Madhya Pradesh or the Konark Festival in Odisha, which are held annually to celebrate classical dance against the backdrop of heritage monuments.
• Rangmanch: This term literally means "Stage" or "Theater" in Hindi. It refers to the performing arts sector rather than a specific online documentary festival of 2020.
• Context of 2020: During the lockdown, several cultural bodies shifted to the OTT (Over-the-top) or virtual platform. Nrityanjali was unique because it used archival documentary films rather than live-streamed performances to educate the youth about the history of classical arts.

The correct answer is Usual Principal Status Unemployment.

Key Points

• The Usual Principal Status (UPS) measurement is used to identify individuals who remained unemployed for a relatively longer period during the 365 days preceding the date of the survey.
• Under this method, a person is classified as unemployed if he or she was available for work but did not find gainful employment for the major part of the year (i.e., 183 days or more).
• This measurement specifically reflects chronic unemployment or open unemployment, as it focuses on the long-term status of an individual rather than temporary or seasonal fluctuations in the labor market.
• In India, the National Sample Survey Office (NSSO), under the Ministry of Statistics and Programme Implementation (MoSPI), traditionally uses this method to provide a comprehensive picture of the structural unemployment prevailing in the economy.
• This status is determined by the major time criterion, where the activity status (employed, unemployed, or out of the labor force) on which a person spent the maximum time during the reference year is recorded. Hence, the statement identifying UPS as the measure for chronic unemployment is correct.

Additional Information

• Usual Subsidiary Status (USS):
• This refers to individuals who are classified as unemployed based on their principal status but might have worked for a short period of at least 30 days during the reference year.
• When Usual Principal Status and Subsidiary Status are combined, it is known as UPSS (Usual Principal and Subsidiary Status), which provides a broader estimate of the workforce by including part-time or intermittent workers.
• Current Weekly Status (CWS):
• The reference period for this measurement is the seven days preceding the date of the survey.
• A person is considered employed if they worked for at least one hour on any one day during the reference week.
• It is useful for capturing seasonal unemployment and short-term changes in the employment patterns of India.
• Current Daily Status (CDS):
• This is considered the most rigorous and accurate measure of unemployment and underemployment.
• It records the activity status of a person for each of the seven days in the reference week, measuring person-days rather than just individuals.
• It helps in understanding the intensity of work and is often used to calculate the unemployment rate in the Periodic Labour Force Survey (PLFS) reports.
• Structural and Frictional Unemployment:
• Structural unemployment occurs due to a mismatch between the skills of the workforce and the requirements of the employers, often found in developing nations like India.
• Frictional unemployment is temporary and occurs when individuals are between jobs or looking for better opportunities.

Important Points

• Statistical Background: The concept of measuring unemployment through different statuses was recommended by the Dantwala Committee in 1970 to better understand the multi-dimensional nature of the Indian labor market.
• PLFS Reports: The Periodic Labour Force Survey, launched in April 2017, publishes annual reports that use Usual Status and Current Weekly Status to estimate the Labour Force Participation Rate (LFPR) and Worker Population Ratio (WPR).
• Demographic Focus: These measurements are crucial for drafting government policies like the Mahatma Gandhi National Rural Employment Guarantee Act (MGNREGA), which aims to provide 100 days of wage employment to rural households to combat chronic unemployment.
• Age Criteria: In most surveys, the labor force is measured for the age group of 15 to 59 years, which constitutes the working-age population.

The correct answer is More than 110%.

Key Points

• According to the Economic Survey 2024–25, India’s foreign exchange reserves were adequate to cover approximately 90% of its external debt as of late 2024.
• Forex Reserves Value: Stood at USD 640.3 billion at the end of December 2024.
• External Debt Context: The reserves provided coverage for 90% of the country's external debt, which was recorded at USD 711.8 billion as of September 2024.
• Import Cover: The reserves were also sufficient to cover 10.9 months of imports as of December 2024.
• Global Standing: India maintained its position as the fourth-largest foreign exchange reserve holder globally, following China, Japan, and Switzerland.

Additional Information

• Foreign Exchange Reserves (Forex):
• Forex reserves are assets held on reserve by a central bank in foreign currencies. In India, the Reserve Bank of India (RBI) manages these reserves.
• The four components of India's forex reserves include Foreign Currency Assets (FCA), Gold, Special Drawing Rights (SDRs) with the IMF, and the Reserve Tranche Position (RTP) in the IMF.
• As of the year 2024, Foreign Currency Assets constitute the largest component of these reserves, followed by Gold.
• External Debt of India:
• External debt refers to the total debt the country owes to foreign creditors, including multilateral (like World Bank), bilateral (other countries), and commercial borrowers (External Commercial Borrowings).
• The Economic Survey 2024–25 mentions that External Commercial Borrowings (ECBs) and Non-Resident Indian (NRI) deposits are significant contributors to the debt profile.
• A major portion of India’s external debt is denominated in US Dollars, followed by the Indian Rupee.
• Import Cover:
• Another important metric mentioned in the Economic Survey is the import cover. In December 2024, India's reserves were adequate to cover more than 11 months of projected imports.
• This high import cover is essential for food and energy security, especially given India's dependence on crude oil imports.

Important Points

• Debt Composition: India’s long-term debt accounts for the majority (over 80%) of the total external debt, which reduces the risk of immediate repayment pressure.
• SDR Allocation: The International Monetary Fund (IMF) occasionally allocates Special Drawing Rights to member countries, which significantly boosted India's reserves in recent fiscal years.
• Policy Intervention: The RBI uses forex reserves to intervene in the Foreign Exchange Market to curb excessive volatility in the exchange rate of the Indian Rupee (INR).

Given: F, G, H, I, V, W and X are sitting around a circular table facing the centre.

H sits third to the left of F.

I sits second to the left of V.

Only F sits between G and I.

W is not an immediate neighbour of H.

 

Thus, number of persons between X and I = 2

Hence, the correct answer is Option 4.

Shortcut Trick

⇒ Net rate = 1/4 + 1/24 − 1/6

⇒ LCM = 24 ⇒ (6 + 1 − 4)/24 = 3/24 = 1/8

⇒ So tank fills in 8 hours

⇒ Half tank ⇒ 8/2 = 4 hours

∴ Answer = 4 hours

Alternate Method

Given:

Pipe A fills in 4 hr

Pipe B fills in 24 hr

Pipe C empties in 6 hr

Formula Used:

Net work rate = Sum of filling rates − emptying rate

Calculation:

⇒ Net rate = 1/4 + 1/24 − 1/6

⇒ = (6 + 1 − 4)/24 = 3/24 = 1/8

⇒ Time for full tank = 8 hr

⇒ Time for half tank = 4 hr

∴ The correct answer is 4 hours.

Additional Information

Net Rate: Add filling, subtract emptying

LCM Method: Use common denominator for speed

Half Work: Time halves if rate same

Exam Tip: Always find net rate first

Shortcut Trick

⇒ Downstream speed = 120/6 = 20

⇒ Upstream speed = 120/10 = 12

⇒ Still water speed = (20 + 12) / 2 = 16

∴ Answer = 16 km/hr

Alternate Method

Given:

Downstream: 120 km in 6 hr

Upstream: 120 km in 10 hr

Formula Used:

Downstream = u + v

Upstream = u − v

Calculation:

⇒ Downstream speed = 120 ÷ 6 = 20 km/hr

⇒ Upstream speed = 120 ÷ 10 = 12 km/hr

⇒ u + v = 20

⇒ u − v = 12

⇒ Adding:

⇒ 2u = 32

⇒ u = 16 km/hr

∴ The correct answer is 16 km/hr.

Additional Information

Still Water Speed: (Downstream + Upstream) ÷ 2

Stream Speed: (Downstream − Upstream) ÷ 2

Key Concept: u ± v relation

Exam Tip: Direct average saves time

The correct answer is El Nino.

Key Points

• El Nino is a climate pattern that describes the unusual warming of surface waters in the central and eastern tropical Pacific Ocean. This phenomenon is the warm phase of a larger cycle called the El Nino-Southern Oscillation (ENSO).
• When El Nino occurs, the Trade Winds that normally blow from east to west along the Equator weaken or even reverse direction. This allows warm water to move toward the coast of South America, specifically near Peru and Ecuador.
• The rise in Sea Surface Temperature (SST) in the Pacific Ocean disrupts the global atmospheric circulation. In the context of India, this disruption often results in a weakening of the Southwest Monsoon.
• Deficient rainfall and drought conditions in India are frequently associated with El Nino years. Statistical data suggests that since 1950, about 60% of El Nino events have led to droughts in the Indian subcontinent.
• The phenomenon typically occurs at irregular intervals of 2 to 7 years and usually lasts for nine to twelve months, though it can sometimes persist for years.

Additional Information

• La Nina:
• Known as the "cold phase" of ENSO, it is the opposite of El Nino. It involves the cooling of surface waters in the central and eastern Pacific.
• In India, La Nina is generally associated with above-normal rainfall and a strong Southwest Monsoon, which is beneficial for Kharif crops.
• ENSO Cycle:
• The El Nino-Southern Oscillation consists of three phases: El Nino (warm), La Nina (cold), and a Neutral phase.
• Scientists monitor this using the Oceanic Nino Index (ONI), which tracks the SST in the Nino 3.4 region of the Pacific Ocean.
• Southern Oscillation:
• This refers to the atmospheric component of the phenomenon, characterized by changes in air pressure between Tahiti (central Pacific) and Darwin, Australia (western Pacific).
• A negative Southern Oscillation Index (SOI) usually accompanies El Nino events.
• Economic Impact:
• El Nino has severe economic implications for India because its agriculture sector is heavily dependent on monsoon rainfall. Deficits can lead to inflation in food prices.
• In South America, it affects fisheries as the warm water stops the upwelling of nutrient-rich cold water, drastically reducing the fish population.

Important Points

• The Walker Circulation: This is the east-west atmospheric circulation over the Equatorial Pacific. During El Nino, this circulation breaks down or reverses, causing convection (and rain) to shift from the Western Pacific (near Australia/Indonesia) to the Central/Eastern Pacific.
• Historical Context: Severe El Nino years like 1997-1998 and 2015-2016 were among the strongest on record, causing global temperature spikes and extreme weather events worldwide.
• Nomenclature: The name El Nino is Spanish for "The Little Boy" or "Christ Child," coined by Peruvian fishermen because the warming often peaked around December (Christmas time).
• Teleconnections: This term describes how weather changes in the Pacific affect distant locations like India, Africa, and North America. For India, the teleconnection manifests as suppressed rainfall due to the shifting of low-pressure zones.

Given Statements:

I. Mohit is older than Kunal but younger than Sandeep.

⇒ Sandeep > Mohit > Kunal

II. Tarun is younger than Sandeep but older than Mohit.

⇒ Sandeep > Tarun > Mohit

Analysis:

Statement I alone → Not sufficient (Only gives relation among Sandeep, Mohit, Kunal; no info about Tarun and Rohan).

Statement II alone → Not sufficient (Only gives relation among Sandeep, Tarun, Mohit; no info about Kunal and Rohan).

Combining I and II:

⇒ Sandeep > Tarun > Mohit > Kunal

But, Rohan’s position is unknown, so oldest cannot be determined.

Here, both statements together are NOT sufficient.

Hence, the correct answer is Option 4.

Shortcut Trick

⇒ Net rate = 1/4 + 1/32 − 1/32

⇒ = 1/4 (since 1/32 cancels)

⇒ Time for full tank = 4 hr

⇒ For 1/4 tank ⇒ 4 × 1/4 = 1 hr

∴ Answer = 1 hour

Alternate Method

Given:

Tap A fills in 4 hr

Tap B fills in 32 hr

Tap C empties in 32 hr

Concept Used:

Net rate = Sum of filling − emptying

Calculation:

⇒ Net rate = 1/4 + 1/32 − 1/32

⇒ = 1/4

⇒ Time for full tank = 4 hr

⇒ Time for 1/4 tank = 4 × 1/4 = 1 hr

∴ The correct answer is 1 hour.

Additional Information

Net Rate: Add filling, subtract emptying

Cancellation Trick: Equal opposite rates cancel

Work-Time: Time = Work / Rate

Exam Tip: Always simplify rates first

Shortcut Trick

⇒ For cone, inscribed sphere radius r = (R × h) / (R + l)

⇒ Given R = 42√3, l = 2R = 84√3

⇒ h = √(l² − R²) = √(3R²) = R√3 = 126

⇒ r = (42√3 × 126) / (42√3 + 84√3) = 42

⇒ Volume = (4/3)πr³ = (4/3) × (22/7) × 42³ = 310464

∴ Answer = 310464 cm³

Alternate Method

Given:

Base radius R = 42√3

Slant height l = diameter = 84√3

Formula Used:

h = √(l² − R²)

r = (R × h) / (R + l)

Volume = (4/3)πr³

Calculation:

⇒ h = √[(84√3)² − (42√3)²]

⇒ = √(21168 − 5292) = √15876 = 126

⇒ r = (42√3 × 126) / (42√3 + 84√3)

⇒ = (42 × 126) / 126 = 42

⇒ Volume = (4/3) × (22/7) × 42³

⇒ = (88/21) × 74088

⇒ = 310464 cm³

∴ The correct answer is 310464 cm³.

Additional Information

Inscribed Sphere: r = (R×h)/(R+l)

Cone Relation: l² = R² + h²

Volume: (4/3)πr³

Exam Tip: Use relation l = 2R to simplify fast

The correct answer is Article 243 X.

Key Points

• Article 243 X of the Constitution of India specifically empowers the State Legislature to authorize Municipalities to levy, collect, and appropriate taxes, duties, tolls, and fees. Hence, the option Article 243 X is correct.
• Under this Article, the State Government may assign to a Municipality such taxes, duties, tolls, and fees levied and collected by the State Government for purposes related to the local body's finances.
• It also provides for making grants-in-aid to the Municipalities from the Consolidated Fund of the State to ensure they have sufficient resources to perform their functions.
• Article 243 X further mandates the constitution of Funds for crediting all money received by or on behalf of the Municipalities and also the withdrawal of such money therefrom.
• Article 243 P defines various terms used in Part IX-A, such as "Committee", "District", "Metropolitan area", and "Municipality", but it does not deal with financial powers. Hence, this statement is incorrect in the context of the question.
• Article 243 U dictates the duration of Municipalities, stating that every Municipality shall continue for 5 years from the date appointed for its first meeting unless dissolved earlier under any law. Hence, this statement is incorrect.
• Article 243 ZB describes the application of Part IX-A to Union Territories, allowing the President of India to direct its application with certain exceptions or modifications. Hence, this statement is incorrect.

Additional Information

• The 74^th Constitutional Amendment Act, passed in 1992, introduced Part IX-A (Articles 243-P to 243-ZG) to the Indian Constitution, which provides a constitutional basis for Urban Local Bodies (ULBs).
• This amendment also added the Twelfth Schedule to the Constitution, which contains 18 functional items placed under the purview of Municipalities, such as urban planning, regulation of land use, and public health.
• Article 243 Y is another crucial financial provision that mandates the State Finance Commission to review the financial position of Municipalities and make recommendations to the Governor regarding the distribution of net proceeds of taxes between the State and the Municipalities.
• There are three types of Municipalities created under Article 243 Q: Nagar Panchayats for transitional areas, Municipal Councils for smaller urban areas, and Municipal Corporations for larger urban areas.
• The State Election Commission, under Article 243 ZA, is responsible for the superintendence, direction, and control of the preparation of electoral rolls and the conduct of all elections to the Municipalities.

Important Points

• Article 243 W details the powers, authority, and responsibilities of Municipalities, enabling them to function as institutions of self-government.
• The Central Finance Commission also plays a role in augmenting the Consolidated Fund of a State to supplement the resources of the Municipalities in the State on the basis of recommendations made by the Finance Commission of the State.
• Reservation of seats for Scheduled Castes (SCs), Scheduled Tribes (STs), and women (not less than one-third of the total number of seats) is provided under Article 243 T to ensure inclusive local governance.
• The District Planning Committee (DPC) is constituted under Article 243 ZD to consolidate the plans prepared by the Panchayats and the Municipalities in the district and to prepare a draft development plan for the district as a whole.

Given: (Left) Ω % + # 3 ? = £ 1 4 9 2 6 5 @ 7 & $ ~ * 8 (Right)

Now, Symbols, which are immediately preceded by a number and also immediately followed by another number.

So, Needed pattern is: Number – Symbol – Number.

(Left) Ω % + # 3 ? = £ 1 4 9 2 6 5 @ 7 & $ ~ * 8 (Right)

So, Only one symbol satisfies the condition.

Hence, the correct answer is Option 3.

The correct answer is increase.

Key Points

• Elastic Potential Energy is the energy stored as a result of applying a force to deform an elastic object. The energy is stored until the force is removed and the object springs back to its original shape, doing work in the process.
• In the case of a spring, the potential energy is given by the formula U = 1/2 kx², where k is the spring constant (a measure of the stiffness of the spring) and x is the displacement from the equilibrium position.
• At the equilibrium position, the displacement x is zero, which means the potential energy is at its minimum (zero). Hence, the statement that potential energy increases when moving away from equilibrium is correct.
• When a spring is compressed, work is done against the restoring force of the spring. This work is stored in the form of potential energy. Since the displacement x is squared in the formula, whether the spring is compressed (negative x) or stretched (positive x), the value of x² is always positive, leading to an increase in energy. Hence, the correct answer is that it will increase.
• If the potential energy were to decrease, it would mean the spring is returning toward its equilibrium point from a deformed state. Hence, the statement that potential energy decreases during compression is incorrect.
• The restoring force exerted by the spring is proportional to the displacement but in the opposite direction, described by Hooke’s Law as F = -kx.

Additional Information

• Hooke’s Law: Proposed by Robert Hooke in 1676, this law states that for relatively small deformations of an object, the displacement or size of the deformation is directly proportional to the deforming force or load.
• Spring Constant (k): The SI unit for the spring constant is Newton per meter (N/m). A higher value of k indicates a stiffer spring that requires more force to compress or extend.
• Conservation of Energy: In an ideal system without friction or air resistance, the mechanical energy (the sum of kinetic energy and potential energy) remains constant. When a compressed spring is released, the potential energy is converted into kinetic energy as the spring moves back toward equilibrium.
• Applications of Spring Energy: This principle is utilized in various mechanical devices such as clocks, shock absorbers in vehicles, trampolines, and recoil mechanisms in firearms.
• Work Done: The work done to compress a spring by a distance x is equal to the area under the Force-Displacement graph, which forms a triangle with area 1/2 × base × height, resulting in 1/2 × x × kx = 1/2 kx².

Important Points

• Equilibrium Position: This is the natural length of the spring where no external forces are acting on it, and it exerts no restoring force.
• Conservative Force: The force exerted by a spring is a conservative force, meaning the work done by or against the force depends only on the initial and final positions and not on the path taken.
• Elastic Limit: If a spring is compressed or stretched beyond its elastic limit, it will not return to its original shape and the Hooke's Law relation fails. This results in permanent deformation or plasticity.
• Direction of Force: During compression, the displacement is inward, but the restoring force acts outward. During extension, the displacement is outward, and the restoring force acts inward. In both cases, the potential energy increases as you move away from the center.

Shortcut Trick

⇒ Let ₹5 coins = x ⇒ ₹2 coins = x + 50

⇒ Remaining coins = 112 − (2x + 50) = 62 − 2x

⇒ Value: 5x + 2(x + 50) + (62 − 2x) = 212

⇒ 5x + 2x + 100 + 62 − 2x = 212 ⇒ 5x + 162 = 212

⇒ 5x = 50 ⇒ x = 10 ⇒ ₹1 coins = 62 − 20 = 42

∴ Answer = 42

Alternate Method

Given:

Total coins = 112

Total value = ₹212

₹2 coins = 50 more than ₹5 coins

Formula Used:

Sum of coins and total value equations

Calculation:

⇒ Let ₹5 coins = x

⇒ ₹2 coins = x + 50

⇒ ₹1 coins = y

⇒ Total coins: x + (x + 50) + y = 112

⇒ 2x + y = 62 ⇒ y = 62 − 2x

⇒ Total value:

⇒ 5x + 2(x + 50) + y = 212

⇒ 5x + 2x + 100 + (62 − 2x) = 212

⇒ 5x + 162 = 212

⇒ 5x = 50 ⇒ x = 10

⇒ y = 62 − 2(10) = 42

∴ The correct answer is 42.

Additional Information

Linear Equations: Use two equations to solve

Substitution: Express one variable in terms of another

Value Equation: Multiply coins with values

Exam Tip: Reduce variables quickly

The correct answer is Suez Canal.

Key Points

• The Suez Canal is an artificial sea-level waterway located in Egypt, which effectively connects the Mediterranean Sea to the Red Sea through the Isthmus of Suez. This makes the statement about it linking these two seas correct.
• It was officially opened on November 17, 1869, after a construction period of 10 years led by the Suez Canal Company, founded by Ferdinand de Lesseps.
• The canal serves as a vital boundary separating Africa from Asia and provides the shortest maritime route between Europe and the lands surrounding the Indian and western Pacific Oceans.
• It is considered one of the world's most heavily used shipping lanes, facilitating approximately 12% of global trade and nearly 30% of the world's daily container traffic.
• The total length of the waterway is approximately 193.30 km (120.11 miles), which includes the northern and southern access channels that allow ships to transit between the Port Said and Port Tewfik.

Additional Information

• Panama Canal:
• This is an 82 km (51 mile) artificial waterway in Panama that connects the Atlantic Ocean with the Pacific Ocean.
• Opened in 1914, it utilizes a sophisticated system of locks to lift ships 26 meters above sea level to Gatun Lake.
• It is essential for trade between the East and West coasts of the United States and for routes connecting Asia with the American East Coast.
• Strait of Malacca:
• Located between the Malay Peninsula and the Indonesian island of Sumatra, it is the primary shipping channel between the Indian Ocean and the Pacific Ocean.
• It is a major maritime "chokepoint" through which about 25% of the world's traded goods pass annually, linking major economies like China, India, Japan, and South Korea.
• Bosporus Strait:
• Also known as the Strait of Istanbul, it is a narrow, natural strait in northwestern Turkey.
• It forms part of the continental boundary between Europe and Asia and connects the Black Sea with the Sea of Marmara, which eventually leads to the Mediterranean.
• It is strategically significant for the transport of oil and agricultural products from the Black Sea region.

Important Points

• The New Suez Canal Expansion: In August 2015, Egypt inaugurated a major expansion project known as the "New Suez Canal," which involved digging a new 35 km lane parallel to the existing one and deepening the current path. This allowed for two-way traffic in certain sections and significantly reduced transit time.
• Ever Given Incident: In March 2021, a massive container ship called the Ever Given ran aground in the canal due to high winds. The blockage lasted for 6 days, causing a massive backup of hundreds of ships and highlighting the canal's critical role in the global supply chain.
• Economic Revenue: The canal is a primary source of foreign exchange for the Egyptian government, contributing billions of dollars (reaching record highs of over $9 billion in the 2022-2023 fiscal year) to the national economy$.

Family Chart:

Decoding the Symbols:

Given: D + F ÷ G – H x J

It means: D is the daughter of F, F is the father of G, G is the brother of H, H is the wife of J.

 

Here, D is J’s wife’s sister.

Hence, the correct answer is Option 1.

Shortcut Trick

⇒ Monthly saving = 18000 − 5000 − 2000 = 11000

⇒ He saves for only 11 months

⇒ Total saving = 11000 × 11 = 121000

∴ Answer = 121000

Alternate Method

Given:

Salary = ₹18000 per month

Expenses = ₹5000 + ₹2000

Formula Used:

Saving = Income − Expenses

Calculation:

⇒ Monthly expenses = 5000 + 2000 = 7000

⇒ Monthly saving = 18000 − 7000 = 11000

⇒ In birthday month, saving = 0

⇒ So savings for 11 months

⇒ Total saving = 11000 × 11

⇒ = 121000

∴ The correct answer is ₹121000.

Additional Information

Saving Formula: Saving = Income − Expenses

Annual Saving: Monthly × number of months

Special Case: Exclude months with zero saving

Exam Tip: Always adjust exceptional months

The correct answer is Biconvex.

Key Points

• A simple microscope is an optical instrument used to obtain a magnified image of small objects. It essentially consists of a single biconvex lens with a short focal length.
• A biconvex lens (also known as a convex lens or converging lens) is thicker in the middle than at the edges. It works by converging light rays that pass through it to a specific point.
• The principle of a simple microscope is based on the fact that when an object is placed between the optical center and the principal focus of a convex lens, the image formed is virtual, erect, and magnified.
• The magnifying power of a simple microscope is defined by the formula M = 1 + (D/f), where D is the least distance of distinct vision (standardized at 25 cm for a normal human eye) and f is the focal length of the lens.
• These instruments are commonly used by watchmakers, jewelers, and students to observe tiny parts or organisms. Because it uses only one lens, the magnification is limited compared to a compound microscope.

Additional Information

• Biconcave Lens:
• A biconcave lens is a diverging lens that is thinner at the center than at the edges.
• It is primarily used in the correction of Myopia (nearsightedness), as it helps spread out light rays before they reach the eye.
• It always forms a virtual, erect, and diminished image, regardless of the object's position.
• Cylindrical Lens:
• A cylindrical lens focuses light into a line rather than a point.
• It is specifically used to correct Astigmatism, a vision condition caused by an irregular curvature of the cornea or lens.
• These lenses have different refractive powers in different planes.
• Plano-concave Lens:
• This lens has one flat (plano) surface and one inward-curving (concave) surface.
• It has a negative focal length and is used to expand light beams or increase focal lengths in optical systems.
• History and Inventor:
• The simple microscope was famously improved and used by Antonie van Leeuwenhoek in the 17^th century.
• Using high-quality biconvex lenses, he achieved magnifications of up to 275x, allowing him to be the first to observe bacteria and protozoa.

Important Points

• Nature of Image: In a simple microscope, the object must be very close to the lens (within its focal length). If the object is moved beyond the focal point, the image becomes real and inverted, which is not suitable for microscopic observation.
• Power of Lens: The power (P) of the lens is the reciprocal of its focal length (f) in meters, expressed in Dioptres (D). A higher power lens provides greater magnification.
• Least Distance of Distinct Vision (LDDV): This is the minimum distance at which the human eye can see an object clearly without any strain. For a healthy adult, this value is 25 cm.
• Materials: Modern lenses are typically made from high-quality optical glass or plastics like polycarbonate to ensure high refractive index and low chromatic aberration.

The correct answer is Registered Environment Auditor.

Key Points

• The Environment Audit Rules, 2025, formulated by the Ministry of Environment, Forest and Climate Change (MoEFCC), officially authorize a Registered Environment Auditor to conduct environmental audits for industrial and developmental projects.
• A Registered Environment Auditor is a professional or an entity that has undergone specific training and is formally registered with the National Board for Quality Promotion (NBQP) or the Quality Council of India (QCI) to ensure they meet the competency standards required for environmental assessment.
• The audit process is designed to evaluate the environmental performance of an organization, ensuring that its operations align with the Environment (Protection) Act, 1986 and the Air and Water Acts.
• These auditors are responsible for verifying the Environmental Statement (commonly known as Form V), which industries must submit to the State Pollution Control Boards (SPCBs) annually.
• The Environment Audit Rules, 2025 aim to bring transparency and accountability to the environmental compliance mechanism by shifting from self-declaration to verified auditing by third-party Registered Auditors.

Additional Information

• Scope of Environment Audit:
• The audit encompasses resource consumption (water, electricity, raw materials), waste generation (solid, hazardous, and electronic waste), and pollution control measures.
• It identifies gaps in compliance and suggests mitigation strategies to reduce the carbon footprint of the industry.
• The Environment Audit Rules, 2025 apply to Category A and B projects as defined under the Environmental Impact Assessment (EIA) Notification.
• Role of the Ministry (MoEFCC):
• The MoEFCC acts as the apex body for policy-making and implementation regarding environmental protection in India.
• The year 2025 marks a significant shift towards digital monitoring and real-time data integration in environmental auditing through the PARIVESH 2.0 portal.
• Eligibility for Auditors:
• To become a Registered Environment Auditor, an individual typically requires a Post-Graduate Degree in Environmental Science, Chemistry, or a Bachelor's Degree in Engineering (Chemical/Environmental/Civil).
• Minimum 5 to 7 years of work experience in environmental management or industrial pollution control is generally mandatory for registration.
• Candidates must pass a National Level Examination conducted by designated agencies to obtain their certification and registration number.

Important Points

• Distinction between Roles:
• An Environmental Consultant may provide advice on project planning and EIA reports, but they do not possess the statutory authority to sign off on a formal Environment Audit unless they are also a Registered Auditor.
• A Certified Environment Auditor is a broader term, whereas Registered Environment Auditor is the specific legal designation used in the 2025 Rules.
• Legal Framework:
• Section 3 and Section 25 of the Environment (Protection) Act, 1986 grant the Central Government the power to frame such rules for environmental conservation.
• Failure to conduct an audit by a Registered Auditor or submitting fraudulent data can lead to heavy monetary penalties or the closure of industrial units.
• The National Green Tribunal (NGT) often refers to these audit reports during judicial proceedings involving environmental degradation or accidental pollution.

The logic followed here is:

Given:

LITE → 8196

FELT → 6481

Thus, F = 4

Hence, the correct answer is Option 4.

The logic followed here is based on the alphabetical position pattern:

Option 1: PS − UX

Option 2: LO − PV

Option 3: NQ − SV

Option 4: JM − OR

Here, LO − PV is different from others.

Hence, the odd one out is Option 2.

Shortcut Trick

⇒ Difference (CI − SI) for 2 years = P × (r/100)²

⇒ = P × (4/100)² = P × 16/10000

⇒ Given difference = 53

⇒ P × 16/10000 = 53

⇒ P = 53 × 10000 / 16 = 33125

∴ Answer = 33125

Alternate Method

Given:

Rate = 4%

Time = 2 years

Difference = ₹53

Formula Used:

SI = (P × r × t)/100

CI = P[(1 + r/100)^t − 1]

Calculation:

⇒ SI = (P × 4 × 2)/100 = 8P/100 = 0.08P

⇒ CI = P[(1.04)² − 1]

⇒ = P(1.0816 − 1) = 0.0816P

⇒ Difference = CI − SI

⇒ = 0.0816P − 0.08P = 0.0016P

⇒ 0.0016P = 53

⇒ P = 53 / 0.0016 = 33125

∴ The correct answer is ₹33125.

Additional Information

Key Formula: CI − SI (2 yrs) = P × (r/100)²

SI Formula: (P × r × t)/100

CI Formula: P(1 + r/100)^t

Exam Tip: Use shortcut directly for 2 years

BODMAS Table: 

Given equation: 22 A 2 B 1 C 3 D 2 = ?

Now, if A means ‘÷’, B means ‘×’, C means ‘+’, and D means ‘−’, then:

⇒ 22 ÷ 2 × 1 + 3 − 2

⇒ 11 × 1 + 3 − 2

⇒ 11 + 3 − 2

⇒ 14 − 2

⇒ 12

Hence, the correct answer is "Option 2".

Shortcut Trick

⇒ CP per calculator = 54000 ÷ 45 = 1200

⇒ Profit part: 30 items at 25% ⇒ gain = 30 × 1200 × 25% = 9000

⇒ Loss part: 15 items at 20% ⇒ loss = 15 × 1200 × 20% = 3600

⇒ Net gain = 9000 − 3600 = 5400

⇒ % gain = (5400 ÷ 54000) × 100 = 10%

∴ Answer = 10% profit

Alternate Method

Given:

Total CP = ₹54000 for 45 calculators

30 sold at 25% profit, 15 sold at 20% loss

Formula Used:

Profit% = (Profit / Total CP) × 100

Calculation:

⇒ CP per item = 54000 ÷ 45 = 1200

⇒ For 30 items:

⇒ SP = 1200 × 1.25 = 1500

⇒ Total SP = 30 × 1500 = 45000

⇒ For 15 items:

⇒ SP = 1200 × 0.8 = 960

⇒ Total SP = 15 × 960 = 14400

⇒ Total SP = 45000 + 14400 = 59400

⇒ Profit = 59400 − 54000 = 5400

⇒ Profit% = (5400 ÷ 54000) × 100 = 10%

∴ The correct answer is 10% profit.

Additional Information

Profit/Loss: SP − CP

Mixed Cases: Handle parts separately

Percentage: Always on total CP

Exam Tip: Find per unit CP first

The correct answer is 5.

Key Points

• The Natyanjali Dance Festival is a prestigious annual event held for a duration of 5 days.
• The festival is hosted in the holy city of Chidambaram, located in the Cuddalore district of Tamil Nadu, India.
• The venue for this grand celebration is the Thillai Nataraja Temple, which is an architectural masterpiece over 1000 years old, primarily built during the Chola Dynasty.
• This cultural event begins on the auspicious occasion of Maha Shivaratri, which usually occurs in the month of February or March.
• It is dedicated to Lord Shiva in his form as Nataraja, the "Lord of Dance," symbolizing the cosmic dance of creation and destruction.
• The festival is organized collaboratively by the Natyanjali Trust, the Department of Tourism of Tamil Nadu, and the Ministry of Culture of the Government of India.

Additional Information

• Etymology and Meaning: The word Natyanjali is a combination of two Sanskrit words: Natya (meaning dance) and Anjali (meaning offering). Collectively, it translates to "offering through dance."
• History and Origin: The festival was first established in the year 1981 to promote the traditional Indian classical dance forms and to revive the ancient temple tradition of performing arts.
• Diversity of Dance Forms: While Bharatanatyam (the native dance of Tamil Nadu) is the most prominent, the festival provides a platform for various classical styles, including Kathak, Kuchipudi, Mohiniyattam, Odissi, Manipuri, and Kathakali.
• Global Participation: It attracts over 300 to 500 dancers every year, ranging from renowned maestros to budding students, arriving from across India and international locations like the USA, UK, and Canada.
• Significance of the Temple: The Chidambaram temple is one of the Pancha Bhoota Stalams, representing the element of Akasha (Aether/Sky). It is unique because Lord Shiva is worshipped here as a dancer rather than through a traditional Lingam.

Important Points

• Architectural Features: The Thillai Nataraja Temple is famous for its Gopurams (gateway towers), which feature intricate stone carvings of all the 108 karanas (dance movements) described in the Natya Shastra, the foundational text of Indian classical arts.
• Spiritual Context: For the performers, the Natyanjali Dance Festival is not merely a stage performance but a form of Sadhana (spiritual practice) and a way to seek the blessings of the cosmic dancer.
• Location and Connectivity: Chidambaram is located approximately 250 kilometers south of Chennai. It remains a major pilgrimage and cultural hub in South India.
• Extended Celebrations: Although the core festival at the main temple is traditionally 5 days, several associated cultural programs in the city sometimes extend the festive atmosphere for up to 10 to 13 days to accommodate the large number of participating artists.

Shortcut Trick

⇒ Modal class = 20–30 (highest freq = 36)

⇒ l = 20, f₁ = 36, f₀ = 16, f₂ = 34, h = 10

⇒ Mode = 20 + [(36−16)/(2×36−16−34)] × 10

⇒ = 20 + (20/22) × 10 = 20 + 9.09

∴ Answer = 29.09

Alternate Method

Given:

Class intervals and frequencies

Formula Used:

Mode = l + [(f₁ − f₀) / (2f₁ − f₀ − f₂)] × h

Calculation:

⇒ Modal class = 20–30

⇒ l = 20, h = 10

⇒ f₁ = 36, f₀ = 16, f₂ = 34

⇒ Mode = 20 + [(36 − 16) / (2×36 − 16 − 34)] × 10

⇒ = 20 + (20 / 22) × 10

⇒ = 20 + 9.09

⇒ = 29.09

∴ The correct answer is 29.09.

Additional Information

Mode: Most frequent value

Modal Class: Class with highest frequency

Formula: Uses neighboring frequencies

Exam Tip: Identify f₀, f₁, f₂ carefully

Shortcut Trick

⇒ Right triangle with AC = 13, AB = 12 ⇒ BC = 5 (Pythagoras)

⇒ tan A = BC/AB = 5/12

⇒ cot C = BC/AB = 5/12 (since A + C = 90)

⇒ tan A − cot C = 5/12 − 5/12 = 0

∴ Answer = 0

Alternate Method

Given:

Right triangle ABC, ∠B = 90°

AB = 12 cm, AC = 13 cm

Formula Used:

Pythagoras: AC² = AB² + BC²

tan A = opposite/adjacent

cot C = adjacent/opposite

Calculation:

⇒ BC = √(13² − 12²)

⇒ = √(169 − 144) = √25 = 5

⇒ tan A = BC/AB = 5/12

⇒ cot C = BC/AB = 5/12

⇒ tan A − cot C = 5/12 − 5/12 = 0

∴ The correct answer is 0.

Additional Information

Pythagoras Theorem: Hyp² = base² + height²

Complementary Angles: A + C = 90° ⇒ tan A = cot C

Right Triangle Ratios: tan = opposite/adjacent

Exam Tip: Use 5-12-13 triangle directly

The logic followed here is:

thus, "37" will replace the question mark in the given series.

Hence, the correct option is "Option 4"

Given: Seven friends – A, B, C, D, E, F and G – each have a meeting on a different day of the week, starting from Monday to Sunday.

Only one person has a meeting between C and F.

A’s meeting is immediately before F’s, but not on a Monday.

Only two persons have meetings between A and G.

B’s meeting is before E’s but after D’s.

Here, B has meeting on Wednesday.

Hence, the correct answer is Option 2.

The correct answer is 96^th Amendment.

Key Points

• The 96^th Constitutional Amendment Act was passed by the Parliament of India in the year 2011.
• This amendment specifically aimed to substitute the spelling of the language listed in the Eighth Schedule from ‘Oriya’ to ‘Odia’. Hence, the 96^th Amendment is the correct option.
• The Eighth Schedule of the Constitution of India consists of a list of 22 official languages recognized by the state, and Odia is one of the prominent classical languages included in this list.
• The change in the name of the language was a follow-up to the Orissa (Alteration of Name) Act, 2011, which changed the name of the state from Orissa to Odisha.
• This modification was sought to reflect the correct phonetic and linguistic pronunciation of the language as used by the native speakers in the state of Odisha.

Additional Information

• 97^th Amendment Act, 2011:
• This amendment provided constitutional status and protection to co-operative societies in India.
• It inserted Article 43B in the Directive Principles of State Policy and added Part IXB to the Constitution.
• It also made the right to form co-operative societies a Fundamental Right under Article 19(1)(c). Hence, this statement is not related to the renaming of the language.
• 95^th Amendment Act, 2009:
• It extended the reservation of seats for Scheduled Castes (SCs) and Scheduled Tribes (STs) in the Lok Sabha and the State Legislative Assemblies.
• The period of reservation was extended from 60 years to 70 years (until January 25, 2020).
• It also extended the representation of the Anglo-Indian community by nomination. Hence, this statement is incorrect in the context of the question.
• 94^th Amendment Act, 2006:
• This amendment concerned the appointment of a Minister of Tribal Welfare in certain states.
• It exempted Bihar from the obligation to have a tribal welfare minister while extending this provision to the newly created states of Jharkhand and Chhattisgarh under Article 164(1). Hence, this statement is not the correct answer.

Important Points

• Evolution of the Eighth Schedule: Originally, the Eighth Schedule contained 14 languages. Over the years, through various Constitutional Amendments, the number has increased to 22.
• Significant Language Amendments:
• 21^st Amendment Act, 1967: Added Sindhi as the 15^th language.
• 71^st Amendment Act, 1992: Added Konkani, Manipuri, and Nepali.
• 92^nd Amendment Act, 2003: Added Bodo, Dogri, Maithili, and Santhali.
• Constitutional Provisions: Article 344(1) and Article 351 of the Indian Constitution are the primary articles that deal with the Eighth Schedule and the development of the Hindi language and other regional languages.
• Odia as a Classical Language: In February 2014, Odia was declared the sixth classical language of India by the Union Cabinet, joining the ranks of Tamil, Sanskrit, Telugu, Kannada, and Malayalam.

The correct answer is 72.

Key Points

• Based on the United Nations Treaty Collection, one nation, Fiji, became a signatory to the United Nations Convention against Cybercrime in December 2025.
• While the treaty officially opened for signature at a high-level ceremony in Hanoi, Vietnam, on 25–26 October 2025, where 72 participants (71 states and the European Union) signed, the process remains open at the UN Headquarters in New York until 31 December 2026.

Additional Information

• Comparison with the Budapest Convention: Before the UN treaty, the Council of Europe’s Budapest Convention (2001) was the primary international treaty on cybercrime, but it was not globally universal as many developing nations and countries like Russia and China were not parties to it.
• Role of UNODC: The United Nations Office on Drugs and Crime (UNODC) serves as the secretariat for the convention, providing technical assistance and capacity-building support to member states to implement the treaty's provisions effectively.
• Scope of Digital Crimes: The convention covers a wide range of crimes, including financial fraud, identity theft, cyber-terrorism, and online grooming, ensuring that perpetrators cannot find safe havens in countries with weak digital laws.
• Human Rights Safeguards: During the drafting phase, several civil society organizations and tech companies expressed concerns regarding state surveillance; hence, the final text includes provisions to balance security needs with fundamental human rights and privacy.
• Global Inclusion: Unlike previous regional agreements, this United Nations led initiative ensures that low-income and developing nations receive the necessary technological resources and training to protect their critical infrastructure.

Important Points

• Ratification Process: Becoming a signatory is the first step; however, the convention only comes into force once a specific number of nations (usually 30 to 40 depending on the treaty clause) complete the ratification process in their respective national parliaments.
• Electronic Evidence: One of the most vital features of the 2025 agreement is the streamlined process for cross-border data requests, allowing law enforcement agencies to obtain digital evidence from service providers located in other signatory nations.
• Signatory vs. Accession: While 151 nations signed the treaty during the initial window in 2025, other countries can join later through a process called accession, which carries the same legal obligations.
• Historical Context: The push for this treaty was notably led by Russia and supported by a diverse group of nations, reflecting a shift toward a multipolar approach to internet governance and cybersecurity.

Shortcut Trick

⇒ Match b: LCM(3,5) = 15 ⇒ a:b = 5:15, b:c = 15:21

⇒ Match c: LCM(21,9) = 63 ⇒ scale to a:b:c = 15:45:63

⇒ c:d = 9:5 ⇒ 63:35

⇒ Final = 15 : 45 : 63 : 35

∴ Answer = 15 : 45 : 63 : 35

Alternate Method

Given:

a : b = 1 : 3

b : c = 5 : 7

c : d = 9 : 5

Formula Used:

Equalize common terms to combine ratios

Calculation:

⇒ a : b = 1 : 3

⇒ b : c = 5 : 7

⇒ LCM of 3 and 5 = 15

⇒ a : b = 5 : 15

⇒ b : c = 15 : 21

⇒ a : b : c = 5 : 15 : 21

⇒ c : d = 9 : 5

⇒ LCM of 21 and 9 = 63

⇒ a : b : c = 15 : 45 : 63

⇒ c : d = 63 : 35

⇒ a : b : c : d = 15 : 45 : 63 : 35

∴ The correct answer is 15 : 45 : 63 : 35.

Additional Information

Chain Ratio: Combine ratios by matching common terms

LCM Method: Equalize middle variables

Scaling Rule: Multiply ratios to align values

Exam Tip: Always match b, then c stepwise

Shortcut Trick

⇒ Loss 20% ⇒ SP = 0.8 CP

⇒ Gain 40% ⇒ SP/CP = 1.4

⇒ Weight factor = 0.8 / 1.4 = 4/7

⇒ Actual weight = (4/7) × 1000 = 571.4 g

∴ Answer = 571.4 g

Alternate Method

Given:

Loss = 20%

Gain = 40%

Formula Used:

Profit% = (SP − CP) / CP × 100

Calculation:

⇒ Let CP of 1 kg = 100

⇒ Due to 20% loss, SP = 80

⇒ Let actual weight given = w kg

⇒ CP of w kg = 100w

⇒ Given profit = 40%

⇒ SP = 1.4 × CP

⇒ So, 80 = 1.4 × (100w)

⇒ 80 = 140w

⇒ w = 80 / 140 = 4/7 kg

⇒ In grams = (4/7) × 1000 = 571.4 g

∴ The correct answer is 571.4 g.

Additional Information

False Weight: Less quantity increases profit

Profit Formula: SP = CP × (1 + profit%)

Loss Formula: SP = CP × (1 − loss%)

Exam Tip: Assume CP = 100 for simplicity

Shortcut Trick

⇒ Initial total ratio = 3 + 5 + 7 = 15

⇒ Increase = 40% ⇒ New total = 15 × 1.4 = 21

⇒ New ratio = 3 + 5 + 7 + x = 15 + x

⇒ 15 + x = 21 ⇒ x = 6

∴ Answer = 6

Alternate Method

Given:

Initial ratio A : B : C = 3 : 5 : 7

Increase in total cost = 40%

New ratio = 3 : 5 : 7 : x

Formula Used:

Total ratio ∝ total cost

Calculation:

⇒ Initial total = 3 + 5 + 7 = 15

⇒ Let initial total cost = 15k

⇒ After adding D, total cost increases by 40%

⇒ New total = 15k × 1.4 = 21k

⇒ New ratio sum = 3 + 5 + 7 + x = 15 + x

⇒ So, 15 + x = 21

⇒ x = 6

∴ The correct answer is 6.

Additional Information

Ratio Sum: Total cost proportional to sum of ratios

Percentage Increase: Multiply by (1 + %/100)

Scaling Rule: Ratios scale with totals

Exam Tip: Compare sums directly

The correct answer is Quick Access.

Key Points

• Quick Access is a feature introduced in Windows 10 that serves as a personalized navigation hub within File Explorer. It replaces the "Favorites" functionality found in older versions like Windows 7 and Windows 8.
• The primary function of Quick Access is to automatically track and display a list of recently opened files and frequently used folders, allowing users to resume their work quickly without digging through deep directory structures. Hence, this option is correct.
• By default, when a user opens a new File Explorer window, it lands on the Quick Access view. This view typically shows the 10 most frequent folders and the 20 most recent files.
• It offers a customization feature where users can "Pin" specific folders to the Quick Access section in the Navigation Pane. This ensures that essential project folders remain permanently accessible regardless of how many other files are opened.
• The location of the Quick Access icon is usually at the very top of the left-hand Navigation Pane in any folder window, marked with a blue star icon.

Additional Information

• Recycle Bin:
• The Recycle Bin is a system folder where deleted files are temporarily stored before they are permanently removed from the hard drive.
• Its use is to provide a safety net for accidental deletions, but it does not track or store shortcuts to recently opened active files. Hence, this statement is incorrect.
• Desktop:
• The Desktop is the primary user interface and workspace seen immediately after logging into Windows.
• While users can manually place shortcuts or files on the Desktop for easy reach, it does not function as an automated log of recently accessed documents from across the system. Hence, this statement is incorrect.
• Control Panel:
• The Control Panel is a centralized utility used to manage system settings, hardware configurations, and software installations.
• It contains applets for User Accounts, Network and Sharing Center, and Device Manager, but it is not intended for file navigation or viewing document history. Hence, this statement is incorrect.
• File Explorer:
• Formerly known as Windows Explorer, this application is the file management system for the Windows Operating System. It allows users to browse local disks, cloud storage like OneDrive, and network locations.

Important Points

• Privacy and Management: Users can manage what appears in Quick Access through Folder Options (or File Explorer Options). Under the Privacy section of the General tab, users can click Clear to wipe the history of File Explorer.
• Data Handling: Disabling the "Show recently used files in Quick access" checkbox prevents Windows from recording recent file history in this specific location, which is a common privacy feature for shared computers.
• Windows 11 Updates: In Windows 11, the Start Menu also incorporates a "Recommended" section that functions similarly to Quick Access, showing recent files and cloud-synced documents from Office 365.
• Jump Lists: Another related feature is Jump Lists, which appear when you right-click an application icon on the Taskbar, showing the most recent files specific to that application (e.g., recent spreadsheets in Excel).

Shortcut Trick

⇒ Successive increase ⇒ multiply factors

⇒ 2,90,000 × 1.05 × 1.30

⇒ = 2,90,000 × 1.365

⇒ = 3,95,850

∴ Answer = 3,95,850

Alternate Method

Given:

Initial population = 2,90,000

Increase = 5% in first year

Increase = 30% in second year

Formula Used:

New Value = Initial × (1 + r₁) × (1 + r₂)

Calculation:

⇒ After 1^st year = 2,90,000 × 1.05 = 3,04,500

⇒ After 2^nd year = 3,04,500 × 1.30

⇒ = 3,95,850

∴ The correct answer is 3,95,850.

Additional Information

Successive Change: Multiply growth factors

Growth Factor: (1 + rate/100)

Not Additive: % changes are multiplicative

Exam Tip: Combine factors early