DSSSB TGT (Maths) Official Paper (Held On: 13 Nov, 2025 Shift 1) (Previous Year Paper)

Given:

Total number of people = 96

Sonu is 16^th from the left.

Esha is 29^th from the right.

Esha's position from left = Total − Position from right + 1

= 96 − 29 + 1

= 67 + 1

= 68^th

Number of people between them = Difference of positions − 1

= (68 − 16) − 1

= 52 − 1

= 51

Hence, the correct answer is "Option 4".

"12" person own both MS and WB but not HM.

Hence, the correct answer is “Option 1”.

Logic followed here is,

OXEN – NOXE – OENX

And,

WAKE – EWAK – WKEA

Similarly,

Option (4): KIDS – SKID – KDSI

Hence, the correct answer is “Option 4”.

Six boxes, A, B, C, D, E and F, are kept one over the other but not necessarily in the same order.

1. B is kept third from the top.
2. Only one box is kept between C and D.
3. B is kept immediately above C.
4. Only three boxes are kept between F and E.
5. D is kept immediately below F.
6. F is not kept at the topmost position.
7. A is kept immediately below E.

Two boxes are kept between A and F.

Hence, the correct answer is “Option 4”.

Family tree,

D is A's father' father.

Hence, the correct answer is “Option 1”.

Pattern followed here is,

Hence, the correct answer is “Option 4”.

Given: (Left) 825 555 382 239 789 (Right)

Largest number = 825 → Second digit = 2

Smallest number = 239 → Second digit = 3

Result = 2 + 3 = 5

Hence, the correct answer is "Option 2".

Six people, A, B, C, D, E and F, are sitting in a row, facing north.

1. Only two people sit to the left of F.
2. Only one person sits between C and E.
3. F sits to the immediate left of C.
4. A sits to the immediate right of D.
5. B sits third to the right of A. 

D sits at the extreme left end of the line.

Hence, the correct answer is “Option 1”.

'oven law video' is coded as 'yo eg dc'

And

'video card zebra' is coded as 'eg ro mv'. 

'video' coded in the given language as "eg".

Hence, the correct answer is “Option 3”.

(1) CV : SL

(2) KD : AT

(3) QJ : GC

(4) FY : VO

Hence, the correct answer is “Option 3”.

Given:

A = ÷, B = ×, C = +, D = −

Let's check each option one by one:

Option 1)

100 D 30 A 3 C 8 B 9

⇒ 100 − 30 ÷ 3 + 8 × 9

⇒ 100 − 30 ÷ 3 + 8 × 9

⇒ 100 − 10 + 72

⇒ 100 − 10 + 72

⇒ 90 + 72

⇒ 162

Since 162 is obtained, this option is correct.

Option 2)

100 B 30 A 3 C 8 D 9

⇒ 100 × 30 ÷ 3 + 8 − 9

⇒ 100 × 30 ÷ 3 + 8 − 9

⇒ 3000 ÷ 3 + 8 − 9

⇒ 3000 ÷ 3 + 8 − 9

⇒ 1000 + 8 − 9

⇒ 1000 + 8 − 9

⇒ 1008 − 9 = 999

Since 999 ≠ 162, this option is incorrect.

Option 3)

100 A 30 B 3 D 8 C 9

⇒ 100 ÷ 30 × 3 − 8 + 9

⇒ 100 ÷ 30 × 3 − 8 + 9

⇒ (10/3) × 3 − 8 + 9

⇒ (10/3) × 3 − 8 + 9

⇒ 10 − 8 + 9

⇒ 10 − 8 + 9

⇒ 2 + 9 = 11

Since 11 ≠ 162, this option is incorrect.

Option 4)

100 C 30 B 3 A 8 D 9

⇒ 100 + 30 × 3 ÷ 8 − 9

⇒ 100 + 30 × 3 ÷ 8 − 9

⇒ 100 + 90 ÷ 8 − 9

⇒ 100 + 90 ÷ 8 − 9

⇒ 100 + 11.25 − 9

⇒ 100 + 11.25 − 9

⇒ 111.25 − 9 = 102.25

Since 102.25 ≠ 162, this option is incorrect.

Hence, the correct answer is "Option 1".

Logic: Second number = (First number)² - First number

20 : 380

(20)² - 20 = 400 - 20 = 280

And,

25 : 600

(25)² - 25 = 625 - 25 = 600

Similarly,

15 : ?

(15)² - 15 = 225 - 15 = 210

Hence, the correct answer is “Option 2”.

(1) IL – NH

(2) HE – DA

(3) KH – GD

(4) QN – MJ

Hence, the correct answer is “Option 1”.

Logic followed here is,

Hence, the correct answer is “Option 4”.

Pattern followed here is,

Hence, the correct answer is “Option 2”.

BODMAS Table: 

Given expression: 147 + 28 ÷ 4 × 391 − 23

After replacing the signs:

= 147 − 28 × 4 + 391 ÷ 23

= 147 − 28 × 4 + 391 ÷ 23

= 147 − 112 + 17

= 147 − 112 + 17

= 35 + 17

= 52

Hence, the correct answer is "Option 1".

According to the given information,

To reach point A again, he should drive 15 - (8 + 4) = 3 km in West direction.

Hence, the correct answer is “Option 1”.

Logic:

(1^st number × same number) = 2^nd number

(2^nd number × 2) = 3^rd number

(3^rd number + 25) = 4^th number

Now,

For, 5 – 25 – 50 – 75

⇒ (5 × 5) = 25

⇒ (25 × 2) = 50

⇒ (50 + 25) = 75

For, 9 – 81 – 162 – 187

⇒ (9 × 9) = 81

⇒ (81 × 2) = 162

⇒ (162 + 25) = 187

Similarly, 

Option 2) 6 – 36 – 72 – 97

⇒ (6 × 6) = 36 

⇒ (36 × 2) = 72 

⇒ (72 + 25) = 97 

Hence, the correct answer is "Option 2".

Statement:

During the monsoon season, green leafy vegetables become more susceptible to microbes due to the presence of dust, wet soil, and worms.

**Analysis of

Courses of Action:

**

I) Salads should always be consumed only after boiling them. - Not logical  (Salads are generally eaten raw, and the statement does not suggest boiling as a necessary or practical solution.)

II) Leafy vegetables should be avoided during the monsoon season. - Logical (Since they are more prone to contamination, avoiding them is a reasonable precaution.)

Only II follows.

Hence, the correct answer is “Option 2”.

Given : (Left) OPT SEW DAY BYE (Right)

Second word from right  = DAY

Second letter = A

First word from left = OPT

Second letter = P

Letters between A and P in English alphabetical order = 14

Hence, the correct answer is “Option 3”.

The correct answer is Water supply from dual sources in the form of snow melt and seasonal precipitation.

Key Points

• The perennial nature of the Himalayan rivers, such as the Ganga, Sindhu (Indus), and Brahmaputra, is defined by their continuous flow of water throughout the year, regardless of the season.
• This consistency is primarily due to dual sources of water: the melting of glaciers and snow during the summer months and heavy monsoon rainfall during the rainy season.
• During the peak summer, when Peninsular rivers often dry up or see a significant reduction in volume, the high temperatures trigger the melting of Himalayan glaciers, ensuring the rivers remain full.
• The Ganga originates from the Gangotri Glacier near Gaumukh in the Uttarkashi district of Uttarakhand. Its perennial flow sustains the Indo-Gangetic Plain, which is one of the most fertile regions globally.
• The Sindhu (Indus) originates from the Bokhar Chu glacier in the Tibetan region near Lake Mansarovar. It is fed by some of the largest glaciers in the world outside the polar regions, such as those in the Karakoram range.
• The Brahmaputra originates from the Chemayungdung glacier in the Kailas range. It receives massive amounts of water from snowmelt and is further augmented by the world's highest rainfall zones in Assam and Meghalaya. Hence, the statement regarding dual water sources is correct.

Additional Information

• Comparison with Peninsular Rivers: Unlike Himalayan rivers, Peninsular rivers like the Godavari, Krishna, Cauvery, and Mahanadi are seasonal. They depend entirely on monsoon precipitation and lack glacial sources, causing them to shrink significantly during the summer.
• Drainage Patterns: Himalayan rivers often exhibit antecedent drainage. This means they existed before the Himalayas were fully formed and maintained their original courses by cutting deep gorges as the mountains rose.
• Erosional Activity: Because of their perennial flow and the steep gradient of the Himalayas, these rivers perform intensive erosional activity, carrying huge loads of silt and sand to the plains.
• Geographical Reach: These river systems are international; the Indus basin is shared by India, Pakistan, and China, while the Brahmaputra flows through China (Tibet), India, and Bangladesh.
• Delta Formation: The Ganga and Brahmaputra combine to form the Sundarbans Delta in West Bengal and Bangladesh, which is the largest mangrove forest and delta in the world.

Important Points

• Economic Significance: The perennial flow is vital for hydroelectric power generation. Major dams like the Bhakra-Nangal on the Sutlej and the Tehri Dam on the Bhagirathi rely on this steady water supply.
• Irrigation: Large-scale canal systems, such as the Upper Ganges Canal and the Indira Gandhi Canal, are possible only because these rivers do not dry up, supporting agriculture for millions of farmers.
• River Lengths: The Ganga is approximately 2,525 km long, the Indus is about 3,180 km, and the Brahmaputra is roughly 2,900 km.
• Tributaries: The perennial nature is also supported by large perennial tributaries. For example, the Yamuna, which joins the Ganga at Prayagraj, also originates from a glacier (Yamunotri).
• Historical Context: The Indus Valley Civilization, one of the world's earliest urban civilizations, flourished around 2500 BCE primarily due to the reliable, perennial water supply of the Sindhu river system.

The correct answer is Pallavas.

Key Points

• Mahendravarman-I was a powerful and influential ruler of the Pallava dynasty, who reigned from approximately 600 AD to 630 AD. He succeeded his father, Simhavishnu, who is credited with the revival of the Pallava power in South India.
• He was a great patron of art, architecture, and literature. He is particularly famous for introducing the rock-cut temple architecture style in the Tamil region. The Mandagapattu Tirumurti Temple contains an inscription where he describes himself as Vichitrachitta (curious-minded) for building a temple without using brick, timber, metal, or mortar. Hence, the option identifying him with the Pallavas is correct.
• Initially, Mahendravarman-I was a follower of Jainism, but he later converted to Shaivism under the influence of the famous Nayanar saint Appar (also known as Tirunavukkarasar). This conversion marked a significant shift in the religious landscape of the Pallava kingdom.
• He was a man of letters and a talented dramatist. He authored the famous Sanskrit satirical play titled Mattavilasa Prahasana (The Delight of the Drunkards), which provides insight into the social and religious conditions of the 7^th century.
• During his reign, the long-standing conflict between the Pallavas and the Chalukyas of Badami began. He faced a major invasion by the Chalukya king Pulakeshin II, which eventually led to the loss of the northern territories of the Pallava kingdom near the Vengi region.

Additional Information

• Pallava Dynasty:
• The Pallavas ruled from their capital at Kanchipuram in present-day Tamil Nadu from the 3^rd to the 9^th centuries AD. They are renowned for their Dravidian style of architecture, most notably the shore temples and Rathas at Mahabalipuram.
• Pandyas:
• The Pandyas were one of the three ancient Tamil dynasties (the others being Cholas and Cheras). They ruled primarily from Madurai and were famous for their pearl fisheries and extensive trade with the Roman Empire. Their emblem was the Fish.
• Chalukyas:
• The Chalukyas of Badami ruled the Deccan plateau (modern-day Karnataka and Andhra Pradesh) between the 6^th and 8^th centuries AD. Their capital was Vatapi. Pulakeshin II was their most famous ruler, who successfully defended his kingdom against Harshavardhana of Kannauj.
• Cholas:
• The Cholas were a Tamil dynasty that reached their zenith under the Imperial Cholas (9^th to 13^th century). Famous kings like Rajaraja Chola I and Rajendra Chola I expanded the empire to Southeast Asia. They are known for the Brihadisvara Temple and their powerful navy.

Important Points

• Titles of Mahendravarman-I: He assumed several titles reflecting his multifaceted personality, including Gunabhara (bearer of virtues), Satyasandha, Chetthakari (temple builder), and Chittakarapuli (tiger among painters).
• Cultural Legacy: He is credited with the Kudumiyamalai inscription, which is an important record regarding ancient Indian music. His reign saw the flowering of the Bhakti movement in South India.
• Succession: He was succeeded by his son, Narasimhavarman I (also known as Mamalla), who eventually defeated Pulakeshin II and took the title Vatapikonda (Conqueror of Vatapi).

The correct answer is Output method.

Key Points

• The Output method, also widely known as the Product Method or Inventory Method, calculates the National Income by identifying the total market value of all final goods and services produced within the geographical boundaries of a country during a specific financial year.
• This method focuses on the supply side of the economy. It involves summing up the Gross Value Added (GVA) across all sectors—Primary (agriculture), Secondary (manufacturing), and Tertiary (services).
• To avoid the error of Double Counting, this method only considers the value of final products and excludes intermediate goods (raw materials used in the production process). Alternatively, it calculates the value added at every stage of production.
• The total value obtained is termed as Gross Domestic Product (GDP) at Market Prices. To derive the National Income (NNP at Factor Cost), adjustments for Depreciation, Net Indirect Taxes, and Net Factor Income from Abroad (NFIA) are made.
• The Output method is particularly useful for analyzing the sectoral contribution to the economy and identifying which industry is driving economic growth.

Additional Information

• Expenditure Method:
• This approach measures National Income by summing all final expenditures incurred by individuals, firms, and the government within an accounting year.
• The formula used is GDP = C + I + G + (X - M), where C is Private Consumption, I is Investment, G is Government Spending, and (X - M) represents Net Exports.
• It reflects the demand side of the economy and is frequently used in countries like the USA and India for GDP estimation.
• Income Method:
• This method calculates National Income from the perspective of factor payments. It sums the incomes earned by the factors of production: Land (Rent), Labour (Wages/Salaries), Capital (Interest), and Entrepreneurship (Profit).
• In India, it is also called the Factor Cost Method. It includes Compensation of Employees, Operating Surplus, and Mixed Income of the self-employed.
• Transfer payments like pensions, scholarships, and lottery winnings are excluded because they do not reflect productive activity.
• Value Added Method:
• While often used synonymously with the Output method, the Value Added Method specifically refers to the difference between the Value of Output and the Value of Intermediate Consumption.
• It helps in tracking the incremental value added by each firm or enterprise in the production chain.

Important Points

• In India, the Central Statistics Office (CSO), now merged into the National Statistical Office (NSO) under the Ministry of Statistics and Programme Implementation (MoSPI), is responsible for the measurement of National Income.
• The base year for calculating Real GDP in India was revised to 2011-2012 to provide a more accurate picture of the economic structure.
• The first scientific estimate of National Income in India was prepared by Dr. V.K.R.V. Rao in 1931-32, while the official National Income Committee was formed in 1949 under the chairmanship of P.C. Mahalanobis.
• National Income is technically defined as Net National Product (NNP) at Factor Cost. It excludes Indirect Taxes and includes Subsidies provided by the government.

The correct answer is Parliament of India.

Key Points

• Article 2 of the Constitution of India grants the Parliament the exclusive power to admit into the Union, or establish, new states on such terms and conditions as it thinks fit. This power specifically refers to the admission of territories that were not previously part of the Indian Union.
• Under the constitutional framework, the Parliament acts as the supreme legislative authority for the country. Article 2 provides two distinct powers: the power to admit into the Union states already in existence and the power to establish new states that were not in existence before.
• While Article 2 deals with the admission or establishment of states that are external to the existing Union, Article 3 deals with the internal reorganization of the existing states within the Union of India.
• The Parliament of India consists of the President and the two houses—Rajya Sabha (Council of States) and Lok Sabha (House of the People). However, the specific power to legislate for the admission of new states rests with the Parliament as a legislative body.
• The Election Commission of India is a permanent and independent body established by Article 324 to ensure free and fair elections. It has no constitutional authority to admit or create new states. Hence, option A is incorrect.
• The President of India is the formal head of the executive. Although the President's recommendation is required to introduce a bill for the reorganization of states under Article 3, the actual power to "admit" or "establish" a state resides with Parliament via legislation. Hence, option C is incorrect.
• The Prime Minister of India is the head of the government and leads the Council of Ministers. While the Prime Minister and the Cabinet may initiate the policy decision to admit a new state, they do not possess the legal power to do so without an Act of Parliament. Hence, option D is incorrect.

Additional Information

• Article 1 of the Constitution: India, that is Bharat, is described as a "Union of States." Currently, the Union of India comprises 28 states and 8 Union Territories. The names of states and territories are mentioned in the First Schedule of the Constitution.
• Admission of Sikkim: A notable historical application of Article 2 (and a special Article 2A) was the admission of Sikkim. Through the 35^th Constitutional Amendment Act (1974), Sikkim was given the status of an "associate state." Later, via the 36^th Constitutional Amendment Act (1975), it was admitted as a full-fledged state of the Union of India.
• Article 3 - Internal Reorganization: This article empowers Parliament to:
• Form a new state by separation of territory from any state or by uniting two or more states.
• Increase or diminish the area of any state.
• Alter the boundaries or the name of any state.
• Supreme Court Rulings: The Supreme Court in the Berubari Union case (1960) held that the power of Parliament to diminish the area of a state (under Article 3) does not cover the cession of Indian territory to a foreign country. Such cession can only be done by amending the Constitution under Article 368.
• Simple Majority: Laws made for the admission or establishment of new states under Article 2 and the formation of new states or alteration of boundaries under Article 3 are not considered amendments of the Constitution under Article 368. This means such laws can be passed by a simple majority and by the ordinary legislative process.

Important Points

• President's Role in Reorganization: For a bill under Article 3, the President must refer the bill to the State Legislature concerned for expressing its views within a specified period. However, the Parliament is not bound by the views of the State Legislature and may either accept or reject them.
• Evolution of States: Since 1950, the map of India has changed significantly. The States Reorganisation Act, 1956 was a major milestone that created 14 states and 6 union territories on a linguistic basis. Recent examples include the formation of Telangana in 2014 and the reorganization of Jammu and Kashmir into two Union Territories in 2019.
• Federalism in India: The power of Parliament to admit or change states highlights the "destructible" nature of the states within an "indestructible" Union, which is a unique feature of Indian Federalism.

The correct answer is Mecca.

Key Points

• The direction in which Muslims face during their ritual prayers (Salat) is known as the Qibla. This direction is fixed towards the city of Mecca, specifically towards the Kaaba, which is located within the Great Mosque of Mecca (Al-Masjid al-Haram) in Saudi Arabia.
• Facing the Qibla is a mandatory condition (Shart) for the validity of the five daily prayers performed by believers across the world.
• Originally, for the first few years of the Islamic mission in Medina, the direction of prayer was towards Jerusalem (Masjid al-Aqsa). This was later changed by divine revelation.
• The Kaaba is considered the holiest site in Islam and is believed to have been rebuilt by the Prophet Ibrahim (Abraham) and his son Ismail (Ishmael).
• In mosques, the direction of Mecca is indicated by a semicircular niche in the wall known as the Mihrab, ensuring that the Imam and the congregation face the correct way during communal worship.

Additional Information

• The Kaaba: It is a cuboid-shaped building made of granite, covered with a black silk cloth known as the Kiswa. It is not an object of worship itself but acts as a focal point for unity among Muslims worldwide.
• Jerusalem: It is often referred to as the "First Qibla" (Qibla-e-Awwal). While Muslims no longer face it for Salat, it remains the third holiest city in Islam due to the Isra and Mi'raj (the Night Journey) of Prophet Muhammad.
• Medina: This is the second holiest city in Islam, located in Saudi Arabia. It is the site of the Al-Masjid an-Nabawi (The Prophet's Mosque) and the burial place of the Prophet. While significant, it is not the direction of prayer.
• Baghdad: Historically, Baghdad in Iraq was the capital of the Abbasid Caliphate and a major center of the Islamic Golden Age. However, it holds no ritual significance regarding the direction of Salat.
• Hajj and Umrah: During these pilgrimages, millions of Muslims travel to Mecca to perform rituals around the Kaaba, including the Tawaf (circumambulation).

Important Points

• Date of Change: The shift of the Qibla from Jerusalem to Mecca occurred in the year 624 CE, approximately 17 months after the Prophet's Hijra (migration) to Medina.
• Quranic Reference: The command to change the direction of prayer is mentioned in Surah Al-Baqarah (Chapter 2, Verse 144) of the Holy Quran.
• Masjid al-Qiblatayn: Located in Medina, the "Mosque of the Two Qiblas" is where the congregation historically changed their direction from Jerusalem to Mecca mid-prayer following the revelation.
• Scientific Impact: The necessity to determine the Qibla accurately from distant geographical locations led to significant advancements in Spherical Trigonometry, Mathematics, and Geography by Muslim scientists during the Middle Ages.
• Modern Tools: Today, Muslims use specialized Qibla compasses, mobile applications, and GPS technology to find the precise direction of Mecca from any point on Earth.

The correct answer is Rajasthan.

Key Points

• The Great Indian Bustard (Ardeotis nigriceps) is primarily found in the state of Rajasthan, which is home to the largest surviving population of the species in the world.
• It was officially designated as the State Bird of Rajasthan in 1981 and is locally referred to as Godawan.
• The Desert National Park, located in the Jaisalmer and Barmer districts, serves as the most critical habitat and breeding ground for this species. Hence, the option B is correct.
• The bird is listed as Critically Endangered on the IUCN Red List, with a total global population estimated at fewer than 150 individuals.
• It is accorded the highest level of protection under Schedule I of the Wildlife (Protection) Act, 1972, in India.

Additional Information

• Physical Features: The Great Indian Bustard is among the heaviest flying birds in the world. An adult can stand about 1 meter tall and weigh up to 15 kilograms. It is characterized by a horizontal body and long bare legs, giving it an ostrich-like appearance.
• Habitat Preferences: These birds are found in arid and semi-arid grasslands, open country with thorn scrub, and tall grass interspersed with cultivation. They generally avoid irrigated areas and dense forests.
• Geographic Distribution: While Rajasthan is the stronghold, small isolated populations have historically been found in Gujarat, Maharashtra, Karnataka, and Andhra Pradesh. It has become locally extinct in many other parts of its former range across India and Pakistan.
• Diet and Behavior: They are omnivorous, feeding on a variety of items including insects (like grasshoppers and beetles), seeds, grains, and small rodents or reptiles. They are mostly terrestrial birds, preferring to walk or run rather than fly.

Important Points

• Major Threats: The primary threats to their survival include habitat loss due to agricultural expansion, electrocution by high-voltage overhead power lines, and predation of eggs by feral dogs and foxes.
• Conservation Initiatives: The Government of Rajasthan launched Project Great Indian Bustard in 2013 to strengthen conservation efforts. Additionally, a Conservation Breeding Center was established at Sam in Jaisalmer in 2019 as a joint venture between the Wildlife Institute of India (WII) and the state forest department.
• Global Recognition: The Great Indian Bustard was the mascot for the 13^th Conference of Parties (COP13) of the Convention on the Conservation of Migratory Species (CMS) held in Gandhinagar, India, in 2020, where it was nicknamed 'Gibi'.
• Judicial Intervention: In 2021, the Supreme Court of India passed a landmark order directing that all overhead power lines in the priority and potential habitats of the bird should be moved underground to prevent further fatalities.

The correct answer is Peas (Pisum sativum).

Key Points

• Gregor Johann Mendel, widely recognized as the Father of Genetics, conducted his historic experiments on heredity using the Garden Pea plant, scientifically known as Pisum sativum. Hence, option D is the correct answer.
• His experiments were carried out over a period of seven years, specifically from 1856 to 1863, in the garden of the Augustinian St Thomas's Abbey in Brno (then part of the Austrian Empire, now in the Czech Republic).
• Mendel chose the pea plant because it has distinct contrasting characters, is easy to grow, has a short life cycle (annual plant), and allows for controlled pollination (both self-pollination and cross-pollination).
• He studied seven pairs of contrasting traits, including stem height (tall vs. dwarf), flower color (violet vs. white), flower position (axial vs. terminal), pod shape (inflated vs. constricted), pod color (green vs. yellow), seed shape (round vs. wrinkled), and seed color (yellow vs. green).
• The results of his work were published in 1866 under the title "Experiments on Plant Hybridization" in the Proceedings of the Natural History Society of Brünn.

Additional Information

• Cotton (Gossypium herbaceum): This is a major fiber crop belonging to the Malvaceae family. While it is significant in agricultural genetics today, it was not the subject of Mendel's primary heredity studies. Hence, statement A is incorrect.
• Mustard (Brassica campestris): This plant belongs to the Brassicaceae family and is primarily used for oilseed production. It was not used by Mendel for his laws of inheritance. Hence, statement B is incorrect.
• Maize (Zea mays): Also known as Corn, it is a staple food and belongs to the Poaceae family. While used extensively in modern cytogenetics (notably by Barbara McClintock), Mendel did not use it for his foundational research. Hence, statement C is incorrect.
• Mendel's Laws of Inheritance: Through his work on peas, Mendel proposed three fundamental laws: the Law of Dominance (one trait masks another), the Law of Segregation (alleles separate during gamete formation), and the Law of Independent Assortment (genes for different traits are inherited independently).
• Monohybrid and Dihybrid Crosses: Mendel used monohybrid crosses (studying one trait at a time) to determine the 3:1 ratio in the F2 generation, and dihybrid crosses (studying two traits) to determine the 9:3:3:1 ratio.

Important Points

• Rediscovery of Mendel's Work: Mendel's findings remained largely ignored until 1900, long after his death in 1884. His work was independently rediscovered by three scientists: Hugo de Vries (Holland), Carl Correns (Germany), and Erich von Tschermak (Austria).
• The Term 'Gene': Mendel used the term "Factors" (elements) to describe the units of inheritance. The word "Gene" was coined later by Wilhelm Johannsen in 1909.
• Statistical Analysis: Mendel was one of the first biologists to apply mathematical logic and statistical analysis to biological problems, which allowed him to predict the outcome of crosses with high numerical accuracy.
• Bisexual Nature: The pea plant is bisexual (having both male and female reproductive organs in the same flower), which made it easier for Mendel to perform emasculation and artificial cross-pollination to create hybrids.

The correct answer is Article 108.

Key Points

• Article 108 of the Constitution of India provides for a joint sitting of both the Lok Sabha and the Rajya Sabha to resolve a deadlock over the passage of a Ordinary Bill.
• A deadlock is deemed to have occurred if a bill passed by one House is rejected by the other House, the Houses have finally disagreed as to the amendments to be made in the bill, or more than six months elapse from the date of the reception of the bill by the other House without the bill being passed by it.
• The power to summon a joint sitting rests with the President of India. The President notifies their intention to summon the Houses to meet in a joint sitting for the purpose of deliberating and voting on the bill. Hence, Article 108 is the correct constitutional provision.
• The Speaker of the Lok Sabha presides over a joint sitting. In the absence of the Speaker, the Deputy Speaker of the Lok Sabha presides. If the Deputy Speaker is also absent, the Deputy Chairman of the Rajya Sabha takes the chair. It is important to note that the Chairman of the Rajya Sabha (Vice-President) never presides over a joint sitting.
• The bill in a joint sitting is passed by a simple majority of the total number of members of both Houses present and voting. This usually gives the Lok Sabha an advantage due to its larger membership.

Additional Information

• Article 123: This article deals with the legislative power of the President to promulgate Ordinances during the recess of Parliament. An ordinance has the same force and effect as an Act of Parliament but is a temporary measure.
• Article 111: This article pertains to the Assent to Bills. When a bill has been passed by the Houses of Parliament, it is presented to the President, who shall declare either that he assents to the bill or that he withholds assent therefrom. The President may also return the bill (if it is not a Money Bill) for reconsideration.
• Article 110: This article defines a Money Bill. A bill is deemed to be a Money Bill if it contains only provisions dealing with taxation, borrowing of money by the government, Consolidated Fund of India, etc. The Speaker of the Lok Sabha has the final authority to decide whether a bill is a Money Bill or not.
• Joint Sitting Exceptions: It is crucial to remember that a joint sitting cannot be summoned for Money Bills or Constitution Amendment Bills under Article 368. In the case of Money Bills, the Lok Sabha has overriding powers, and for Constitution Amendment Bills, each House must pass the bill separately with the prescribed special majority.

Important Points

• Since 1950, the provision of a joint sitting has been invoked only three times in the history of Indian Parliament to resolve deadlocks.
• The first instance was for the Dowry Prohibition Bill, 1959, where the joint sitting was held in May 1961.
• The second instance was for the Banking Service Commission (Repeal) Bill, 1977, with the joint sitting held in May 1978.
• The third and most recent instance was for the Prevention of Terrorism Bill, 2002, where the joint sitting was held in March 2002.
• The rules of procedure for a joint sitting are formulated by the President in consultation with the Chairman of the Rajya Sabha and the Speaker of the Lok Sabha.

The correct answer is Chola.

Key Points

• The Chola Dynasty was one of the longest-ruling dynasties in world history, establishing a formidable empire in South India that reached its absolute zenith between 1000 AD and 1200 AD.
• During this period, specifically under the reigns of Rajaraja Chola I (985–1014 AD) and his son Rajendra Chola I (1014–1044 AD), the empire expanded beyond the Indian subcontinent, reaching Sri Lanka, the Maldives, and parts of Southeast Asia.
• The Cholas were renowned for their centralized administration and a highly organized system of local self-government. The Uttiramerur inscriptions provide detailed evidence of how village assemblies, known as Sabhas, functioned during this era.
• They possessed a powerful Navy, which allowed them to control the trade routes in the Indian Ocean and launch successful maritime expeditions against the Srivijaya Empire (modern-day Indonesia) in 1025 AD.
• The dynasty is also famous for its architectural marvels, most notably the Brihadisvara Temple in Thanjavur, which was completed in 1010 AD and is a UNESCO World Heritage Site.

Additional Information

• Sangama Dynasty (1336 AD – 1485 AD):
• This was the first dynasty of the Vijayanagara Empire, founded by Harihara I and Bukka Raya I in the 14^th century. It does not fall within the 1000–1200 AD primary peak period of the Cholas.
• Kadamba Dynasty (345 AD – 525 AD):
• Founded by Mayurasharma, this was an ancient royal family of Karnataka that ruled from Banavasi. Their power had significantly diminished long before the 11^th century.
• Chalukya Dynasty:
• The Western Chalukyas (Kalyani Chalukyas) were indeed active between 973 AD and 1189 AD in the Deccan region. However, the Cholas are the definitive answer for the "South India" (Tamil region) empire that dominated the socio-political landscape of the 1000–1200 AD era.
• Chola Economy:
• The economy was primarily agrarian, supported by an extensive network of irrigation tanks and canals built across the Cauvery Delta. Trade with China and the Arab world also contributed significantly to their wealth.

Important Points

• Art and Literature: The Chola period is considered the Golden Age of Tamil culture. Significant works like the Kamba Ramayanam were composed during this time. The Chola Bronzes, particularly the Nataraja (dancing Shiva) statues, are world-famous for their craftsmanship.
• Imperial Titles: Rajendra I assumed the title Gangaikonda Chola (the Chola who conquered the Ganges) after his successful expedition to North India, and he established a new capital named Gangaikondacholapuram.
• Social Structure: The society was divided into Valangai (Right-hand) and Idangai (Left-hand) factions, and the caste system was prevalent, though temple-centered activities provided a common social ground for various communities.

The correct answer is Thiruvalluvar.

Key Points

• The statement "Those who till the soil live in right; the rest of the chain eat the bread of their shelter" is a profound observation by the Tamil poet-philosopher Thiruvalluvar. It is found in his magnum opus, the Tirukkural, specifically in the chapter titled Uzhavu (Agriculture).
• Thiruvalluvar emphasizes that agriculture is the most fundamental and honorable profession. According to him, farmers are the linchpin of the world because they support all other people who cannot till the soil but depend on it for sustenance.
• The Tirukkural consists of 1,330 couplets (known as Kurals) organized into 133 chapters. The quote reflects the economic and social philosophy of ancient Tamil Nadu, highlighting the self-sufficiency of the agrarian community.
• In the context of the Tirukkural, the ploughman (the one who tills) is considered the only one who truly lives an independent life of dignity, while others are seen as dependents on the food produced by the farmer.

Additional Information

• Thiruvalluvar: He is a celebrated Tamil saint and author who likely lived between the 4^th century BCE and the 6^th century CE. He is regarded as a cultural icon in India, particularly in Tamil Nadu, and his work is considered a "Universal Veda" due to its non-denominational and ethical teachings.
• Tirukkural Structure: The work is divided into three sections: Aram (Virtue/Ethics), Porul (Wealth/Polity), and Inbam (Love). The discussion on Agriculture falls under Porutpal (the section on Wealth), signifying that farming is the primary source of a nation's prosperity.
• Geographical Landmark: A massive 133-foot tall statue of Thiruvalluvar stands at Kanyakumari, at the southernmost tip of India. The height represents the 133 chapters of the Tirukkural. It was designed by the renowned sculptor V. Ganapati Sthapati and inaugurated on January 1, 2000.
• Thiruvalluvar Day: The government of Tamil Nadu celebrates Thiruvalluvar Day annually on January 15 or January 16, as part of the Pongal (harvest festival) celebrations, to honor his contributions to humanity.
• Universal Reach: The Tirukkural has been translated into more than 40 languages, including Latin, English, and French, making it one of the most translated non-religious works in the world.

Important Points

• Comparison with other figures: While Mahatma Gandhi frequently spoke about the importance of villages and farmers ("The soul of India lives in its villages"), the specific quote regarding "those who till the soil" being the "linchpin" or the "only ones living in right" is uniquely attributed to Thiruvalluvar.
• Socio-Economic Relevance: The teachings of Thiruvalluvar regarding Uzhavu (Agriculture) remain relevant in modern India, where a large percentage of the population is still involved in farming activities. It serves as a reminder of the food security provided by the unorganized sector of farmers.
• Historical Context: During the Sangam period and post-Sangam era, Tamil literature placed immense value on the land and the tillers. The Tirukkural codified these values into a moral and social guide for kings and citizens alike.

The correct answer is a military communication satellite enhancing secure naval and defence communication networks.

Key Points

• CMS-03, also known by its project designation GSAT-7R, is a next-generation military communication satellite developed by the Indian Space Research Organisation (ISRO). Its primary objective is to provide dedicated and secure communication for the Indian Navy.
• The satellite is intended to act as a replacement for the aging GSAT-7, which was launched in September 2013. GSAT-7, nicknamed Rukmini, was India’s first dedicated satellite for defence applications, specifically serving maritime security needs.
• CMS-03 is designed to enhance the Network Centric Operations of the Indian Armed Forces. It facilitates real-time communication between warships, submarines, maritime patrol aircraft, and shore-based facilities across the vast Indian Ocean Region (IOR).
• The satellite operates across multiple frequency bands, including UHF, S-band, C-band, and Ku-band, ensuring high-speed and jam-resistant data transfer. This makes the primary design focused on defence communication rather than civil earth observation or navigation. Hence, the option related to military communication is correct.
• The Ministry of Defence approved the project with a budget of approximately  ₹1,589 crore, highlighting its strategic importance for national security.

Additional Information

• The GSAT-7 Series Evolution:
• The GSAT-7 (Rukmini) was the first dedicated satellite for the Navy, providing a coverage footprint of nearly 2,000 nautical miles in the Indian Ocean.
• GSAT-7A, launched in December 2018, is often called the "Angry Bird" satellite. It is dedicated to the Indian Air Force (IAF) and enables communication between ground stations, Airborne Early Warning and Control (AWACS) aircraft, and Unmanned Aerial Vehicles (UAVs).
• GSAT-7B is an upcoming satellite approved for the Indian Army, which will fulfill the long-standing need for dedicated tactical communication for land-based forces.
• ISRO’s CMS Nomenclature:
• ISRO has transitioned to the CMS (Communication Satellite) naming series for its newer missions. CMS-01 (formerly GSAT-12R) was launched in 2020 to replace GSAT-12.
• CMS-02 (formerly GSAT-24) was launched in 2022 for DTH (Direct-to-Home) applications. CMS-03 continues this series but focuses on strategic military requirements.
• Launch Vehicle and Orbit:
• The satellite is typically launched into a Geostationary Transfer Orbit (GTO) using the GSLV Mk II or the more powerful LVM3 (Launch Vehicle Mark 3).
• Once operational, it resides in the Geostationary Orbit (GEO) at an altitude of approximately 35,786 kilometers, staying fixed relative to a point on India.

Important Points

• Strategic Autonomy: By developing indigenous military satellites like CMS-03, India reduces its reliance on foreign satellite networks, which is critical during times of conflict to prevent jamming or data interception by adversaries.
• Data and Connectivity: The satellite allows for the integration of various naval sensors, helping in over-the-horizon targeting and improving the Maritime Domain Awareness (MDA) of the country.
• Project Scale: The GSAT-7R mission is a significant part of the Buy (Indian-IDDM) category under the Defence Acquisition Procedure, promoting Atmanirbhar Bharat in space technology.

The correct answer is Yamas and Niyamas.

Key Points

• The Eightfold Path of Yoga, also known as Ashtanga Yoga, was systematically compiled by the sage Patanjali in the Yoga Sutras around 2^nd Century BCE. It provides a structural framework for spiritual growth and attaining the ultimate goal of Samadhi.
• Yamas represent the first limb and consist of universal ethical disciplines or "restraints" that govern our interaction with the external world. There are five Yamas: Ahimsa (non-violence), Satya (truthfulness), Asteya (non-stealing), Brahmacharya (continence/right use of energy), and Aparigraha (non-greed/non-possessiveness).
• Niyamas constitute the second limb, focusing on internal disciplines and spiritual observances. These include: Saucha (cleanliness/purity), Santosha (contentment), Tapas (disciplined use of energy/austerity), Svadhyaya (self-study), and Ishvara Pranidhana (surrender to a higher power).
• Together, Yamas and Niyamas form the moral and ethical foundation of the yogic journey. Without mastering these disciplines, the practitioner cannot successfully progress through the more advanced stages of meditation and breath control.

Additional Information

• The Remaining Six Limbs of Ashtanga Yoga:
• Asana (3^rd Limb): Refers to the physical postures designed to purify the body and provide physical stability for long periods of meditation.
• Pranayama (4^th Limb): Involves breath control and the regulation of Prana (life force) to calm the mind and nervous system.
• Pratyahara (5^th Limb): The withdrawal of the senses from external objects, turning the attention inward to prepare for concentration.
• Dharana (6^th Limb): The practice of focused concentration on a single point or object to prevent the mind from wandering.
• Dhyana (7^th Limb): An uninterrupted flow of meditation where the observer and the object of meditation begin to merge.
• Samadhi (8^th Limb): The final stage of enlightenment or union with the divine, characterized by a state of pure consciousness and bliss.
• Dharma and Artha: These are part of the Purusharthas (four goals of human life) in Indian philosophy, which also include Kama (desire) and Moksha (liberation). Dharma refers to righteousness/duty, while Artha refers to prosperity/economic values.
• Shruti and Smriti: These are the two primary categories of Hindu scriptures. Shruti (that which is heard) includes the Vedas and Upanishads, while Smriti (that which is remembered) includes the Puranas, Itihasas (Ramayana/Mahabharata), and Dharmashastras.

Important Points

• Karma and Bhakti: These represent different Paths of Yoga rather than steps in the Eightfold Path. Karma Yoga is the path of selfless action, while Bhakti Yoga is the path of devotion and love toward the divine.
• Application of Yamas: In modern contexts, Ahimsa was significantly popularized by Mahatma Gandhi during the Indian Independence Movement as a tool for non-violent resistance.
• Function of Yoga Sutras: Patanjali did not invent yoga but codified existing practices into 196 Sutras, making it a definitive guide for Raja Yoga.
• Universal Nature: The Yamas are often called the Mahavratas (Great Vows) because they are intended to be practiced regardless of location, time, or circumstance.

The correct answer is Haryana.

Key Points

• The state of Haryana is the host for the first-ever Global Women’s Kabaddi League (GPKL), which is scheduled to take place in 2024. This initiative represents a significant step in promoting women's sports in India. Hence, the statement is correct.
• The league is officially named the Global Pravasi Women’s Kabaddi League (GPKL), emphasizing the participation of the Indian diaspora along with international athletes. Hence, the statement is correct.
• The matches are set to be organized at the Tau Devi Lal Stadium located in Panchkula, Haryana, which is a premier sports complex in Northern India. Hence, the statement is correct.
• The primary objective of the GPKL 2024 is to provide a professional platform for female Kabaddi players from across the globe, enhancing the international footprint of this indigenous Indian sport. Hence, the statement is correct.
• This league is supported by the Haryana Kabaddi Association and various global pravasi organizations to ensure the participation of 15 or more countries, showcasing the global appeal of the game. Hence, the statement is correct.

Additional Information

• Haryana as a Sports Hub:
• Haryana is often referred to as the sports capital of India because it produces a disproportionately high number of international athletes, particularly in Wrestling, Boxing, and Kabaddi.
• The state government provides significant incentives under its Sports Policy, offering cash awards and government jobs to medal winners in the Olympics, Commonwealth Games, and Asian Games.
• Location: Haryana is located in North India, surrounding the national capital Delhi on three sides.
• The Sport of Kabaddi:
• Kabaddi is an ancient contact sport that originated in Ancient India. It is played in two main styles: the Standard Style (played on a rectangular court) and the Circle Style (played on a circular field).
• It is the State Game of Indian states like Haryana, Punjab, Tamil Nadu, and Andhra Pradesh.
• At the international level, the International Kabaddi Federation (IKF) is the governing body responsible for overseeing the Kabaddi World Cup.
• Global Pravasi Involvement:
• The term Pravasi refers to the Non-Resident Indians (NRIs) and Persons of Indian Origin (PIOs).
• The GPKL aims to reconnect the Indian diaspora with their cultural roots through sports. Teams are expected to represent countries with significant Indian populations, such as the USA, UK, Canada, Australia, and South Africa.

Important Points

• Women's Empowerment in Sports: The launch of GPKL follows the success of the Women’s Premier League (WPL) in cricket, aiming to provide similar financial stability and fame to women kabaddi players.
• Pro Kabaddi League (PKL) Influence: The massive success of the Pro Kabaddi League, launched in 2014, paved the way for professionalizing the sport. While PKL is primarily male-dominated, GPKL fills the vacuum for a dedicated global women's league.
• Key Figures: High-profile personalities and athletes from Haryana, such as Geeta Phogat and Sakshi Malik, have historically inspired women in the state to take up combat and contact sports.
• Economic Impact: Hosting such global events boosts sports tourism in the region and encourages the development of world-class infrastructure in cities like Panchkula and Gurugram.

The correct answer is Interfaith harmony and dialogue among diverse religious communities in India.

Key Points

• The National Commission for Minorities (NCM) organized the Sarvadharma Samvad (Interfaith Dialogue) in November 2024 to reinforce the spirit of communal harmony and mutual coexistence in India.
• The primary objective of this program was to provide a common platform for spiritual leaders and representatives from different faiths to discuss shared values and resolve misunderstandings through constructive dialogue. Hence, statement B is correct.
• The event emphasized the ancient Indian philosophy of Vasudhaiva Kutumbakam, which translates to "the world is one family," highlighting the importance of universal brotherhood and peace.
• During the dialogue, Shri Iqbal Singh Lalpura, the Chairman of the National Commission for Minorities, underlined the role of religious leaders in guiding their followers toward national integration and social stability.
• The dialogue focused on fostering tolerance and respect among the six notified minority communities—Muslims, Christians, Sikhs, Buddhists, Parsis, and Jains—alongside the majority community.

Additional Information

• National Commission for Minorities (NCM):
• The NCM is a statutory body established under the National Commission for Minorities Act, 1992.
• It functions under the Ministry of Minority Affairs, Government of India, and is tasked with safeguarding the rights and interests of minorities as enshrined in the Constitution of India.
• The commission consists of a Chairperson, a Vice-Chairperson, and five Members, all nominated by the Central Government from among persons of eminence and integrity.
• Constitutional Provisions for Minorities:
• Article 25 to 28: Provide for the Right to Freedom of Religion, ensuring every citizen has the right to practice and propagate their religion.
• Article 29: Protects the interests of minorities by giving them the right to conserve their distinct language, script, or culture.
• Article 30: Grants minorities (whether based on religion or language) the right to establish and administer educational institutions of their choice.
• Minority Communities in India:
• The Union Government initially notified five communities—Muslims, Christians, Sikhs, Buddhists, and Zoroastrians (Parsis)—as minority communities in October 1993.
• In January 2014, the Jain community was also added to the list of notified minority communities.

Important Points

• Role in Nation Building: Interfaith dialogues like Sarvadharma Samvad are pivotal in 2024 to counter radicalization and promote a culture of peace, which is essential for achieving the Viksit Bharat @2047 goal.
• Social Issues: These programs often extend beyond religious discussions to address common social challenges such as drug addiction, poverty alleviation, environmental sustainability, and women’s empowerment.
• International Context: Such initiatives align with United Nations guidelines on intercultural dialogue and human rights, showcasing India's pluralistic heritage to the global community.
• Administrative Redressal: Apart from dialogue, the NCM actively looks into complaints regarding the deprivation of rights and safeguards for minorities, acting as a quasi-judicial body in certain aspects.

The correct answer is Raja Ram Mohan Roy.

Key Points

• Raja Ram Mohan Roy was a pioneering social reformer who led a relentless crusade against the inhuman practice of Sati, where a widow was immolated on her husband's funeral pyre.
• In December 1829, his tireless advocacy and petitioning resulted in the enactment of the Bengal Sati Regulation (Regulation XVII), which declared the practice of Sati illegal and punishable by criminal courts.
• He founded the Brahmo Samaj in 1828 in Calcutta, which served as a platform to challenge orthodox Hindu customs and promote monotheism and social equality.
• He collaborated extensively with the then Governor-General of India, Lord William Bentinck, providing scriptural evidence to prove that the practice of Sati had no mandatory religious sanction in ancient Hindu texts.
• His motivation for this reform was deeply personal; he had witnessed the forced immolation of his own sister-in-law in 1811, which drove him to dedicate his life to the protection of women's rights.

Additional Information

• Raja Ram Mohan Roy (1772–1833):
• Known as the "Father of the Indian Renaissance" and the "Maker of Modern India".
• He was a polyglot who mastered languages like Sanskrit, Persian, Arabic, English, and Greek.
• He published journals such as 'Sambad Kaumudi' (Bengali) and 'Mirat-ul-Akbar' (Persian) to educate the public on social issues.
• The title of 'Raja' was conferred upon him by the Mughal Emperor Akbar II in 1830.
• Atmaram Pandurang (1823–1898):
• He was a physician and social reformer who founded the Prarthana Samaj in 1867 in Bombay.
• His work focused on religious and social reform in Maharashtra, emphasizing widow remarriage, the abolition of child marriage, and women's education.
• Swami Vivekananda (1863–1902):
• A key figure in the introduction of Indian philosophies of Vedanta and Yoga to the Western world.
• He founded the Ramakrishna Mission in 1897 to engage in social service and humanitarian work.
• He is famous for his groundbreaking speech at the Parliament of the World's Religions in Chicago in 1893.
• B.R. Ambedkar (1891–1956):
• Known as the "Chief Architect of the Indian Constitution" and a champion for Dalit rights.
• He served as India's first Law Minister and led the movement against untouchability, organizing the Mahad Satyagraha in 1927.
• He was posthumously awarded the Bharat Ratna in 1990.

Important Points

• Legislative Impact: The Sati Abolition Act of 1829 was initially applicable only to the Bengal Presidency but was extended to the Madras and Bombay Presidencies in 1830.
• Educational Reforms: Raja Ram Mohan Roy played a crucial role in establishing the Hindu College in 1817 and the Vedanta College in 1825 to provide Western education combined with Indian learning.
• International Presence: He was the first educated Indian to travel to England (in 1831) to advocate for Indian rights and ensure the British Parliament did not overturn the Sati ban.

The correct answer is Article 16(1) and 16(2).

Key Points

• Article 16 of the Constitution of India provides for equality of opportunity in matters of public employment. It is a specific application of the general right to equality enshrined in Article 14.
• Article 16(1) explicitly states that there shall be equality of opportunity for all citizens in matters relating to employment or appointment to any office under the State. This ensures that every citizen has an equal right to apply for government jobs and be considered on merit. Hence, the provision under 16(1) is correct regarding the guarantee of opportunity.
• Article 16(2) prohibits discrimination in respect of any employment or office under the State on grounds only of religion, race, caste, sex, descent, place of birth, residence, or any of them. It expands the scope of non-discrimination specifically for the public sector. Hence, the provision under 16(2) is correct regarding the prohibition of discrimination in employment.
• Together, Article 16(1) and 16(2) form the core guarantee of equality in the civil service and government sectors for Indian citizens. Unlike Article 14, which applies to "any person," Article 16 is available only to citizens of India.
• The term "State" for the purpose of this article includes the Government and Parliament of India, the Government and Legislature of each of the States, and all local or other authorities within the territory of India.

Additional Information

• Article 15: Prohibition of Discrimination
• Article 15(1) directs the State not to discriminate against any citizen on grounds only of religion, race, caste, sex, or place of birth. This is a general provision covering all aspects of state interaction.
• Article 15(3) allows the State to make any special provision for women and children. This acts as an enabling provision for protective discrimination. Hence, Article 15 is broader and not limited solely to public employment.
• Article 18: Abolition of Titles
• Article 18(1) prohibits the State from conferring any title except military or academic distinctions.
• Article 18(2) prevents a citizen of India from accepting any title from a foreign state.
• Article 18(3) states that a person who is not a citizen but holds an office of profit or trust under the State shall not accept any title from a foreign state without the consent of the President. Hence, Article 18 is related to social equality through titles, not employment.
• Fundamental Rights Context
• These Articles fall under Part III of the Constitution (Articles 12 to 35). The Right to Equality specifically spans from Article 14 to Article 18.
• The concept of equality of opportunity aims to establish social and economic justice as mentioned in the Preamble.

Important Points

• Exceptions to Article 16: While Article 16(1) and (2) guarantee equality, clauses 16(3), 16(4), 16(4A), and 16(4B) provide exceptions.
• Article 16(3): Allows Parliament to prescribe residence as a requirement for certain jobs in a State or Union Territory.
• Article 16(4): Empowers the State to make provisions for reservation of appointments in favor of any backward class of citizens which, in the opinion of the State, is not adequately represented in the services under the State.
• Indra Sawhney Case (1992): Also known as the Mandal Case, the Supreme Court upheld 27% reservation for OBCs but stated that total reservations should not exceed 50%.
• Significant Amendments:
• The 77^th Constitutional Amendment Act, 1995, added Article 16(4A), allowing reservation in promotions for SCs and STs.
• The 81^st Constitutional Amendment Act, 2000, introduced Article 16(4B), dealing with the carry-forward rule for unfilled reserved vacancies.
• The 103^rd Constitutional Amendment Act, 2019, added Article 16(6) to provide up to 10% reservation for the Economically Weaker Sections (EWS).

The correct answer is Ahimsa.

Key Points

• Ahimsa is the most fundamental principle of Jainism, representing the absolute practice of non-violence toward all living beings. It is based on the belief that every living entity, from the smallest microorganism to complex humans, possesses a soul (Jiva) that is equal in potential. Hence, statement A is correct.
• In the context of Jain ethics, Ahimsa is not merely the absence of physical violence but extends to Kayika (action), Vachika (speech), and Manasa (thought). Practicing non-violence in thoughts and words is considered as important as avoiding physical harm.
• The doctrine was emphasized most strictly by Lord Mahavira, the 24^th Tirthankara, who lived in the 6^th Century BCE. He taught that "Ahimsa Paramo Dharma" (Non-violence is the highest religion).
• Samsara refers to the worldly cycle of birth, death, and rebirth through which a soul travels based on its Karma. While it is a core concept in Jainism, it describes the condition of the soul rather than the principle of non-violence. Hence, statement B is incorrect.
• Nirvana (or Moksha) in Jainism signifies the final liberation of the soul from the cycle of Samsara. It is the state of infinite bliss and knowledge achieved when all Karma is shed. Hence, statement D is incorrect.

Additional Information

• The Five Great Vows (Mahavratas): Ascetics in Jainism must strictly follow five vows: Ahimsa (Non-violence), Satya (Truthfulness), Asteya (Non-stealing), Brahmacharya (Chastity), and Aparigraha (Non-attachment). For laypeople, these are called Anuvratas (small vows) with less rigid standards.
• Jain Sects: Jainism is primarily divided into two major sects: the Digambara (sky-clad) and the Svetambara (white-clad). The Digambaras follow a more rigorous code of conduct, including the renunciation of clothes for monks, whereas Svetambara monks wear white garments.
• Geographical Presence: While Jainism originated in India (specifically the Magadha region of modern-day Bihar), it has a significant presence today in states like Gujarat, Rajasthan, Maharashtra, and Karnataka.
• Dietary Practices: Due to the strict adherence to Ahimsa, Jains are strictly vegetarian and avoid eating root vegetables (like potatoes, onions, and garlic) because uprooting them kills the entire plant and the microorganisms living in the soil.

Important Points

• Ratnatraya (The Three Jewels): The path to liberation in Jainism consists of Samyak Darshana (Right Faith), Samyak Jnana (Right Knowledge), and Samyak Charitra (Right Conduct). Ahimsa is the core component of Right Conduct.
• Anekantavada: This is the Jain doctrine of "non-absolutism" or "many-sidedness." It suggests that truth and reality are complex and have multiple aspects. This intellectual Ahimsa prevents dogmatism and encourages the respect of different viewpoints.
• Karma Theory: Unlike other Indian philosophies where Karma is often viewed as a metaphysical law, Jainism views Karma as physical matter (Pudgala) that sticks to the soul due to passions and actions, weighing it down in Samsara.
• Sallekhana: This is a highly specialized spiritual practice in Jainism involving voluntary fasting unto death. It is not considered suicide but a supreme form of self-discipline to purge Karma before the natural end of life.

The correct answer is To establish India as a global aluminium production hub by 2047 through sustainable practices.

Key Points

• The Aluminium Vision Document, strategically focused on 2047, aims to transform India into a self-reliant and global leader in the aluminium industry. The document underscores the transition from a primary producer to a sophisticated global production hub.
• A core objective is the adoption of sustainable practices, specifically focusing on Decarbonization and Green Aluminium production to meet international ESG (Environmental, Social, and Governance) standards. This is essential for India to bypass potential Carbon Border Adjustment Mechanisms (CBAM) imposed by regions like the European Union.
• The roadmap targets a significant increase in domestic production capacity, aiming for approximately 10 million tonnes of primary aluminium by the year 2047 to support infrastructure, defence, and renewable energy sectors.
• It prioritizes the Circular Economy by enhancing the recycling of aluminium scrap. Since secondary aluminium production requires 95% less energy than primary production, this strategy is vital for energy efficiency and reducing the carbon footprint of the industry.
• The policy is a collaborative initiative involving the Ministry of Mines and NITI Aayog, ensuring that the aluminium sector aligns with the broader Viksit Bharat @ 2047 vision for an advanced Indian economy. Hence, option D is the correct objective.

Additional Information

• Strategic Importance of Aluminium:
• Aluminium is often called the "Metal of the Future" due to its high strength-to-weight ratio, corrosion resistance, and 100% recyclability. It is a critical component in Strategic Sectors including Aerospace, Space Exploration (via ISRO), and Electric Vehicles (EVs).
• The National Mineral Policy emphasizes the sustainable extraction of Bauxite, the primary ore for aluminium, to ensure long-term resource security.
• India's Global Standing:
• India is currently the second-largest producer of primary aluminium in the world. Major industry players include National Aluminium Company Limited (NALCO), Hindustan Aluminium Corporation (HINDALCO), and Vedanta Aluminium.
• The state of Odisha holds over 50% of India's bauxite reserves, followed by Andhra Pradesh, Gujarat, and Chhattisgarh.
• Economic and Policy Framework:
• The Production Linked Incentive (PLI) Scheme has been discussed for the specialty steel and non-ferrous sectors to boost value-added manufacturing and reduce dependency on imports.
• The National Non-Ferrous Metal Scrap Recycling Policy was introduced to promote a formal ecosystem for recycling, which helps in saving foreign exchange and reducing landfill waste.

Important Points

• Technological Innovation: The vision document encourages the use of Inert Anode Technology and Carbon Capture, Utilization, and Storage (CCUS) to achieve Net Zero emissions in the industrial sector.
• Energy Intensity: Since aluminium smelting is highly energy-intensive, the shift towards Renewable Energy (solar and wind) and Green Hydrogen for power is a key pillar of the July 2025 policy updates.
• Market Dynamics: The global demand for aluminium is expected to grow by 40% by 2030, driven largely by the global energy transition and the shift toward lightweighting in the transportation sector.

The correct answer is Eating → Digestion → Absorption → Transportation → Utilisation.

Key Points

• Nutrition is a biological process that involves the intake of nutrients by an organism and their subsequent utilisation for various life processes such as growth, repair, and energy production.
• Eating (Ingestion): This is the initial stage where food is taken into the body through the mouth or buccal cavity. In humans, the process of mechanical digestion begins here with teeth. Hence, the placement of eating at the start is correct.
• Digestion: This step involves the breakdown of complex, insoluble organic food substances into simpler, soluble molecules with the help of enzymes like Salivary Amylase, Pepsin, and Trypsin. This occurs in the stomach and small intestine. Hence, digestion following eating is correct.
• Absorption: Once the food is digested into simpler forms like glucose, amino acids, and fatty acids, it is taken up by the bloodstream through the walls of the small intestine, specifically via finger-like projections called villi. Hence, absorption following digestion is correct.
• Transportation: The absorbed nutrients are then transported by the circulatory system (blood) to every cell of the body to fulfill metabolic requirements. Hence, transportation following absorption is correct.
• Utilisation (Assimilation): This is the final functional stage where the cells use the transported nutrients for energy (via respiration), synthesis of proteins, and cellular repair. Hence, utilisation following transportation is correct.

Additional Information

• Holozoic Nutrition: This is the type of heterotrophic nutrition seen in humans, amoeba, and animals, where solid or liquid organic matter is ingested, digested, and absorbed.
• Role of the Small Intestine: It is the site of complete digestion of carbohydrates, proteins, and fats. It receives secretions from the liver (bile) and pancreas (pancreatic juice) to aid this process.
• Egestion vs. Excretion: While the question focuses on the flow until utilisation, the process of removing undigested food is called egestion, which occurs through the anus. This is different from excretion, which is the removal of metabolic nitrogenous wastes like urea via the kidneys.
• Basal Metabolic Rate (BMR): The nutrients utilised by the body help maintain the BMR, which is the minimum amount of energy required to keep the body functioning at rest.
• Circulatory System: In humans, the heart and blood vessels act as the primary medium for transportation, ensuring that oxygen and nutrients reach every tissue.

Important Points

• Enzymatic Action: In the stomach, Hydrochloric Acid (HCl) creates an acidic medium for Pepsin to act on proteins. In the small intestine, the environment is alkaline for the action of lipase and proteases.
• Villi Functions: These multicellular structures increase the surface area for absorption by nearly 30 to 60 times, ensuring maximum nutrient uptake.
• Glucose Utilisation: Glucose is the primary source of energy, which is broken down in the mitochondria during cellular respiration to produce ATP (Adenosine Triphosphate).
• Lacteals: While most nutrients enter the blood capillaries, fatty acids and glycerol are absorbed into lymphatic vessels called lacteals before entering the bloodstream.

The correct answer is Ministry of AYUSH.

Key Points

• The Ministry of AYUSH was officially formed on 9^th November 2014 to provide a focused impetus to the development of Education and Research in Ayurveda, Yoga and Naturopathy, Unani, Siddha, and Homoeopathy.
• Prior to its elevation to a full-fledged ministry, it existed as the Department of Indian Systems of Medicine and Homoeopathy (ISM&H), which was established in March 1995 under the Ministry of Health and Family Welfare.
• The department was later renamed the Department of AYUSH in November 2003, with a primary objective to upgrade the educational standards of Indian Systems of Medicine and ensure the availability of raw materials.
• The ministry focuses on the revival of profound knowledge of ancient medical systems and their integration into the national healthcare delivery system to provide holistic health coverage to the citizens of India.
• It is responsible for the formulation of policy for the development and propagation of these traditional systems, which are deeply rooted in the socio-cultural heritage of the country.

Additional Information

• Ayurveda: One of the oldest systems of medicine, originating in India over 3,000 years ago, based on the balance of three doshas (Vata, Pitta, and Kapha).
• Yoga and Naturopathy: Yoga is a 5,000-year-old Indian body of knowledge that promotes physical and mental well-being, while Naturopathy is a drugless system of healing based on the Five Great Elements (Mahabhutas).
• Unani: This system originated in Greece and was introduced to India around the 11^th century; it emphasizes the balance of four humors (blood, phlegm, yellow bile, and black bile).
• Siddha: One of the oldest systems of medicine in the world, practiced primarily in South India (Tamil Nadu), emphasizing Kayakalpa (longevity and rejuvenation).
• Homoeopathy: Introduced in the 18^th century by Samuel Hahnemann, it operates on the principle of "Similia Similibus Curentur" (Like cures like) and was integrated into the AYUSH framework for its widespread popularity.

Important Points

• National AYUSH Mission (NAM): Launched in September 2014, this flagship scheme aims to provide cost-effective AYUSH services and strengthen institutional capacity at the state level.
• Sowa-Rigpa: Commonly known as the "Amchi" system, it is the traditional medical system of the Himalayan belt and was officially recognized and added to the Ministry of AYUSH portfolio in 2010.
• WHO Global Centre for Traditional Medicine: In 2022, the World Health Organization and the Government of India signed an agreement to establish this center in Jamnagar, Gujarat, making it the first and only global outpost for traditional medicine.
• International Day of Yoga: Following a proposal by PM Narendra Modi at the United Nations General Assembly, 21^st June was declared as the International Day of Yoga, significantly boosting the global profile of Indian traditional practices.
• Ayush Visa: Introduced in 2023, this special visa category facilitates foreign nationals seeking Medical Value Travel to India for therapeutic care, wellness, and yoga.

Shortcut Trick

Net percentage increase = 15 + 25 + (15 × 25) ÷ 100 = 43.75%

Multiplying Factor = 1 + 43.75/100 = 1.4375

Population after 2 years = 210000 × 1.4375

Population after 2 years = 301875

∴ Answer = 301875

Alternate Method 

Given:

Initial population = 210000

Growth rate in 1^st year = 15%

Growth rate in 2^nd year = 25%

Formula used:

Final Population = P × (1 + r₁/100) × (1 + r₂/100)

2,10,000 Initial +15% 2,41,500 Year 1 +25% 3,01,875 Year 2 Population Growth Timeline

Calculations:

Population after first year = 210000 × (115/100)

⇒ 2100 × 115 = 241500

Population after second year = 241500 × (125/100)

⇒ 241500 × 5/4

⇒ 60375 × 5 = 301875

∴ The correct answer is 301875 (Option 1).

Additional Information

Successive Percentage Formula

The effective change for two successive percentage changes of x% and y% is given by (x + y + xy/100)%.

Population Depreciation

If population decreases by r% per annum, the population after n years is P × (1 − r/100)ⁿ.

Fractional Conversion

Using fractions often simplifies calculation: 15% = 3/20 (multiplier 23/20) and 25% = 1/4 (multiplier 5/4).

Shortcut Trick

Difference in percentage = 35% − 25% = 10%

This 10% value corresponds to the given difference of 18.

To find the full number (100%), scale the value by 10:

100% = 18 × 10 = 180

∴ Answer = 180

Alternate Method 

Given:

35% of a number exceeds 25% of the same number by 18.

Formula used:

Value of Number = (Difference in value ÷ Difference in percentage) × 100

Calculations:

Let the number be x.

⇒ (35 ÷ 100) × x − (25 ÷ 100) × x = 18

⇒ (35 − 25)% × x = 18

⇒ 10% × x = 18

⇒ (10 ÷ 100) × x = 18

⇒ x = 18 × 10 = 180

∴ The correct answer is 180 (Option 1).

Additional Information

Percentage Change

To find the percentage increase or decrease between two values, use: [(New Value − Old Value) ÷ Old Value] × 100.

Successive Percentage

For two successive percentage changes of a% and b%, the effective change is given by: [a + b + (a × b ÷ 100)]%.

Percentage to Fraction

Any percentage x% can be written as a fraction by dividing by 100: x% = x ÷ 100. For example, 25% = 1/4 and 10% = 1/10.

Base Change Rule

If A is x% more than B, then B is [x ÷ (100 + x)] × 100% less than A.

Shortcut Trick

Ratio of LCM to HCF = 165 : 1

Total units = 165 + 1 = 166 units

166 units = 2158 → 1 unit (HCF) = 2158 ÷ 166 = 13

LCM = 165 × 13

Other Number = (LCM × HCF) ÷ Given Number = (165 × 13 × 13) ÷ 195

∴ Answer = 143

Alternate Method 

Given:

LCM = 165 × HCF

LCM + HCF = 2158

One number = 195

Formula used:

Product of two numbers = LCM × HCF

LCM (165 Units) HCF (1 Unit) Sum = 166 Units = 2158 1 Unit (HCF) = 13

Calculations:

Let HCF be H. Then LCM = 165H.

⇒ H + 165H = 2158

⇒ 166H = 2158

⇒ H = 2158 ÷ 166 = 13

⇒ LCM = 165 × 13 = 2145

⇒ First Number × Second Number = LCM × HCF

⇒ 195 × Second Number = 2145 × 13

⇒ Second Number = 27885 ÷ 195

⇒ Second Number = 143

∴ The correct answer is 143.

Additional Information

Product of Two Numbers

The product of any two numbers is always equal to the product of their HCF and LCM. Formula: n₁ × n₂ = HCF × LCM.

Co-prime Factors of LCM

If HCF is H and the numbers are Hx and Hy (where x and y are co-prime), then LCM = H × x × y. Therefore, LCM ÷ HCF = x × y.

Divisibility Rule

The LCM of a set of numbers is always exactly divisible by the HCF of those same numbers.

HCF and LCM of Fractions

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

Shortcut Trick

Punjab = 25% and ratio 2 : 1

225 lakh tonnes ⇒ 3 parts ⇒ 1 part = 75

Haryana 2011 = 35% × (2 ÷ 5) = 14% of total

Tamil Nadu total = 20% of total

Required % = (14 ÷ 20) × 100 = 70%

∴ The correct answer is 70%.

Alternate Method

Given:

Punjab share in both years = 25%

Punjab ratio (2011 : 2012) = 2 : 1

Total Punjab production = 225 lakh tonnes

Formula Used:

Required % = (Haryana 2011 production ÷ Tamil Nadu total production) × 100

Calculations:

⇒ Punjab total = 225 lakh tonnes

⇒ Punjab ratio = 2 : 1 ⇒ Total parts = 3

⇒ Punjab 2011 = (2 ÷ 3) × 225 = 150 lakh tonnes

⇒ Punjab total represents 25% of overall production

⇒ Total production of all states = 225 ÷ 25 × 100 = 900 lakh tonnes

⇒ Haryana total production = 35% of 900 = 315 lakh tonnes

⇒ Haryana ratio = 2 : 3

⇒ Haryana 2011 production = (2 ÷ 5) × 315 = 126 lakh tonnes

⇒ Tamil Nadu total production = 20% of 900 = 180 lakh tonnes

⇒ Required percentage = (126 ÷ 180) × 100

⇒ = 70%

∴ The correct answer is 70%.

Additional Information

Ratio Distribution

If total quantity and ratio are known, divide total into ratio parts first.

Percentage to Quantity

Quantity = Percentage × Total ÷ 100

Shortcut in DI

Use percentage comparison directly instead of calculating every state separately.

Ratio Sum Rule

For ratio a : b, total parts = a + b and individual share = part ÷ total parts.

Shortcut Trick

Let distance covered = 3x ⇒ remaining = 4x ⇒ total = 3x + 4x = 7x

7x = 68 ⇒ x = 68/7 ⇒ distance covered = 3x = 3 × 68/7 = 204/7 km

Time = 1 hr 10 min = 7/6 hr

Speed = (204/7) ÷ (7/6) = 204/7 × 6/7 = 1224/49 ≈ 24.98 ≈ 25 kmph

∴ Answer = 25 kmph (approx)

Alternate Method

Given:

Total distance = 68 km

Time cycled = 1 hr 10 min = 1 + 10/60 = 7/6 hr

Distance covered = 3/4 of remaining distance

Formula used:

If covered = 3/4 of remaining ⇒ covered : remaining = 3 : 4 ⇒ total = 7 parts

Speed = Distance ÷ Time

 Start   P   End   Covered = 3 parts   Remaining = 4 parts     Total = 7 parts = 68 km ⇒ 1 part = 68/7 km  Covered = 3 × 68/7 = 204/7 km  Time = 7/6 hr Speed ≈ 25 kmph

Calculations:

Let covered distance = 3x and remaining distance = 4x

⇒ 3x + 4x = 68

⇒ 7x = 68

⇒ x = 68/7 km

⇒ Distance covered = 3x = 3 × 68/7 = 204/7 km

Time = 1 hr 10 min = 1 + 10/60 = 60/60 + 10/60 = 70/60 = 7/6 hr

⇒ Speed = Distance ÷ Time = (204/7) ÷ (7/6)

⇒ Speed = 204/7 × 6/7 = 1224/49

⇒ Speed = 24.979... ≈ 25 kmph

∴ Speed of the man ≈ 25 kmph.

Additional Information

Average Speed Formula

When a person travels two equal distances at speeds u and v, average speed = 2uv ÷ (u + v). This is the harmonic mean of the two speeds — always less than the arithmetic mean. Never add speeds and divide by 2 when distances are equal.

Relative Speed

When two objects move in the same direction, relative speed = difference of speeds. When moving in opposite directions, relative speed = sum of speeds. Used in train problems, boat & stream and meeting point problems.

Time Conversion — Common Values

Always convert time to hours before applying Speed = Distance ÷ Time. Key conversions: 10 min = 1/6 hr | 15 min = 1/4 hr | 20 min = 1/3 hr | 30 min = 1/2 hr | 40 min = 2/3 hr | 45 min = 3/4 hr | 70 min = 7/6 hr.

Ratio Method for Distance Problems

When distance covered is given as a fraction of remaining distance (e.g. 3/4 of remaining), convert to ratio: covered : remaining = 3 : 4 ⇒ total = 7 parts. Find value of 1 part from total distance, then compute covered distance directly without algebra.

Shortcut Trick

Radius (r) = Diameter ÷ 2 = 12 ÷ 2 = 6 cm

Volume of sphere = (4/3) × π × r³

Volume = (4/3) × π × 6 × 6 × 6 = 4 × π × 2 × 36 = 288π cm³

∴ Answer = 288π

Alternate Method 

Given:

Diameter of the sphere = 12 cm

Formula used:

Volume of a sphere = (4/3) × π × r³

Radius (r) = Diameter ÷ 2

Diameter = 12 cm  r = 6 cm  Volume (V) = (4/3) × π × r<sup>3</sup>

Calculations:

Radius of sphere (r) = 12 ÷ 2 = 6 cm

⇒ Volume = (4/3) × π × (6)³ ⇒ Volume = (4/3) × π × 216 ⇒ Volume = 4 × π × 72 ⇒ Volume = 288π cm³

∴ The correct answer is 288π.

Additional Information

Surface Area of Sphere

The total surface area of a sphere is the amount of region covered by its outer surface: A = 4 × π × r².

Volume of Hemisphere

A hemisphere is exactly half of a sphere. Its volume is calculated as: V = (2/3) × π × r³.

Total Surface Area of Hemisphere

For a solid hemisphere, the TSA includes the curved surface (2πr²) and the flat base (πr²): TSA = 3 × π × r².

Shortcut Trick

Capital Ratio = (Profit ÷ Time) Ratio

Ratio of Capital A : B = (9 ÷ 12) : (2 ÷ 5)

⇒ (3/4) : (2/5) = 15 : 8

Since 15 units = 4,98,000 → 1 unit = 33,200

B investment = 8 units = 8 × 33,200 = 2,65,600

∴ Answer = 2,65,600

Alternate Method 

Given:

Capital of A = ₹4,98,000

Time period of A = 12 months

Time period of B = 12 − 7 = 5 months

Profit Ratio (A : B) = 9 : 2

Formula used:

Profit = Capital × Time

A
12 Months
₹4,98,000

B
5 Months
₹x

Profit Ratio A:B = 9:2

Calculations:

Let B investment be x.

⇒ (Capital_A × Time_A) ÷ (Capital_B × Time_B) = Profit_A ÷ Profit_B

⇒ (4,98,000 × 12) ÷ (x × 5) = 9 ÷ 2

⇒ 5,976,000 ÷ 5x = 9 ÷ 2

⇒ 11,952,000 = 45x

⇒ x = 11,952,000 ÷ 45

⇒ x = 2,65,600

∴ The correct answer is 2,65,600.

Additional Information

Partnership Profit Ratio

Profit sharing ratio is directly proportional to the product of capital and the time period for which it is invested: P₁ : P₂ = C₁ × T₁ : C₂ × T₂.

Working vs Sleeping Partner

A working partner manages the business and may receive a salary or extra profit share, while a sleeping partner only invests capital.

Investment Period

If a partner joins after n months in a yearly business, their time period is (12 − n) months.

Varying Capital

If capital changes over time, Total Investment = (C₁ × T₁) + (C₂ × T₂) + ...

Shortcut Trick

For a mean proportion a : y :: y : c, the shortcut is y = √(a × c).

Given a = 6 and c = 150.

y = √(6 × 150) = √900

y = 30

∴ Answer = 30

Alternate Method 

Given:

6 : y :: y : 150

Formula used:

Product of Means = Product of Extremes

6 : y :: y : 150 Means (y × y) Extremes (6 × 150)

Calculations:

According to the property of proportion, the product of internal terms (means) is equal to the product of external terms (extremes).

⇒ y × y = 6 × 150

⇒ y² = 900

⇒ y = √900

⇒ y = 30

∴ The correct answer is 30.

Additional Information

Mean Proportional

When three numbers a, b, and c are in continued proportion (a:b :: b:c), b is the mean proportional, and b = √(ac).

Third Proportional

In the continued proportion a : b :: b : c, the term c is called the third proportional, where c = b² ÷ a.

Fourth Proportional

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

Shortcut Trick

Ratio CP : SP (Machine 1 at 10% Gain) = 10 : 11

Ratio CP : SP (Machine 2 at 5% Loss) = 20 : 19

Equating SP parts (LCM 209): CP₁ : SP₁ = 190 : 209 and CP₂ : SP₂ = 220 : 209

Total CP = 190 + 220 = 410 units; Total SP = 209 + 209 = 418 units

Overall Gain % = (8 ÷ 410) × 100 ≈ 1.95%

∴ Answer = 1.95% gain

Alternate Method 

Given:

Selling Price of each machine (SP) = ₹7,315, Gain % = 10%, Loss % = 5%

Formula used:

Cost Price (CP) = SP × 100 ÷ (100 ± P/L %)

Machine 1: CP ₹6650 + Gain ₹665 SP ₹7315 Machine 2: CP ₹7700 − Loss ₹385 SP ₹7315 Total CP: ₹14350 | Total SP: ₹14630 Net Transaction Result: 1.95% Gain

Calculations:

CP of Machine 1 = 7315 × 100 ÷ 110 = ₹6,650

⇒ CP of Machine 2 = 7315 × 100 ÷ 95 = ₹7,700

⇒ Total Cost Price = 6650 + 7700 = ₹14,350

⇒ Total Selling Price = 7315 × 2 = ₹14,630

⇒ Total Gain = 14630 − 14350 = ₹280

⇒ Gain % = (280 ÷ 14350) × 100 ≈ 1.95%

∴ The correct answer is 1.95% gain (Option 1).

Additional Information

Case of Equal Selling Price with Same % Change

If two items are sold at the same price, one at a gain of x% and the other at a loss of x%, there is always an overall loss given by: Loss % = (x ÷ 10)².

Overall Profit/Loss % with Different CP

When CP of two items is same, the net profit or loss % is simply the algebraic average of individual percentages: (P% − L%) ÷ 2.

Marked Price and Cost Price Relation

The ratio of Marked Price to Cost Price can be directly calculated using: MP ÷ CP = (100 + Gain %) ÷ (100 − Discount %).

Shortcut Trick

For half-yearly compounding, periodic Rate = 20% ÷ 2 = 10% and Periods = 1 × 2 = 2.

Effective compound interest rate for 2 periods of 10% = 10 + 10 + (10 × 10)/100 = 21%.

Total Amount = 100% + 21% = 121% of Principal.

Amount = 15,700 × 1.21 = 18,997.

∴ Answer = ₹18,997

Alternate Method 

Given:

Principal (P) = ₹15,700, Rate (R) = 20% p.a., Time (T) = 1 year, Compounding = Half-yearly.

Formula used:

A = P(1 + r/100)ⁿ

 Start (P) ₹15,700 6 Months 1 Year   Rate = 10% Rate = 10% Total Amount (A) = ₹18,997

Calculations:

Since interest is compounded half-yearly, periodic rate (r) = 20% ÷ 2 = 10%.

⇒ Number of conversion periods (n) = 1 × 2 = 2 periods.

⇒ A = 15,700 × (1 + 10/100)²

⇒ A = 15,700 × (1.1)²

⇒ A = 15,700 × 1.21

⇒ A = 18,997

∴ The correct answer is ₹18,997 (Option 1).

Additional Information

Effective Rate of Interest

The overall rate for two successive periods of r% is given by the formula R_eff = r + r + (r × r)/100.

Quarterly Compounding

When compounded quarterly, the rate is divided by 4 (R/4) and the time is multiplied by 4 (4T).

CI vs SI Difference (2 years)

The difference between compound interest and simple interest for 2 years is P(R/100)².

Rule of 72

To find the approximate time required to double an investment, divide 72 by the annual interest rate (T ≈ 72/R).

Shortcut Trick

If n pipes have identical filling times (T), the combined time is T ÷ n.

Given: Filling time (T) = 6 hours and Number of pipes (n) = 3.

Total time = 6 ÷ 3 = 2 hours.

∴ Answer = 2

Alternate Method 

Given:

Time taken by Pipe A = 6 hours, Pipe B = 6 hours, Pipe C = 6 hours.

Formula used:

Total Work = LCM of all given days

Efficiency = Total Work ÷ Number of Days

Combined Efficiency (A+B+C) = 1 + 1 + 1 = 3 units/hour

Total time taken = 6 ÷ 3 = 2 hours

Calculations:

Total Efficiency = Efficiency of A + Efficiency of B + Efficiency of C

⇒ Total Efficiency = 1 + 1 + 1 = 3 units/hour ⇒ Time Taken = Total Work ÷ Total Efficiency ⇒ Time Taken = 6 ÷ 3 = 2 hours ∴ The correct answer is 2.

Additional Information

Combined Efficiency

When multiple pipes work together to fill a tank, their individual efficiencies are added: E_total = E₁ + E₂ + ... + E_n.

Outlet Pipe Concept

If a pipe empties the tank, its efficiency is treated as negative. Total efficiency = Filling Efficiency − Emptying Efficiency.

Efficiency and Time Relationship

Efficiency is inversely proportional to time: Efficiency = Work ÷ Time. If a pipe is twice as efficient, it takes half the time.

Shortcut Trick

Simple Interest for 1 year = 4% of ₹400 = ₹16

Total Interest for 9.5 years = 16 × 9.5

Total Interest = 16 × 9 + 16 × 0.5 = 144 + 8 = 152

∴ Answer = 152

Alternate Method 

Given:

Principal (P) = ₹400

Rate of Interest (R) = 4% per annum

Time Period (T) = 9.5 years

Formula used:

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

Principal (P) = ₹400 Time (T) = 9.5 Years Rate (R) = 4% p.a. SI Interest = ₹152

Calculations:

SI = (400 × 4 × 9.5) ÷ 100

⇒ SI = 4 × 4 × 9.5

⇒ SI = 16 × 9.5

⇒ SI = 152

∴ The correct answer is 152.

Additional Information

Total Amount Formula

The total amount (A) to be paid back after the time period is the sum of Principal and Simple Interest: A = P + SI.

Calculation of Principal

If SI, Rate, and Time are known, Principal can be found using P = (SI × 100) ÷ (R × T).

Calculation of Rate

To find the rate of interest: R = (SI × 100) ÷ (P × T).

Calculation of Time

To find the time duration: T = (SI × 100) ÷ (P × R).

Shortcut Trick

If every observation in a dataset is multiplied by a constant k, the new average also gets multiplied by k.

Original Average = 61

Marks are doubled ⇒ k = 2

New Average = 61 × 2 = 122

∴ Answer = 122

Alternate Method 

Given:

Total students = 13

Initial average marks = 61

New condition: Marks of each student are doubled.

Formula used:

Average = (Sum of all observations) ÷ (Number of observations)

Average Transformation Rule Original Avg 61 New Avg (Doubled) 122 Property: If each value × 2, then Average × 2

Calculations:

Initial Sum of marks = 13 × 61 = 793

⇒ If marks of each student are doubled, New Sum = (61 × 2) + (61 × 2) + ... up to 13 times

⇒ New Sum = 2 × (Sum of initial marks)

⇒ New Sum = 2 × 793 = 1586

⇒ New Average = 1586 ÷ 13

⇒ New Average = 122

∴ The correct answer is 122 (Option 2).

Additional Information

Addition or Subtraction Property

If a constant k is added to or subtracted from every observation, the new average becomes (Old Average ± k).

Division Property

If every observation is divided by a non-zero constant k, the new average is (Old Average ÷ k).

Weighted Average

When two groups with averages x₁ and x₂ and sizes n₁ and n₂ are combined, the weighted average is (n₁x₁ + n₂x₂) ÷ (n₁ + n₂).

Shortcut Trick

Total CP = Purchase Price + Repairs

Total CP = 4,14,000 + 97,000 = 5,11,000

Selling Price (SP) = 111% of Total CP

SP = 5,11,000 × 1.11 = 5,67,210

∴ Answer = 5,67,210

Alternate Method 

Given:

Purchase Price = ₹4,14,000

Repair Expenses = ₹97,000

Desired Profit = 11%

Formula used:

Total Cost Price (CP) = Purchase Price + Overhead Expenses

Selling Price (SP) = Total CP × (100 + Profit%) ÷ 100

Purchase 4,14,000 + Repairs 97,000 = Total CP 5,11,000 +11% Profit Selling Price 5,67,210

Calculations:

Total CP = 4,14,000 + 97,000

⇒ Total CP = 5,11,000

⇒ SP = 5,11,000 × (100 + 11) ÷ 100

⇒ SP = 5,11,000 × (111 ÷ 100)

⇒ SP = 5,110 × 111

⇒ SP = 5,67,210

∴ The correct answer is option (1).

Additional Information

Overhead Expenses

Additional costs such as repairs, transportation, and labor incurred after purchase are always added to the initial purchase price to determine the actual Cost Price (CP).

Profit Percentage Formula

Profit % = (Profit ÷ Total CP) × 100, where Profit = Selling Price − Total Cost Price.

Selling Price for Loss

If a man sells an item at a loss of L%, the Selling Price is calculated as: SP = CP × (100 − L) ÷ 100.

Marked Price and Discount

Selling Price = Marked Price − Discount. Also, SP = Marked Price × (100 − Discount%) ÷ 100.

Shortcut Trick

Substitute exponents directly: (15^0.47)^z = (15^0.09)⁴

Equate the resulting powers: 0.47 × z = 0.09 × 4

0.47z = 0.36

z = 0.36 ÷ 0.47 ≈ 0.7659

∴ Answer = 0.77

Alternate Method 

Given:

x = 15^0.47, y = 15^0.09, and x^z = y⁴

Formula used:

(a^m)ⁿ = a^m×n

If a^m = aⁿ, then m = n

Calculations:

Substitute the values of x and y in the equation x^z = y⁴:

⇒ (15^0.47)^z = (15^0.09)⁴

⇒ 15^{(0.47 × z)} = 15^{(0.09 × 4)}

⇒ 15^0.47z = 15^0.36

⇒ Since the bases are equal, 0.47z = 0.36

⇒ z = 0.36 ÷ 0.47

⇒ z ≈ 0.7659...

∴ The correct answer is 0.77 (Option 2).

Additional Information

Power of a Power Rule

When a power is raised to another power, the exponents are multiplied: (a^m)ⁿ = a^m×n.

Equality of Indices

For any positive base a (where a ≠ 1), if a^x = a^y, then the exponents must be equal (x = y).

Product and Quotient Laws

Multiplication adds exponents (a^m × aⁿ = a^m+n) and division subtracts them (a^m ÷ aⁿ = a^m−n).

Shortcut Trick

LCM of 40, 80, 20 = 80 units (Total Work). Efficiencies: A=2, B=1, C=4.

1 Cycle (3 days) work = 2 + 1 + 4 = 7 units.

In 11 cycles (33 days): Work = 11 × 7 = 77 units. Banti's work = 11 × 1 = 11 units.

Remaining work = 80 − 77 = 3 units. Day 34 (Amit) does 2 units, Day 35 (Banti) does 1 unit.

Total work by Banti = 11 + 1 = 12 units. Wage = (12 ÷ 80) × 40,000 = 6,000.

∴ Answer = ₹6,000

Alternate Method 

Given:

Time taken by Amit = 40 days, Banti = 80 days, Chetan = 20 days. Total Wage = ₹40,000.

Formula used:

Total Work = LCM of all given days

Efficiency = Total Work ÷ Number of Days

Wage of a person = (Work done by person ÷ Total work) × Total Wage

Combined work in 1 cycle (3 days) = 2 + 1 + 4 = 7 units

Calculations:

Number of cycles to complete work = 80 ÷ 7 = 11 cycles and 3 units remaining.

⇒ Work done by Banti in 11 cycles = 11 × 1 = 11 units.

⇒ After 11 cycles (33 days), work remaining = 80 − (11 × 7) = 3 units.

⇒ On 34^th day, Amit does 2 units. Remaining work = 3 − 2 = 1 unit.

⇒ On 35^th day, Banti does the remaining 1 unit.

⇒ Total work done by Banti = 11 + 1 = 12 units.

⇒ Wage of Banti = (12 ÷ 80) × 40,000 = 12 × 500 = 6,000.

∴ The correct answer is ₹6,000.

Additional Information

Work and Wages Principle

Wages are always distributed in the direct proportion of the actual work done by each individual. Wage ∝ (Efficiency × Time).

Alternate Work Cycles

For problems where people work in rotation, calculate the total work for one full cycle of all persons and then find the number of cycles required to reach near the total work.

Efficiency Ratio

If time taken is in ratio a:b:c, then efficiencies are in ratio (1/a):(1/b):(1/c). In this question, Time = 40:80:20 → 2:4:1, so Efficiency = 1/2:1/4:1/1 = 2:1:4.

Shortcut Trick

Discount = 11% → Selling Price = 89% of Marked Price

89% = 51620

1% = 51620 ÷ 89 = 580

Marked Price (100%) = 580 × 100 = 58000

∴ Answer = 58000

Alternate Method 

Given:

Selling Price (SP) = ₹51,620

Discount Percentage = 11%

Formula used:

Marked Price (MP) = (SP × 100) ÷ (100 − Discount%)

Selling Price (89%) Discount (11%) Marked Price (100%) Value = ₹51,620

Calculations:

Let the Marked Price of the television set be MP.

⇒ Selling Price = Marked Price − Discount

⇒ 51620 = MP − (11% of MP)

⇒ 51620 = 89% of MP

⇒ 51620 = (89 ÷ 100) × MP

⇒ MP = (51620 × 100) ÷ 89

⇒ MP = 580 × 100 = 58000

∴ The correct answer is 58000 (Option 2).

Additional Information

Relationship between MP and CP

Marked Price ÷ Cost Price = (100 + Profit%) ÷ (100 − Discount%). This is used to find the markup percentage required for a specific profit.

Successive Discounts

If two discounts a% and b% are given, the effective single discount = [a + b − (a × b) ÷ 100]%.

Selling Price Calculation

Selling Price = MP × (1 − d₁/100) × (1 − d₂/100) for successive discounts d₁ and d₂.

Shortcut Trick

Ratio of r : h = 3 : 7

Volume constant = (22/7) × 3² × 7 = 198

Scaling factor x = ³√(101376 ÷ 198) = 8

r = 3 × 8 = 24, h = 7 × 8 = 56

TSA = 2 × (22/7) × 24 × (24 + 56) ≈ 12070

∴ Answer = 12070

Alternate Method 

Given:

Volume of Cylinder = 1,01,376 cm³

Ratio of Height (h) to Radius (r) = 7 : 3

Formula used:

Volume of Cylinder = πr²h

Total Surface Area (TSA) = 2πr(r + h)

        r = 3x  h = 7x Volume = 1,01,376 cm<sup>3</sup>

Calculations:

Let radius (r) = 3x and height (h) = 7x

⇒ (22/7) × (3x)² × 7x = 101376

⇒ 22 × 9x² × x = 101376

⇒ 198x³ = 101376

⇒ x³ = 512

⇒ x = 8

⇒ Radius (r) = 3 × 8 = 24 cm, Height (h) = 7 × 8 = 56 cm

⇒ TSA = 2 × (22/7) × 24 × (24 + 56)

⇒ TSA = 2 × (22/7) × 24 × 80

⇒ TSA = 84480 ÷ 7 ≈ 12068.57 cm²

Rounding to the nearest tens, we get 12070.

∴ The correct answer is option (2).

Additional Information

Curved Surface Area of a Cylinder

The area of the curved part only, calculated as CSA = 2πrh.

Volume of a Cone

A cone with the same radius and height as a cylinder has 1/3^rd its volume: V = (1/3)πr²h.

Sphere Formulas

Surface Area of a sphere = 4πr² and Volume = (4/3)πr³.

Rounding Rule

To round to the nearest ten, if the unit digit is 5 or more, round up; otherwise, round down.

Shortcut Trick

Remaining Speed Percentage = 100% − 95% = 5%

New Speed = 5% of Original Speed

New Speed = 45 × 0.05

New Speed = 2.25 km/hr

∴ Answer = 2.25

Alternate Method 

Given:

Initial speed of the bus = 45 km/hr

Percentage reduction in speed = 95%

Formula used:

New Speed = Original Speed − (Reduction% × Original Speed)

Alternatively: New Speed = Original Speed × (100 − reduction%)/100

Initial Speed: 45 km/hr (100%) Speed Reduced by 95% New: 5% Remaining Speed = 2.25 km/hr

Calculations:

New speed is the remaining 5% of the original speed.

⇒ New Speed = 45 × (100 − 95)/100

⇒ New Speed = 45 × 5/100

⇒ New Speed = 45 × 0.05

⇒ New Speed = 2.25 km/hr

∴ The correct answer is (1).

Additional Information

Percentage Decrease Formula

To find the final value after a percentage decrease: Final = Initial × (1 − Decrease%/100).

Speed Unit Conversion

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

Successive Percentage Change

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

Shortcut Trick

Average of ratio parts (3, 5, 7) = (3 + 5 + 7) ÷ 3 = 5 units.

Given average value = 5,245 ⇒ 5 units = 5,245.

1 unit = 5,245 ÷ 5 = 1,049.

Costliest item = 7 units = 1,049 × 7 = 7,343.

∴ Answer = 7,343

Alternate Method 

Given:

Average price of 3 items = ₹5,245

Ratio of prices = 3 : 5 : 7

Formula used:

Total Value = Average × Number of items

Individual Value = (Total Sum ÷ Sum of Ratio Parts) × Specific Ratio Part

3 parts 5 parts 7 parts  Total Parts = 15 | Avg = 5,245 Costliest = 7 parts

Calculations:

Total price of 3 furniture items = 5,245 × 3 = 15,735

⇒ Sum of ratio parts = 3 + 5 + 7 = 15

⇒ Value of 1 unit = 15,735 ÷ 15 = 1,049

⇒ Price of costliest item (7 units) = 1,049 × 7

⇒ Price = 7,343

∴ The correct answer is 7,343.

Additional Information

Average of AP Series

If terms are in an Arithmetic Progression (like the ratios 3, 5, 7), the average is simply the middle term (5) or (First + Last) ÷ 2.

Summation Rule

Total sum of N observations = Average × N. This is the fundamental step for solving multi-item price problems.

Ratio Scaling

To find the value of any specific part k in ratio a:b:k, use: (k ÷ (a+b+k)) × Total Sum.

The correct answer is 'Option 2' i.e. the .

Key Points

• The phrase “most exquisite masterpiece” uses a superlative degree, which requires the definite article “the” before it.
• The structure “the + most + adjective” is standard when comparing one entity with all others in a group.
• Since the sentence refers to a specific item among all paintings in the gallery, the definite article “the” is grammatically appropriate.

Correct sentence: Of all the paintings in the gallery, the Mona Lisa is considered the most exquisite masterpiece.

Additional Information

• Option 1 (at): A preposition, not an article; incorrect in this context.
• Option 3 (a): Indefinite article; cannot be used with superlative degree.
• Option 4 (an): Also an indefinite article; used before vowel sounds but not with superlatives.
• Rule: Superlative adjectives always take “the” (e.g., the best, the most beautiful).

The correct answer is: Option 4 i.e. "acommodation".

Key Points

• The word "acommodation" is incorrectly spelled. The correct spelling is "accommodation".
• "Acommodation" does not exist in English vocabulary, and its usage is considered a spelling error.
• Accommodation (आवास) refers to a place to stay or live, especially temporary housing or lodging.
• Example: The hotel offers comfortable accommodation for tourists.
• The correct spelling is "accommodation" (आवास).
• Example: Finding affordable accommodation in the city is quite challenging.

Therefore, the correct answer is: Option 4.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Affordable (सस्ती): Something that is reasonably priced and within one's financial means.
• Example: Many families are looking for affordable housing options.
• Acquire (प्राप्त करना): To gain possession or ownership of something, often through effort.
• Example: She managed to acquire the skills needed for the job through extensive training.
• Tourist (पर्यटक): A person who travels to different places for leisure or exploration.
• Example: The city attracts millions of tourists every year because of its historical monuments.

The correct answer is 'Option 1' i.e. with; in .

Key Points

• The adjective “pleased” is correctly followed by the preposition “with” when referring to satisfaction about something (e.g., pleased with performance).
• The noun “confidence” takes the preposition “in” to indicate trust or belief in something (e.g., confidence in future projects).
• Thus, the correct collocation is “pleased with” and “confidence in”.

Correct sentence: The manager was pleased with the team’s performance and expressed confidence in future projects.

Additional Information

• Option 2 (at; on): “pleased at” is rarely used in this context; “confidence on” is incorrect.
• Option 3 (for; of): “pleased for” implies sympathy, not satisfaction; “confidence of” is incorrect usage.
• Option 4 (by; about): “pleased by” can be used in passive sense but is less appropriate here; “confidence about” is incorrect.
• Rule: Fixed prepositional collocations must be memorized for accuracy in usage.

The correct answer is: Option 4 i.e. "The more you know someone, the more you may come to dislike them."

Key Points

• The proverb "Familiarity breeds contempt" means that too much knowledge or closeness with someone can lead to a loss of respect or dislike for them. (अत्यधिक परिचय घृणा उत्पन्न करता है।)
• Example: John admired his boss initially, but after working closely with him, he realized his flaws, proving that familiarity breeds contempt.
• Explanation of the Correct Option:
• The correct interpretation is that the more time you spend with someone, the more likely you are to notice their imperfections, which can lead to annoyance or dislike. (किसी के साथ अधिक समय बिताने पर उनकी खामियां उजागर हो सकती हैं, जिससे चिढ़ या नापसंदगी हो सकती है।)
• Example: Spending too much time with a friend can sometimes strain the relationship, as familiarity breeds contempt.

Therefore, the correct answer is: Option 4.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Option 1: "The more you know someone, the more you begin to understand and respect them." (जितना अधिक आप किसी को जानते हैं, उतना ही आप उन्हें समझते और सम्मान करते हैं।)
• Explanation: This suggests a positive outcome of familiarity, which contradicts the meaning of the proverb.
• Example: Spending time with my grandmother helped me understand her struggles and respect her more.
• Option 2: "You should avoid becoming too familiar with anyone." (आपको किसी के साथ बहुत अधिक परिचित होने से बचना चाहिए।)
• Explanation: While this is a cautionary statement, it doesn't directly explain the meaning of the proverb.
• Example: He avoided getting too close to his coworkers to maintain professionalism.
• Option 3: "People tend to appreciate what they are familiar with." (लोग आमतौर पर उन चीजों की सराहना करते हैं जिनसे वे परिचित हैं।)
• Explanation: This is the opposite of the proverb, as it implies that familiarity leads to appreciation, not contempt.
• Example: Familiarity with a particular dish often makes it your comfort food.

The correct answer is: Option 2 (delightful).

Key Points

• The word "delightful" means causing delight, highly pleasing, or giving great joy. (आनंददायक)
• Example: The children had a delightful time playing in the park.
• The given sentence describes the beautiful things in a garden, including a vine full of grapes. The word "delightful" perfectly fits the context as it highlights the pleasing and enjoyable nature of the garden's scenery. (आनंददायक दृश्य)
• Example: Among the many delightful things in the garden was a vine laden with bunches of grapes.

Therefore, the correct answer is: Option 2 (delightful).

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Brave (साहसी): Showing courage in the face of difficulty or danger.
• Example: The firefighter was brave as he rescued the children from the burning building.
• Rustic (ग्रामीण): Relating to the countryside; simple or unsophisticated.
• Example: The rustic charm of the old farmhouse attracted many visitors.
• Wretched (दुखी): In a very bad or unfortunate state; miserable.
• Example: He felt wretched after losing his job and his home.

The correct answer is: Option 3 i.e. "Qotations".

Key Points

• The word "Qotations" is incorrectly spelt. The correct spelling is "Quotations".
• Meaning of "Quotations" in English: A group of words taken from a text or speech and repeated by someone other than the original author or speaker. (उद्धरण)
• Example: The teacher provided several quotations from famous authors to inspire the students.
• Correct spelling: "Quotations" (उद्धरण)
• Example: She included quotations from historical figures in her essay to support her arguments.
• Hence, the word "Qotations" is incorrect, and the correct spelling is "Quotations".

Therefore, the correct answer is: Option 3.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Prior (पूर्व): Existing or coming earlier in time.
• Example: He had prior commitments, so he couldn't attend the meeting.
• Equipment (उपकरण): Tools or machinery required for a specific purpose.
• Example: The laboratory is equipped with modern scientific equipment.
• Purchase (खरीद): The action of buying something.
• Example: I need to purchase a new laptop for work.

The correct answer is 'Option 3' i.e. DBCA .

Key Points

• D is the introductory sentence as it sets the context: earthworms emerging during rain.
• B logically follows, explaining what the worms do after emerging (movement to surface and grass).
• C introduces a contrast using “But”, shifting to the consequence when rain stops.
• A concludes the paragraph by describing the worms’ struggle after getting stuck.

Correct sequence: D → B → C → A

Additional Information

• Look for chronological flow: rain → emergence → consequence → struggle.
• Words like “But” indicate contrast and usually do not begin a paragraph.
• Ending sentences often contain descriptive or concluding imagery, as seen in sentence A.

The correct answer is 'Option 3' i.e. had stolen .

Key Points

• The clause “I turned back and found” is in the past tense, indicating a completed action in the past.
• The act of stealing happened before the speaker turned back and discovered it.
• To show an action completed prior to another past action, we use the past perfect tense (had + past participle).

Correct sentence: I turned back and found that someone had stolen my bicycle.

Additional Information

• Option 1 (stolen): Incorrect; missing auxiliary verb “had”.
• Option 2 (steals): Present tense; does not fit past context.
• Option 4 (stole): Simple past; does not clearly indicate that the action occurred before “found”.
• Rule: Use past perfect to indicate the earlier of two past actions.

The correct answer is: Option 4 i.e. "Actions reveal the attitude of a person."

Key Points

• The proverb "Actions speak louder than words" means that what someone does has a stronger impact and is a better reflection of their true intentions or character than what they say. (कर्म शब्दों से अधिक प्रभावशाली होते हैं।)
• Example: A person who promises to help others but never does is less trustworthy than one who silently helps without making promises.
• "Actions" refer to deeds or behaviors that demonstrate a person's true attitude or intentions. (कर्म)
• Example: A teacher who helps students after class instead of just giving motivational speeches exemplifies the proverb.
• Therefore, this proverb emphasizes that actions are a more reliable indicator of a person’s values than words.

Therefore, the correct answer is: Option 4.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Option 1: Actions can have a louder effect on the listener (कर्म का श्रोता पर तेज़ प्रभाव हो सकता है): This option misinterprets the proverb by focusing on the volume or intensity of the effect, rather than the deeper meaning behind actions.
• Example: This is incorrect because the proverb is about revealing intentions, not about sound or volume.
• Option 2: Actions can be effectively used while speaking loudly (कर्म को जोर से बोलते समय प्रभावी रूप से उपयोग किया जा सकता है): This option incorrectly links the proverb to speaking loudly, which is unrelated to its actual meaning.
• Example: This does not align with the core idea of the proverb.
• Option 3: Words are softer than actions (शब्द कर्म से अधिक नरम होते हैं): While this option might seem close, it incorrectly focuses on a comparison of softness, which is not the intended interpretation of the proverb.
• Example: This is an incorrect interpretation because the proverb is not about physical softness.

The correct answer is 'Option 2' i.e. an; an .

Key Points

• The question specifically asks for indefinite articles, so only “an” or “an” can be used.
• “Expert” begins with a vowel sound → requires “an”.
• “Existing” also begins with a vowel sound → requires “an”.
• Hence, grammatically correct structure (restricted to indefinite articles) is “an expert” and “an existing framework.”

Correct sentence: The committee appointed an expert to review an existing framework for corporate governance.

Additional Information

• “An” is used before vowel sounds (a, e, i, o, u sounds).
• If the question allowed definite article, “the existing framework” would be more contextually precise.
• But since only indefinite articles are required, option 2 is the best answer.