SSC CHSL Tier-1 2022: Official Paper (Held On: 16 March, 2023 Shift 2) (Previous Year Paper)

The relationship established in "Caterpillar : Butterfly" is "Young form : Mature form". A caterpillar is the immature form (larva) of a butterfly.

Following this logic, from the given options, a lamb is the young form of a sheep. Therefore, "Lamb : Sheep" follows the same relationship.

As for the other options:

• "Tadpole : Cat" is incorrect because a tadpole (young form of a frog or toad) does not mature into a cat.
• "Hen : Chick" and "Deer : Fawn" have the relationship reversed. A chick is a young hen and a fawn is a young deer, so they do not match the initial relationship pattern.

Hence,the correct answer is "Lamb : Sheep".

From the given open Dice:

Z and W is the opposite sides.

X and P is the opposite sides.

Y and R is the opposite sides.

And, two opposite sides can not be the adjacent surfaces, so it can't be shows in a dice.

Now,

Option 1) 

→ Can not be made, because Z and W is the opposite sides.

Option 2) 

→ Can be made, because all the surfaces are adjacent sides.

Option 3) 

→ Can not be made, because X and P is the opposite sides.

Option 4) 

→ Can not be made, because Y and R is the opposite sides.

Hence, the correct answer is "Option 4".

The logic followed here is:

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

Hence, the correct answer is "BSCW".

The logic followed here is:

Dogs, Cats and Elephant all are different types of Animals.

Hence, the correct answer is "Option 2".

BODMAS Table: 

Given equation I: 4  × 3 - 7 + 8 ÷ 2 = 23

Now, if '7 and 4' are interchanged, then:

⇒ 7 × 3 - 4 + 8 ÷ 2 = 23

⇒ 7 × 3 - 4 + 4 = 23

⇒ 21 - 4 + 4 = 23

⇒ 25 - 4 = 23

⇒ 21 ≠ 23.

LHS ≠ RHS.

Given equation II: 7 × 5 - 9 ÷ 3 + 4 = 24

Now, if '7 and 4' are interchanged, then:

⇒ 4 × 5 - 9 ÷ 3 + 7 = 24

⇒ 4 × 5 - 3 + 7 = 24

⇒ 20 - 3 + 7 = 24

⇒ 27 - 3 = 24

⇒ 24 = 24

LHS = RHS.

Here, Only 'Equation I' are incorrect after interchanging the given symbol.

Hence, the correct answer is "Option 3".

BODMAS Rule: 

According to the question:

Now,

Given equation: 64 ÷ 13 + 65 - 15 × 48 + 8 = ?

After replacing the symbols:

⇒ 64 + 13 ÷ 65 × 15 - 48 ÷ 8 = ?

⇒ 64 + 3 - 6 = ?

⇒ 67 - 6 = 61.

Hence, the correct answer is "61".

The logic followed here is:

Logic: (1^st number)³ + 1 = 2^nd number.

Now,

For, 9 ∶ 730

⇒ 9³ + 1

⇒ 729 + 1 = 730.

For, 5 ∶ 126

⇒ 53 + 1

⇒ 125 + 1 = 126.

Similarly, for 7 ∶ ?

⇒ 73 + 1

⇒ 343 + 1 = 344.

Hence, the correct answer is "Option 2".

Family Chart:

Given: 

E is the brother of F.

D is the wife of E.

G is the mother of H.

F is the sister of G.

So, E is the Maternal uncle of H.

Hence, the correct answer is "Option 1".

The relationship in "Captivity : Imprisonment" is one of synonyms - words that have very similar meanings.

Following this logic, "Dense : Opaque" are also synonyms as they both can mean "not allowing light to pass through".

As for the other options:

• "Cheap : Dear" and "Accept : Deny", "Agree : Disagree" are pairs of antonyms - words with opposite meanings. Therefore, they do not follow the same relationship.

Hence, the correct answer is "Dense : Opaque".

The triangles are:

So, there are '17' triangles in the given figure.

Hence, the correct answer is "17".

The logic followed here is:

'ANSWER' is coded as 'APPWGO',

Similarly, for 'DEFINE'

So, 'DEFINE' is coded as 'DGCIPB'.

Hence, the correct answer is "Option 1".

In the pairs "Question - Answer", "Cup - Saucer", and "Chair - Table", the two words are directly related and often used together in a complementary way.

A question is often followed by an answer.

• A cup is often placed on a saucer.
• A chair is often paired with a table.

However, the pair "Pencil - Rub" doesn't follow the same pattern of complementary use. While you might use an eraser (not 'rub') to remove pencil markings, the word 'rub' itself doesn't have a direct, complementary relationship to 'pencil'. Therefore, "Pencil - Rub" is the odd one out.

Hence, the correct answer is "Pencil - Rub".

The logic followed here is :-

(392, 29, 449) ⇒ 392 + 449 = 841 = 29² 

(395, 31, 566)  ⇒  395 + 566 = 961 = 31²

1) (486, 32, 538)

⇒ 486 + 566 = 1024 = 322 

2) (391, 45, 834)

⇒ 391 + 834 = 1225 = 352 ≠ 45²

3) (487, 34, 809)

⇒ 487 + 809 = 1296 = 36² ≠ 34²

4) (562, 35, 594)

⇒  562+ 594 = 1156= 342 ≠ 352

Hence, the correct answer is "Option 1"

Mistake Points

The logic followed here is

Hence, the correct answer is "Option 4".

Given Statements:

I. Some H are D.

II. AII D are M.

The least possible Venn diagram for the given statement is:

Conclusions:

I. Some M are D - True (Because, All D are M, it also means Some M are D)

II. Some H are M - True (Because, those part of H that is D is also M)

III. Some D are H - True (Because, Some H are D, so Some D are H)

So, All conclusion follows.

Hence, the correct answer is "Option 3".

The logic followed here is:

Logic: 1^st number × 2 = 2^nd number.

Now, checking the options:

Option 1) 3926 - 7852 → 3926 × 2 = 7852.

Option 2) 7624- 15248 → 7624 × 2 = 15248.

Option 3) 1658 - 3216 → 1658 × 2 = 3316 ≠ 3216.

Option 4) 5826 - 11652 → 5826 × 2 = 11652.

So, '1658 - 3216' is odd among the given options.

Hence, the correct answer is "Option 3".

The logic followed here is:

Logic: 1^st number × 6 = 2^nd number.

Now, checking the options:

Option 1) 260 - 1560 → 260 × 6 = 1560.

Option 2) 540 - 3240 → 540 × 6 = 3240.

Option 3) 480 - 2860 → 480 × 6 = 2880 ≠ 2860.

Option 4) 320 - 1920 → 320 × 6 = 1920.

So, '480 - 2860' is odd among the given options.

Hence, the correct answer is "Option 3".

The logic here followed is

Hence, the correct answer is "Option 1".

The logic followed here is:

So, '109' will complete the series.

Hence, the correct answer is "Option 2".

NR ∶ OT ⇒

N + 1 = O

R + 2 = T

Similarly,

P + 1 = Q

S + 2 = U

Hence, the correct answer is "Option 4".

The logic followed here is:

Logic: The Triangles are rotated by 90 degree in clockwise direction, and increase by an triangle in each next images.

Hence, the correct answer is "Option 1".

The pattern followed here is:

1) RTW  

2. FHK

3) SVY 

4. KMP

Hence, the correct answer is "SVY".

The image embedded in given figure is as shown below:

Hence, "Option 4" is the correct answer.

The logic followed here is:

Here,

'WOULD + ALL' is coded as '8', 

Number of Letters in WOULD + Number of Letters in ALL

→ 5 + 3 = 8.

'MAJOR + EXAMS' is coded as '10'

Number of Letters in MAJOR + Number of Letters in EXAMS

→ 5 + 5 = 10.

Similarly, for 'COMMON + NOW'

Number of Letters in COMMON + Number of Letters in NOW

→ 6 + 3 = 9.

Hence, the correct answer is "9".

The correct dictionary order for the give words are:

5. Mig
6. Might
7. Migrant
8. Migrate
9. Migrator

So, the correct sequence is '5, 3, 2, 1, 4'.

Hence, the correct answer is "Option 2".

The correct answer is 1600.

Key Points:

• In 1600, the East India Company acquired a charter from the ruler of England, Queen Elizabeth I, granting it the sole right to trade with the East, without competition from other British traders.
• But that royal charter could not stop other European powers such as the Portuguese, Dutch, and French.
• And all those European companies wanted to buy the same things from India - fine qualities of cloth and spices.
• As competition grew, profits fell, and the European trading companies started building forts and fighting each other.
• With more business came more conflicts with Indian rulers, and it became difficult for European traders to keep their business separate from Indian politics.

Additional Information:

• Portuguese (1498) were 1^st company that came to India with Vasco da Gama who had discovered the sea route to India via Cape of Good Hope(Africa).
• Dutch East India Company came in 1595.
• English East India Company came to India in 1600.
• Danish East India Company came to India in 1616.
• French East India Company was the last company came to India in 1664.

Correct Answer CaO

Key Points

• Calcium oxide (CaO) has a highest boiling point.
• It undergoes a process called calcination, where it is heated to very high temperatures (around 2,572°C or 4,662°F) to convert it into calcium oxide.
• However, calcium oxide does not boil as a pure substance at atmospheric pressure since it undergoes thermal decomposition before reaching its boiling point.
• Calcium oxide (CaO), also known as quicklime or burnt lime, is an inorganic compound composed of calcium and oxygen.
• Chemical Formula: CaO
• Molar Mass: 56.08 g/mol

Physical Properties:

• Appearance: Calcium oxide is a white, caustic, crystalline solid at room temperature.
• Melting Point: The melting point of calcium oxide is approximately 2,572°C (4,662°F), indicating its solid state at normal conditions.
• Boiling Point: Calcium oxide does not have a distinct boiling point because it undergoes thermal decomposition before reaching its boiling point.
• When heated, calcium oxide decomposes into calcium hydroxide and releases oxygen gas.

Additional InformationCacl₂:

• Calcium chloride (CaCl₂) is a compound that has a relatively high boiling point compared to many other common substances.
• Calcium chloride (CaCl2) is an inorganic compound composed of calcium and chloride ions.
• It is commonly used in various industrial, commercial, and scientific applications.

Physical Properties:

• Appearance: Calcium chloride is typically a white crystalline solid.
• Melting Point: The melting point of calcium chloride is around 772°C (1422°F), indicating its solid state at room temperature.
• Boiling Point: The boiling point of calcium chloride is approximately 1,935°C (3,515°F), which is relatively high compared to many other substances.
• Solubility: Calcium chloride is highly soluble in water, and it forms a clear, colorless solution.
• The solubility of calcium chloride increases with increasing temperature.

Nacl:

• **Sodium chloride (**NaCl) is a common compound that is widely known as table salt. Here are some details about sodium chloride:
• Chemical Formula: NaCl
• Molar Mass: 58.44 g/mol

Physical Properties:

• Appearance: Sodium chloride is a crystalline solid that is typically white or colorless.
• Melting Point: The melting point of sodium chloride is approximately 801°C (1,474°F).
• This is the temperature at which it transitions from a solid to a liquid state.
• Boiling Point: The boiling point of sodium chloride is approximately 1,413°C (2,575°F).
• This is the temperature at which it transitions from a liquid to a gaseous state.

Correct Answer Both I and II

Key PointsVicky Ostwal:

• Vicky Ostwal is an Indian cricketer who plays for the Maharashtra cricket team and the Delhi Capitals in the Indian Premier League (IPL).
• He is a left-arm orthodox spinner and a right-handed batsman.
• Member of the India U-19 team that won the 2022 Under-19 Cricket World Cup
• Leading wicket-taker for India in the 2022 Under-19 Cricket World Cup, with 12 wickets in six matches.
• Named in the ICC's Most Valuable Team of the 2022 Under-19 Cricket World Cup
• Bought by the Delhi Capitals for ₹20 lakhs in the 2023 IPL auction.

Anshu Malik:

• Anshu Malik is an Indian freestyle wrestler who won the silver medal in the women's 57 kg event at the 2021 World Wrestling Championships held in Oslo, Norway.
• She is the first Indian wrestler to win a silver medal at the World Championships in the women's division.
• Silver medal at the 2021 World Wrestling Championships.
• Bronze medal at the 2020 Asian Wrestling Championships.
• Silver medal at the 2020 Matteo Pellicone Ranking Series.
• Gold medal at the 2016 Cadet Wrestling Championships.
• Silver medal at the 2018 Junior Wrestling Championships.
• Malik is a recipient of the Arjuna Award in 2021, India's highest sporting honor.
• She is also a member of the Target Olympic Podium Scheme, a government program that supports India's top athletes.

Correct Answer Only I

Key Points:

• Poverty means that the income level from employment is so low that basic human needs can't be met.
• The poverty line varies with time and place.
• A poor household is defined as one with an expenditure level below a specific poverty line.
• As per the Rangarajan committee report (2014), the poverty line is estimated as a Monthly Per Capita Expenditure of Rs. 1407 in urban areas and Rs. 972 in rural areas.
• A common method used to measure poverty is based on income.
• Poverty line estimation in India is based on consumption expenditure and not on income levels.
• Poverty is measured based on consumer expenditure surveys by the National Sample Survey Organisation.
• The incidence of poverty is measured by the poverty ratio, which is the ratio of the number of poor to the total population expressed as a percentage. It is also known as the head-count ratio.
• Alagh Committee (1979) determined a poverty line based on a minimum daily requirement of 2400 and 2100 calories for an adult in Rural and Urban areas respectively.
• The measurement limits of the poverty line may be based on the consumption levels of the population.
• The poverty line in India is not calculated on a regular ten-year basis. Instead, it is periodically updated by the Government of India. Statement I is Incorrect.
• The poverty line is defined as the minimum level of income or consumption necessary to meet basic needs and lead a decent life.

Additional Information:

• In 2011, the Suresh Tendulkar Committee defined the poverty line on the basis of monthly spending on food, education, health, electricity and transport.
• According to this estimate, a person who spends Rs. 27.2 in rural areas and Rs. 33.3 in urban areas a day are defined as living below the poverty line.

Correct Answer Stringed instruments

Key PointsTat Vadya

• These are stringed instruments.
• Sound is produced by way of vibrating strings or strings stretched between two points.
• These instruments are further classified into plucked, bowed, fretted, and non-fretted instruments.
• The length of the string and the tension in it determines the pitch of the note and the duration of the sound.
• Examples- Sitar, Sarod, Saraswati Vina (South Indian Vina), Surbahar, Gotuvadyam, Rudra Vina,Vichitra Vina, Ektar, Tanpura, Dotar ,Santoor, Surmandal, Bulbul Tarang, Nakula Vina ,Magadi Vina ,Getchu Vadyam (Gettuvadyam) ,Gopichand (ektar), Seni Rabab, Been and Sarangi.

The correct answer is Option 4. 

Key Points

• Miss World 2017 Manushi Chillar Of India Crowned Vanessa Ponce De Leon From Mexico As The Winner At The 68^th Edition Of The Prestigious Miss World Pageant Held At Sanya, China.
• Nicolene Pichapa From Thailand Stood With Runner Up Position At The Same Pageant.

Additional Information

• The Miss World pageant is indeed the oldest existing international beauty pageant, first created in the United Kingdom by Eric Morley in 1951.
• Eric Morley played a significant role in the organization and development of the pageant until his death in 2000.
• Following his passing, his widow, Julia Morley, took over and has co-chaired the Miss World pageant since then.
• Julia Morley has continued to contribute to the pageant's growth and oversee its operations, maintaining its status as one of the most prestigious beauty pageants globally.

The correct answer is Option 2. 

Key Points

• The Constitutional Amendment Act that reduced the age of voting from 21 to 18 for elections to the Lok Sabha and the Legislative Assemblies of states is the 61^st Constitutional Amendment Act of 1988.
• This amendment lowered the voting age in India, making it more inclusive and allowing a larger section of the population to participate in the electoral process.

Additional Information

• Constitutional amendment acts are generally regarded as important tools for adapting a constitution to the changing needs and aspirations of a society.
• However, due to the significance and potential long-lasting effects of constitutional changes, they often require careful deliberation, public consultation, and broad consensus to ensure that they truly reflect the will of the people and maintain the integrity of the constitutional framework.

The correct answer is Option 3. 

Key Points

• The Constitution Amendment Act that added provisions related to municipalities in the Indian Constitution is the 74^th Amendment Act of 1992.
• This amendment is also known as the Constitution (Seventy-fourth Amendment) Act, 1992. It introduced significant changes and provisions related to urban local governance in India.
• The 74^th Amendment Act provided a constitutional framework for the establishment, functioning, and powers of municipalities, which are referred to as "Nagar Palikas" or "Nagar Nigams" in India.
• These provisions aim to empower local self-government bodies and promote decentralization of power and decision-making at the urban level.

The correct answer is Option 2. 

Key Points

• V. Anantha Nageswaran took charge on 28 January 2022.
• He is a former executive with Credit Suisse Group AG and Julius Baer Group.
• He will succeed Krishnamurthy Subramanian.
• The Chief Economic Adviser (CEA) in the Finance Ministry, advises the govt on economic matters and traditionally scripts the economic survey presented in Parliament a day before the Union budget presentation.

Additional Information

• ​Indian Entrepreneur and writer Jaithirth Rao, popularly known as Jerry Rao, has come out with a book on Mahatma Gandhi titled “Economist Gandhi: The Roots and the Relevance of the Political Economy of the Mahatma” in October 2021.
• Noted Economist and former Chief Economic Adviser to the Government of India, Dr. Shankar Acharya has authored a new book titled “An Economist at Home and Abroad: A Personal Journey” in November 2021.
• French-born economist Pierre-Olivier Gourinchas has been named as the chief economist of the International Monetary Fund (IMF).
• International Monetary Fund Chief Economist, Gita Gopinath has taken over from Geoffrey Okamoto as the institution’s No. 2 official in December 2021, she is the Deputy Managing Director of the International Monetary Fund.

The correct answer is Option 3. 

Key Points

• Secondary memory, also known as auxiliary memory or non-volatile memory, is a type of computer memory that retains data even when the power is turned off.
• It is non-volatile, meaning it does not lose its data when the power supply is disconnected.
• Secondary memory is used for long-term storage of data and files, such as hard disk drives (HDDs), solid-state drives (SSDs), magnetic tapes, and optical discs like CDs and DVDs.
• In contrast, volatile memory, such as random access memory (RAM), is temporary and loses its data when the power is removed.

Additional Information

• Memory refers to the electronic storage space where data and instructions are stored for processing by the computer's central processing unit (CPU). Computer memory is an essential component that allows the computer to perform tasks and store information.
• Here are the main types of memory in a computer system:
• Random Access Memory (RAM): RAM is the primary type of computer memory used for temporary data storage while the computer is running. It provides fast access to data and instructions that are actively used by the CPU. RAM is volatile, meaning its contents are lost when the computer is powered off or restarted.
• Read-Only Memory (ROM): ROM is a type of memory that stores permanent instructions or data that cannot be modified or erased. It contains firmware or software instructions that are necessary for booting up the computer and initializing essential components. ROM retains its contents even when the computer is powered off.
• Cache Memory: Cache memory is a small, high-speed memory that resides closer to the CPU. It serves as a buffer between the CPU and main memory (RAM). Cache memory stores frequently accessed data and instructions, allowing the CPU to quickly retrieve them without accessing the slower main memory. It helps improve overall system performance.
• Virtual Memory: Virtual memory is a technique used by operating systems to extend the available memory beyond the physical RAM capacity. It uses a portion of the computer's hard drive as an extension of RAM. Virtual memory allows running more programs and handling larger datasets than what can fit in physical memory alone.
• Flash Memory: Flash memory is a non-volatile memory used for long-term data storage in devices like USB drives, solid-state drives (SSDs), and memory cards. It retains data even when the power is turned off. Flash memory is popular

The correct answer is Indonesia.

Key Points

• The first G20 Foreign Ministers' Meeting of 2022 was held in Bali, Indonesia on July 7-8, 2022.
• The meeting was chaired by Indonesian Foreign Minister Retno Marsudi.
• The main topics of discussion at the meeting were the global economic recovery, the COVID-19 pandemic, and the situation in Ukraine.

Mistake Points

• The G20 Foreign Ministers' Meeting of 2023 was held in New Delhi, India on March 1-2, 2023.
• The meeting was chaired by Indian Foreign Minister S. Jaishankar.

Additional Information

• G20
• The G20, or Group of Twenty, is an intergovernmental forum comprising 19 countries and the European Union (EU).
• The G20 was established in 1999 in response to the financial crises that arose in a number of emerging economies in the 1990s.
• The forum was created to provide a forum for dialogue and cooperation between the world's major economies on key economic issues.
• The G20 is made up of the following countries:
• Argentina
• Australia
• Brazil
• Canada
• China
• France
• Germany
• India
• Indonesia
• Italy
• Japan
• Mexico
• Russia
• Saudi Arabia
• South Africa
• South Korea
• Turkey
• United Kingdom
• United States
• European Union

The correct answer is Rohit Sharma.

Key Points

• Rohit Sharma became the first-ever Indian cricket player to play 400 T20s.
• He achieved the feat on March 8, 2023, during the third T20I match against Sri Lanka in Lucknow.
• Rohit Sharma is also the only Indian cricketer to have scored more than 1000 runs in T20I cricket.
• He has scored 10544 runs in 400 matches.

Additional Information

• T20 cricket was first played in England in 2003, and the first T20 international was played between England and Australia in 2005.
• The format quickly became popular, and the International Cricket Council (ICC) introduced a T20 World Cup in 2007.
• India won the inaugural ICC Men's T20 World Cup in 2007.

The correct answer is Shashi Kapoor.

Key Points

• Shashi Kapoor
• Shashi Kapoor received the Dadasaheb Phalke Award in 2014.
• He was the 46^th recipient of the award, which is the highest honor in Indian cinema.
• The award was presented to him by the then Information and Broadcasting Minister Arun Jaitley.
• Shashi Kapoor was a versatile actor who starred in over 175 films over a 40-year career.

Additional Information

• Dadasaheb Phalke Award
• The award was instituted in 1969 and is named after Dadasaheb Phalke, who is considered the "Father of Indian Cinema" for directing the first Indian feature film, Raja Harishchandra, in 1913.
• The award is presented annually at the National Film Awards ceremony and consists of a Swarna Kamal (Golden Lotus) medallion, a shawl, and a cash prize of ₹1,000,000.
• As of 2023, there have been 52 recipients of the Dadasaheb Phalke Award. Some of the most notable recipients include:
• Devika Rani (1969)
• Satyajit Ray (1976)
• Lata Mangeshkar (1989)
• Raj Kapoor (1987)
• Amitabh Bachchan (2018)
• A. R. Rahman (2012)
• S. S. Rajamouli (2018)
• Rajinikanth (2019)
• Asha Parekh (2020)
• Rekha (2023)

The correct answer is Intercropping.

Key Points

• Intercropping
• Intercropping, on the other hand, involves planting different crops in proximity (in alternate rows or otherwise).
• This technique helps reduce the risk of soil erosion as well as protects the soil from rain wash.
• When crops are sown at different times, the soil surface remains covered for a longer period of time, thereby reducing the direct impact of rainfall.

Additional Information

• Shelterbelt
• Shelter belts are rows of trees or shrubs planted in a line to protect an area from wind.
• They are also known as windbreaks.
• Shelter belts can be used to protect crops, livestock, and homes from the wind.
• They can also help to reduce soil erosion and improve air quality.
• Contour farming 
• Contour farming or contour plowing involves tilling the soil following the contours of the land, rather than up and down the slope.
• Plowing along the natural contours of the land, this method reduces runoff, prevents soil erosion, and allows the soil to retain water better.
• It's a particularly useful method in hilly or sloped areas where water erosion can be a significant issue.
• Terrace farming
• Terrace farming is a method of farming that involves building terraces on sloping land to create level surfaces for cultivation.
• Terraces slow down the flow of water and prevent erosion, and they also provide a more stable surface for crops to grow on.
• Terrace farming is a traditional agricultural practice that has been used for centuries in many parts of the world, and it is still widely used today in some areas.

The correct answer is Sugarcane.

Key Points

• Sugarcane
• It is a member of the grass family Poaceae.
• Sugarcane is a perennial plant.
• Sugarcane is a major source of sugar, and it is also used to make ethanol, paper, and other products.
• Sugarcane is a tropical plant.

Additional Information

• Cotton
• Cotton is the most important natural fiber in the world.
• Cotton is used to make a wide variety of products, including clothing, home textiles, and industrial products.
• Cotton plants are annual plants, and they grow best in warm, sunny climates with well-drained soil.
• Maize 
• Maize is a cereal grain that is native to the Americas.
• Maize is a staple food for millions of people.
• Maize is a versatile crop that can be used to make a variety of products, including food, feed, fuel, and bioethanol.
• Rubber
• ​Rubber is a natural or synthetic polymer.
• Natural rubber is produced from the sap of rubber trees.
• Synthetic rubber is made from petroleum products.
• Rubber has a number of properties that make it a valuable material.

The correct answer is Ctrl + P. 

Key Points

• Ctrl + P is used to print the document.

Additional Information Word shortcut keys

• Ctrl + A -- Select all contents of the page.
• Ctrl + B -- Bold highlighted selection.
• Ctrl + C -- Copy selected text.
• Ctrl + X -- Cut selected text.
• Ctrl + N -- Open new/blank document.
• Ctrl + O -- Open options.
• Ctrl + P -- Open the print window.

​

• Ctrl + F -- Open find box.
• Ctrl + I -- Italicise highlighted selection.
• Ctrl + K -- Insert link.
• Ctrl + U -- Underline highlighted selection.
• Ctrl + V -- Paste.
• Ctrl + Y -- Redo the last action performed.
• Ctrl + Z -- Undo last action.

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• Ctrl + G -- Find and replace options.
• Ctrl + H -- Find and replace options.
• Ctrl + J -- Justify paragraph alignment.
• Ctrl + L -- Align selected text or line to the left.
• Ctrl + Q -- Removes all formatting from a highlighted paragraph
• Ctrl + E -- Align selected text or line to the centre.
• Ctrl + R -- Align selected text or line to the right.
• Ctrl + M -- Indent the paragraph.

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• Ctrl + T -- Hanging indent.
• Ctrl + D -- Font options.
• Ctrl + Shift + F -- Change the font.
• Ctrl + Shift + > -- Increase selected font +1.
• Ctrl + ] -- Increase selected font +1.
• Ctrl + [ -- Decrease selected font -1.

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• Ctrl + Shift + * -- View or hide non printing characters.
• Ctrl + (Left arrow) -- Move one word to the left.
• Ctrl + (Right arrow) -- Move one word to the right.
• Ctrl + (Up arrow) -- Move to the beginning of the line or paragraph.
• Ctrl + (Down arrow) -- Move to the end of the paragraph.
• Ctrl + Del -- Delete word to the right of the cursor.

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• Ctrl + Backspace -- Delete word to the left of the cursor.
• Ctrl + End -- Move cursor to end of the document.
• Ctrl + Home -- Move cursor to the beginning of the document.
• Ctrl + Space -- Reset highlighted text to default font.
• Ctrl + 1 -- Single-space lines.
• Ctrl + 2 -- Double-space lines.
• Ctrl + 5 -- 1.5-line spacing.

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• Ctrl + Alt + 1 Change text to heading 1.
• Ctrl + Alt + 2 Change text to heading 2.
• Ctrl + Alt + 3 Change text to heading 3.
• F1 -- Open help.
• Shift + F3 -- Change case of selected text.
• Shift + Insert -- Paste.

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• F4 -- Repeat the last action performed (Word 2000+).
• F7 -- Spell check selected text and/or document.
• Shift + F7 -- Activate the thesaurus.
• F12 -- Save as.
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The correct answer is 1928.​

Key Points

• In India, the Bardoli movement was a tax-free movement.
• In the year 1928, the Bardoli Satyagraha took place.
• This movement was known as one of the biggest incidents of the Civil Disobedience movement, which was a part of India's war for independence.
• Sardar Vallabhbhai Patel eventually headed the movement, and its success helped pave the way for Patel to become one of the most prominent leaders of the independence struggle.

Additional Information

• Sardar Vallabhbhai  Patel initially wrote to the Governor of Bombay, requesting that the taxes be reduced during the year during which the tragedies were occurring.
• The Governor, on the other hand, ignored the letter and responded by announcing the collection.
• The Bombay Presidency ignored the plight of the farmers and increased tax rates by 22%.
• Patel then informed all of the farmers in the Bardoli taluka to refuse to pay their taxes.
• The government had commissioned the Maxwell-Broomfield Commission to investigate the situation.
• Following a thorough investigation, the tax increase was determined to be only 6.03%.
• Gandhiji also supported the movement through his writings in the periodical 'Young India.'

The correct answer is Pink head duck.

Key Points

• Extinct Species:
• Species that are not found after searches of known or likely areas where they may occur.
• A species may be extinct from a local area, region, country, continent, or the entire earth.
• Examples:
• Pink head duck

Additional Information

• Based on the International Union for Conservation of Nature and Natural Resources (IUCN), we can classify the plant and animal species as:
• Normal Species:
• Species whose population levels are considered to be normal for their survival, such as cattle, sal, pine, rodents, etc.
• Endangered Species:
• Species that are in danger of extinction.
• The survival of such species is difficult if the negative factors that have led to a decline in their population continue to operate.
• Examples:
• Blackbuck, Crocodile, Indian wild ass, Indian rhino, Lion-tailed macaque, Sangai (brow-antlered deer in Manipur)
• Vulnerable Species: 
• Species whose population has declined to levels from where it is likely to move into the endangered category in the near future if the negative factors continue to operate.
• Examples:
• Blue sheep, Asiatic elephant, Gangetic dolphin
• Rare Species:
• Species with a small population may move into the endangered or vulnerable category if the negative factors affecting them continue to operate.
• Examples:
• Himalayan brown bear, Wild Asiatic buffalo, Desert fox and Hornbill

The correct answer is Varanasi.

Key Points

• Varanasi will be the first city in Shanghai Cooperation Organisation (SCO) region to be granted the rotating title of ‘Cultural & Tourism capital of SCO’.
• It will become the Capital for 2022-23 under a new rotating initiative by the SCO to promote people-to-people contacts and tourism among the member states.

Additional Information

• The Shanghai Cooperation Organisation (SCO) is a Eurasian political, economic and security alliance.
• In terms of geographic scope and population, it is the world's largest regional organization.
• It covers approximately 60% of the area of Eurasia, 40% of the world's population, and more than 30% of global GDP.
• The SCO currently comprises eight Member States (China, India, Kazakhstan, Kyrgyzstan, Russia, Pakistan, Tajikistan and Uzbekistan).
• The Shanghai Cooperation Organisation:
• Headquarters: Beijing, China
• Founded: 15 June 2001
• Founders: Russia, China, Uzbekistan, Kazakhstan, Tajikistan, Kyrgyzstan​​

The correct answer is Ennore.

Key Points According to the Ministry of Ports, Shipping, and Waterways, around 95 percent of India's trading by volume and 70 percent by value is done through maritime transport. It is serviced by 13 major ports (12 Government-owned and one private) and 187 notified minor and intermediate ports.

First corporatized port of India:

• Kamarajar port located at Ennore in Tamil Nadu is the only corporate port owned by the Indian government.
• Kamarajar Port Ltd was formed as a company under the Companies Act when it was opened in 2001.
• Ennore Port is located on the Coromandel Coast about 18 km north of Chennai Port, Chennai, it is the 12^th major port of India.
• It is the first port in India which is a public company.
• The Kamarajar Port Limited is the only corporatized major port and is registered as a company.

Additional Information

Corporatized port of India:

• The process of corporatization means that there is a change in legal structure.
• It should not be confused with privatization or disinvestment.
• Thus, no major impact can be expected by a mere change in the legal structure.
• Under the Major Port Trusts Act of 1963, the ports trusts are managed by the Boards of Trustees.
• Major Port Authorities Bill 2020 was recently introduced in the Lok Sabha by the Ministry of Shipping.
• The Bill aims to replace the Major Port Trusts Act, 1963.
• It seeks to provide for the regulation, operation, and planning of Major Ports in India and to vest the administration, control, and management of such ports upon the Boards of Major Port Authorities.
• This will empower the Major Ports to perform with greater efficiency on account of full autonomy in decision making and by modernizing the institutional framework of Major Ports.

The correct answer is Bengaluru FC.

Key Points

• The Durand Cup is one of the oldest football tournaments in the world and the oldest in India.
• It's named after its founder, Sir Mortimer Durand, who started the tournament in 1888.
• The tournament has been held annually, except for some breaks during the World Wars.
• In the 2022 Durand Cup, Bengaluru FC emerged as the winner.
• Bengaluru FC is a professional football club based in Bengaluru, India, that competes in the Indian Super League (ISL).
• The team was established in 2013 and has been successful in Indian football, with several major titles to their name.
• In the 2022 Durand Cup final, Bengaluru FC faced Mumbai City FC.
• The match saw Bengaluru FC come out on top with a 2-1 victory, thus securing their win of the prestigious Durand Cup title​1​.
• This was a significant achievement for Bengaluru FC and its captain, Sunil Chhetri, one of India's most celebrated football players.
• This victory added another feather to their cap and marked a key moment in their history.

The correct answer is blue, green.

Key Points

• When an iron nail is dipped into a solution of copper sulfate, the color of the solution changes due to a displacement reaction that occurs because iron is more reactive than copper.
• The blue colour of copper sulphate solution changes to green because of the formation of iron (II) sulfate.
• This is a type of single replacement reaction where iron replaces copper in the compound because iron is more reactive than copper.
• The equation for this reaction is:
• Fe(s) + CuSO4 (aq) -> FeSO4 (aq) + Cu(s)
• The green colour is due to the formation of FeSO4 or iron (II) sulfate in solution.

The correct answer is Budget set.

Key Points

• The collection of all bundles that the consumer can buy with her income at the prevailing market prices is called the Budget set.
• The budget set represents all the combinations of goods and services that the consumer can afford given the prices and their income.
• This set is subject to the budget constraint, which is the limitation on the consumer's income that they cannot surpass.

Additional Information

• Budget constraint:
• ​A budget constraint represents the limit on the consumption bundles that a consumer can afford.
• It is a line that maps out every combination of goods and services that a consumer can purchase if they spend all of their income.
• The budget constraint is determined by the consumer's income, the price of one good, and the price of the other good.
• Budget anomaly:
• ​This term isn't commonly used in the field of economics.
• An "anomaly" typically refers to something that deviates from the norm or from expectations.
• In the context of a budget, it could hypothetically refer to an unexpected or unusual occurrence in relation to the budget, but it's not a standard term you'd find in economic theory or analysis.
• Budget line:
• ​This is another term for the budget constraint.
• It's a graphical representation of all the combinations of goods that a consumer can afford with a given income, given the prices of those goods.
• The budget line shows the boundary of the budget set.
• If prices or income change, the budget line will shift.

The correct answer is Iodine.

Key Points

• The swelling of glands in the neck is most commonly associated with a deficiency of Iodine
• When there's a deficiency of iodine in the diet, the thyroid gland in the neck swells up, a condition known as goiter.
• Iodine is essential for the production of thyroid hormones, which regulate various body functions such as metabolism and growth.
• When the body doesn't get enough iodine, the thyroid gland works harder to try to produce these hormones, leading to swelling.

Additional Information

• Vitamin C:
• This vitamin is essential for many functions in the body, including the maintenance of skin, blood vessels, bones and cartilage, and the protection of cells.
• It's also crucial for wound healing.
• Scurvy is the classic disease related to Vitamin C deficiency, characterized by bleeding gums and skin spots.
• However, it doesn't cause a swollen neck gland.
• Vitamin D:
• This vitamin helps the body absorb calcium, which is vital for bone health.
• Deficiency of Vitamin D can cause rickets in children (characterized by soft, weak bones) and osteomalacia in adults (leading to bone pain and muscle weakness), but it doesn't lead to a swollen neck gland.
• Calcium:
• ​This mineral is essential for building and maintaining strong bones.
• A deficiency in calcium can lead to conditions like osteoporosis and hypocalcemia, which can cause muscle cramps, convulsions, and abnormal heart rhythms.
• However, a deficiency in calcium doesn't cause swelling of the neck glands.

The correct answer is Odisha.

Key Points

• The Konark Sun Temple is a 13^th-century Hindu temple dedicated to the sun god Surya.
• It is located in Konark, a town in the Puri district of Odisha, India.
• The temple is a UNESCO World Heritage Site and is one of the most popular tourist destinations in India.
• Sun Temple of Konark was built by King Narasimhadeva I of the Eastern Ganga Dynasty about 1250 CE.
• This temple is dedicated to the Hindu god Surya and located 35 km northeast from Puri.

Additional Information

Shortcut Trick

Numbers divisible by both 2 and 9 must be multiples of LCM(2, 9) = 18.

The first 8 such numbers form an Arithmetic Progression (AP): 18, 36, ..., (18 × 8).

Average of an AP = (First term + Last term) ÷ 2

Average = (18 + 144) ÷ 2 = 162 ÷ 2 = 81

∴ The correct answer is 81.

Alternate Method

Given: First 8 positive even numbers divisible by 9.

Formula Used: Average of n terms in AP = [a + l] / 2, where a is the first term and l is the last term.

⇒ A number is even and divisible by 9 if it is a multiple of 18.

⇒ First term (a) = 18 × 1 = 18

⇒ 8^th term (l) = 18 × 8 = 144

⇒ Average = (18 + 144) ÷ 2

⇒ Average = 162 ÷ 2

⇒ Average = 81

∴ The correct answer is 81.

Additional Information

Average of first n multiples

The average of the first n multiples of a number K is given by the formula: K × (n + 1) ÷ 2.

Divisibility Rule of 18

A number is divisible by 18 if it is even (divisible by 2) and the sum of its digits is divisible by 9.

Arithmetic Progression Average

For any series in AP, the average is always the middle term (if n is odd) or the mean of the two middle terms (if n is even).

calculation:

To find the value of cos θ given the equation cosec θ + cot θ = s, we can use trigonometric identities to express cosec θ and cot θ in terms of cos θ.

Recall the following trigonometric identities:

cosec θ = 1/sin θ

cot θ = cos θ / sin θ

Substituting these identities into the given equation, we have:

1/sin θ + cos θ/sin θ = s

Now, we can combine the fractions on the left side:

(1 + cos θ)/sin θ = s

To find the value of cos θ, we need to isolate it on one side of the equation. Let's rearrange the equation:

1 + cos θ = s × sin θ

Now, let's square both sides of the equation to eliminate the denominator:

$(1 + cos θ)^2 = (s × sin θ)^2$

Since$sin^2 θ = 1 - cos^2 θ$ (from the Pythagorean identity), we can substitute it in the equation:

$(1 + cos θ)^2 = s^2 × (1 - cos^2 θ)$

$(1 + cos θ)^2 = s^2 × (1 - cos θ) (1 +cos θ)$

$cos θ + cos θ s^2= s^2 -1$

$cos θ (1+ s^2)= s^2 -1$

$cos θ = \frac{(s^2 - 1)}{(1 + s^2)}$

Therefore, the value of cos θ is $\frac{(s^2 - 1)}{(1 + s^2)}$

Calculation:

The selling price of all articles

(1100 + 950 + 900 + 1100 + 750 + 1350) = 6150

A1 = Average = 6150/6 = 1025

A2 = The value of the average cost price of L, M, N and O

(800 + 700 + 500 + 600)/4 = 2600/4

⇒ 650

A1 + A2 = 1025 + 650 = 1675

∴ Option 3 is the correct answer.

Shortcut Trick

The algebraic identity for the given expression is:

(p³ + q³ + r³ − 3pqr) / (p + q + r) = ½ × [(p − q)² + (q − r)² + (r − p)²]

Substitute the given differences: ½ × [(−6)² + 5² + 1²]

⇒ ½ × [36 + 25 + 1] = 62 / 2 = 31

∴ The correct answer is 31.

Alternate Method

Given:

(p − q) = −6

(q − r) = 5

(r − p) = 1

Formula Used:

p³ + q³ + r³ − 3pqr = (p + q + r) × ½ × [(p − q)² + (q − r)² + (r − p)²]

Calculations:

⇒ Target = (p³ + q³ + r³ − 3pqr) / (p + q + r)

⇒ Target = [(p + q + r) × ½ × {(p − q)² + (q − r)² + (r − p)²}] / (p + q + r)

⇒ Target = ½ × [(−6)² + 5² + 1²]

⇒ Target = ½ × [36 + 25 + 1]

⇒ Target = 62 / 2

⇒ Target = 31

∴ The correct answer is 31.

Additional Information

The Cube Identity

a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca). This is a fundamental expansion used in algebraic simplifications.

Sum of Squares Alternative

The expression (a² + b² + c² − ab − bc − ca) can always be written as ½[(a − b)² + (b − c)² + (c − a)²], which is useful when differences are known.

Special Case: a + b + c = 0

If the sum of the variables is zero, then a³ + b³ + c³ = 3abc. This is frequently tested in competitive exams.

Special Case: a = b = c

If all three variables are equal, then the value of the expression a³ + b³ + c³ − 3abc is always zero.

Concept Used:

In a circle, the following property holds: the angle that a chord subtends on the major arc is 180 degrees minus the angle that the same chord subtends on the minor arc. This is due to the fact that any point on a circle defines an angle of 360 degrees.

Calculation:

So, if the angle made by a chord on the major arc is ∠ACB = 50°, 

then the angle that the same chord makes on the minor arc of the

circle would be  ∠ACB = 180 - 50 = 130°.

∴ Option 2 is the correct answer.

Given:

sin Θ/(cot Θ + cosec Θ) = 1

Calculation:

sin Θ/(cot Θ + cosec Θ) = 1

sin Θ/(cosΘ//sinΘ + 1/sinΘ) = 1

sin² Θ/(cos Θ+1) = 1

1 - cos² Θ/(cos Θ +1) = 1

(1 - cos Θ)(cos Θ +1) (/(cos Θ +1) = 1

(1 - cos Θ) = 1

cos Θ = 0

Θ = 90°

∴ Option 2 is the correct answer.

Given:

P = Rs. 3000

R = 10% per annum

I = Rs. 1200

Concept Used:

I = PRT / 100

where:

I = interest

P = principal amount (the initial amount of money)

R = annual interest rate (in percentage)

T = time the money is invested for (in years).

Calculation:

We are asked to find T (the time of investment), but in months instead of years. So representing T in years, the equation becomes:

1200 = 3000 × 10 ×  T / 100

Which simplifies to:

1200 = 300T

Solving for T gives:

T = 1200/ 300

T = 4 years

Since the question is asking for the time in months, we convert this to months by multiplying by 12 (since there are 12 months in a year):

T = 4 × 12 = 48 months.

So, the sum is invested for 48 months.

Calculation:

Average population of A = (500 + 700 + 550 + 400 + 300)/5

⇒ 2450/5 = 490

Average population of B = (800 + 600 + 450 + 350 + 500)/5

⇒ 2700/5 = 540

Difference between the average population of A and B in all the years = 540 - 490 = 50

∴ Option 3 is the correct answer.

Shortcut Trick

Upstream Speed = Downstream Speed − 2 × Stream Speed = 25 − (2 × 3) = 19 km/hr

Downstream Time = 100 ÷ 25 = 4 hours

Upstream Time = 57 ÷ 19 = 3 hours

Total Time = 4 + 3 = 7 hours

∴ The correct answer is 7 hours.

Alternate Method

Given:

Downstream speed = 25 km/hr

Speed of stream = 3 km/hr

Formula used:

Downstream Speed = Speed of boat in still water + Speed of stream

Upstream Speed = Speed of boat in still water − Speed of stream

Time = Distance ÷ Speed

Upstream 19 km/hr

Still Water 22 km/hr

Downstream 25 km/hr

• 3 (Stream)

− 3 (Stream)

Calculations:

⇒ Speed of boat in still water = Downstream speed − Speed of stream

⇒ Boat speed in still water = 25 − 3 = 22 km/hr

⇒ Upstream speed = Boat speed in still water − Speed of stream

⇒ Upstream speed = 22 − 3 = 19 km/hr

⇒ Time taken for 100 km downstream = 100 ÷ 25 = 4 hours

⇒ Time taken for 57 km upstream = 57 ÷ 19 = 3 hours

⇒ Total time = 4 + 3 = 7 hours

∴ The correct answer is 7 hours.

Additional Information

Speed in Still Water

It is the average of Downstream and Upstream speeds: B = (D + U) ÷ 2.

Speed of Stream

It is half the difference between Downstream and Upstream speeds: S = (D − U) ÷ 2.

Relative Speed in Boats

Downstream speed is always greater than upstream speed by twice the stream speed: D − U = 2S.

Shortcut Trick

Numbers divisible by both 5 and 3 must be divisible by their LCM, which is 15.

Multiples of 15 up to 457 ⇒ 457 ÷ 15 = 30 (quotient)

Multiples of 15 up to 16 (before 17) ⇒ 16 ÷ 15 = 1 (quotient)

Total numbers in range [17, 457] = 30 − 1 = 29.

∴ The correct answer is 29.

Alternate Method

Given: Range = 17 to 457; Divisible by both 3 and 5.

Formula Used: n = [(l − a) ÷ d] + 1; where l = last term, a = first term, d = common difference.

⇒ LCM(3, 5) = 15

⇒ First multiple after 17 = 30 (a)

⇒ Last multiple before 457 = 450 (l)

⇒ Common difference = 15 (d)

⇒ n = [(450 − 30) ÷ 15] + 1

⇒ n = [420 ÷ 15] + 1

⇒ n = 28 + 1 = 29

∴ The correct answer is 29.

Additional Information

Divisibility by Multiple Factors

If a number is divisible by two co-prime numbers x and y, it must be divisible by their product x × y.

Arithmetic Progression (AP)

To find the number of terms in a finite AP, use n = [(l − a)/d] + 1, where l is the last term, a is the first term, and d is the difference.

Counting Multiples Shortcut

The number of multiples of k in the range [1, N] is simply the floor value of N ÷ k.

Given:

a = 10 and b = 3

Calculation:

⇒ $\frac{(a+b)^2}{a^2-b^2}$

⇒ $\frac{(a+b)^2}{(a-b)(a+b)}$

⇒ $\frac{(a+b)}{(a-b)}$

Put the values of a and b

⇒ $\frac{(10+3)}{(10-3)}$

⇒ 13/7 = 169/91

∴ Option 2 is the correct answer.

Shortcut Trick

Find the approximate square root of the product: √7387 ≈ 85.9.

Identify the consecutive prime numbers immediately below and above 86.

The prime numbers are 83 and 89.

Verify the product: 83 × 89 = 7387.

Calculate the difference: 89 − 83 = 6.

∴ The correct answer is 6.

Alternate Method

Given:

Product of two consecutive prime numbers = 7387

Calculations:

⇒ Let the two consecutive prime numbers be p₁ and p₂.

⇒ p₁ × p₂ = 7387

⇒ To find the numbers, approximate the square root: √7387

⇒ We know 80² = 6400 and 90² = 8100.

⇒ Since 85² = 7225, the root is slightly greater than 85.

⇒ Primes near 86 are 83 and 89.

⇒ 83 × 89 = (86 − 3)(86 + 3) = 86² − 3² = 7396 − 9 = 7387.

⇒ Difference = 89 − 83 = 6.

∴ The correct answer is 6.

Additional Information

Prime Numbers

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

Twin Primes

Twin primes are pairs of prime numbers that have a difference of 2, such as (3, 5), (11, 13), or (71, 73).

Consecutive Primes

Consecutive primes are prime numbers that follow each other in order without any other prime numbers between them.

Square Root Method for Factors

If the product of two numbers is P, at least one of the factors must be less than or equal to √P.

Calculation:

Firstly, let's find out the actual number of male faculties in Schools A and B:

For School A, the number of males is 10% of 8400, which equals 840.

For School B, the number of males is 20% of 8400, which equals 1680.

The ratio of male to female faculties in School A is 2 : 5

So, the number of female faculties in School A

⇒ (5/2) × 840 = 2100.

In School B, the ratio of male to female faculties is 4:3, 

So, number of female faculties in School B

⇒(3/4) × 1680 = 1260.

Difference =  2100 - 1260 = 840.

So, the difference in total female faculties in School A and School B is 840.

∴ Option 1 is the correct answer.

Given:

∠M = 90 degrees,

KM = 12 cm and

LM = 5 cm

Concept Used:

Sec θ = Hypotenuse/Base

Pythagoras Theorem 

Hypotenuse² = Perpendicular² + Base²

Calculation:

In the given triangle,

⇒ Perpendicular = KM = 12 cm

⇒ Base = LM = 5 cm

⇒ Hypotenuse² = 12² + 5²

⇒ Hypotenuse = 13

Sec L = Hypotenuse/Base

⇒ 13/5

∴ Option 4 is the correct answer.

Calculation:

According to the question:

Anuj invest for 12 months.

Ajay invest for 6 months

and Ankit invest for 3 months

So the ratio of investment is

30000 × 12 : 45000 × 6 : 60000 × 3

4 : 3 : 2

The ratio of Anuj is 

18000 × 4/9 = 8000

Therefore, Anuj's share in the profit is Rs. 8,000.

∴ Option 3 is the correct answer.

Shortcut Trick

Since only milk is added, the quantity of water remains constant.

Initial Water % = 100% − 30% = 70%

Initial Water = Final Water ⇒ 150 × 70% = (New Total) × 40%

New Total = (150 × 70) ÷ 40 = 262.5 litres.

Milk added = 262.5 − 150 = 112.5 litres.

∴ The correct answer is 112.5 litres.

Alternate Method

Given:

Initial volume = 150 litres

Initial Milk percentage = 30%

Target Water percentage = 40%

Step 1: Calculate initial water quantity.

⇒ Initial Water % = 100% − 30% = 70%

⇒ Quantity of Water = (70 ÷ 100) × 150 = 105 litres.

Step 2: Calculate the new total volume when water is 40%.

⇒ 40% of New Total = 105 litres

⇒ New Total = (105 × 100) ÷ 40

⇒ New Total = 262.5 litres.

Step 3: Calculate the quantity of milk to be added.

⇒ Added Milk = New Total − Initial Total

⇒ Added Milk = 262.5 − 150 = 112.5 litres.

∴ The correct answer is 112.5 litres.

Additional Information

Rule of Constant Component

In mixture problems, identify the component whose quantity does not change. Use the equation: Initial Total × Initial % = Final Total × Final % for that fixed component.

Alligation Method

This can also be solved by alligation using milk percentages: 30% (Initial) and 100% (Added Milk) to get a mean of 60% (since water is 40%).

Inverse Proportion in Mixtures

If the quantity of one component is constant, the total volume of the mixture is inversely proportional to the percentage concentration of that component.

Shortcut Trick

The angle at the orthocenter ∠BOC and the opposite vertex angle ∠A are supplementary.

∠A = 180° − ∠BOC = 180° − 120° = 60°.

In ΔABC, the sum of all angles is 180°.

∠ACB = 180° − (∠A + ∠B) = 180° − (60° + 55°) = 65°.

∴ The correct answer is 65 degree.

Alternate Method

Given:

In ΔABC, O is the orthocenter.

∠B = 55°

∠BOC = 120°

Formula Used:

1. Angle at orthocenter: ∠BOC = 180° − ∠A
2. Angle sum property: ∠A + ∠B + ∠C = 180°

Calculations:

⇒ ∠BOC = 180° − ∠A

⇒ 120° = 180° − ∠A

⇒ ∠A = 180° − 120° = 60°

⇒ In ΔABC, ∠A + ∠B + ∠C = 180°

⇒ 60° + 55° + ∠ACB = 180°

⇒ 115° + ∠ACB = 180°

⇒ ∠ACB = 180° − 115° = 65°

∴ The correct answer is 65 degree.

Additional Information

Orthocenter Properties

The orthocenter is the intersection point of the altitudes. The angle subtended by any side at the orthocenter and the interior angle at the opposite vertex are supplementary (sum = 180°).

Orthocentric System

In any triangle ABC with orthocenter O, each of the four points (A, B, C, or O) is the orthocenter of the triangle formed by the other three points.

Euler Line

In a non-equilateral triangle, the orthocenter (O), centroid (G), and circumcenter (C) are collinear, with the centroid dividing the segment OC in the ratio 2 : 1.

Shortcut Trick

In a cyclic quadrilateral, the sum of opposite angles is always 180°.

Given: ∠P + ∠R = 180°

⇒ (3x + 5) + 4x = 180

⇒ 7x + 5 = 180

⇒ 7x = 175

⇒ x = 25

∴ The correct answer is 25 degree.

Alternate Method

Given:

∠P = 3x + 5

∠R = 4x

Quadrilateral PQRS is cyclic, where P and R are opposite vertices.

According to the Cyclic Quadrilateral Theorem, the sum of either pair of opposite angles is 180°.

⇒ ∠P + ∠R = 180°

⇒ (3x + 5) + 4x = 180

⇒ 7x + 5 = 180

⇒ 7x = 180 − 5

⇒ 7x = 175

⇒ x = 175 ÷ 7

⇒ x = 25

∴ The correct answer is 25 degree.

Additional Information

Cyclic Quadrilateral Property

A quadrilateral is cyclic if and only if its vertices lie on a circle, and its opposite angles sum to 180°.

Exterior Angle Property

The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle.

Ptolemy's Theorem

For a cyclic quadrilateral, the product of the diagonals is equal to the sum of the products of the opposite sides: (PQ × RS) + (QR × PS) = PR × QS.

Shortcut Trick

When a solid cylinder is bisected parallel to the base, two new circular faces are added to the total surface area.

Percentage Increase = [ (Area of 2 new faces) ÷ (Initial Total Surface Area) ] × 100

Simplified formula: Percentage Increase = [ r ÷ (r + h) ] × 100

Applying values: [ 7 ÷ (7 + 5) ] × 100 = 7/12 × 100 = 58.33%.

∴ The correct answer is 58.33 percent.

Alternate Method

Given:

Radius (r) of the cylinder = 7 cm

Height (h) of the cylinder = 5 cm

Formula Used:

Total Surface Area (TSA) of a cylinder = 2πr(r + h)

Area of circular base = πr²

Calculations:

⇒ Initial TSA = 2 × π × 7 × (7 + 5) = 14 × 12 × π = 168π cm²

⇒ When bisected, two identical cylinders are formed, creating two extra circular surfaces.

⇒ Extra Area Added = 2 × (π × 7²) = 2 × 49 × π = 98π cm²

⇒ Percentage Increase = [ (Extra Area) ÷ (Initial TSA) ] × 100

⇒ Percentage Increase = (98π ÷ 168π) × 100

⇒ Percentage Increase = (7 ÷ 12) × 100 = 58.333...

∴ The correct answer is 58.33 percent.

Additional Information

Curved Surface Area (CSA)

The area of the side surface of the cylinder, excluding the top and bottom bases, is 2πrh.

Volume of Cylinder

The amount of space occupied by the cylinder is given by V = πr²h. Bisection does not change the total volume.

Vertical Bisection

If a cylinder is cut vertically through the center of its bases, the extra area added is two rectangles, each with area (diameter × height).

Multiple Horizontal Cuts

If a cylinder is cut into 'n' identical parts horizontally, the number of new circular faces added is 2(n − 1).

Given:

Diamond ring is marked at Rs. 20,000.

Two successive discounts of 25% and x% respectively are given.

He paid Rs. 12,000.

Calculation:

Let's break this down into steps:

First, Nikhil is given a discount of 25%. This means he pays 75% of the original price (because 100% - 25% = 75%).

So, the price after the first discount is:

20000 ×  75% = Rs. 15,000.

Nikhil is then given another discount, of x% on the remaining price of Rs. 15,000. After this discount, the price he pays is Rs. 12,000.

We can set up an equation to find x. If we let x be the second discount, then 100% - x% of the price he pays after the first discount equals the final price. This can be written as:

15000 ×  (100% - x%) = 12000.

This simplifies to:

15000 - 15000 ×  (x/100) = 12000.

Rearranging and solving for x gives us:

15000 ×  (x/100) = 15000 - 12000,

so

150x = 3000,

x = 3000 / 150,

x = 20.

So, the second discount is 20%.

∴ Option 3 is the correct answer.

Shortcut Trick

Ratio of efficiency (Anuj : Vinod) = 150 : 100 = 3 : 2.

Total Work = Anuj’s efficiency × Anuj’s days = 3 × 20 = 60 units.

Combined efficiency of Anuj and Vinod = 3 + 2 = 5 units/day.

Days taken together = 60 ÷ 5 = 12 days.

∴ The correct answer is 12 days.

Alternate Method

Given:

Efficiency of Anuj = 150% of Efficiency of Vinod

Time taken by Anuj = 20 days

Formula Used:

Total Work = Efficiency × Time

Time Taken = Total Work ÷ Efficiency

⇒ Let Vinod’s efficiency be 2 units/day.

⇒ Anuj’s efficiency = 150% of 2 = 3 units/day.

⇒ Total Work = Anuj’s efficiency × Anuj’s time = 3 × 20 = 60 units.

⇒ Time taken by Vinod = 60 ÷ 2 = 30 days.

⇒ Combined Efficiency of Anuj and Vinod = 3 + 2 = 5 units/day.

⇒ Time taken together = 60 ÷ 5 = 12 days.

∴ The correct answer is 12 days.

Additional Information

Efficiency and Time Relation

Efficiency is inversely proportional to the time taken to complete a work. If the efficiency ratio is a : b, then the time ratio will be b : a.

Combined Work Formula

If two individuals take ‘x’ and ‘y’ days respectively, the time taken to complete the work together is (x × y) ÷ (x + y) days.

Work-Efficiency Constant

Total Work = E₁ × T₁ = E₂ × T₂. This formula is useful for calculating unknown time when efficiencies are known.

Calculation:

To find the value of the expression (a + b)² + (a - b)², we can expand it and simplify.

Expanding (a + b)² using the formula (a + b)² = a² + 2ab + b², we get:

(a + b)² = a² + 2ab + b²

Expanding (a - b)² using the formula (a - b)² = a² - 2ab + b², we get:

(a - b)² = a² - 2ab + b²

Now, let's substitute these expressions back into the original expression:

(a + b)² + (a - b)² = (a² + 2ab + b²) + (a² - 2ab + b²)

Expanding further:

(a + b)² + (a - b)² = a² + 2ab + b² + a² - 2ab + b²

Combining like terms, we have:

(a + b)² + (a - b)² = (a² + a²) + (2ab - 2ab) + (b² + b²)

Simplifying, we get:

(a + b)² + (a - b)² = 2a² + 2b²

Therefore, the value of (a + b)² + (a - b)² is 2a² + 2b².

2(a2 + b2).

∴ Option 4 is the correct answer.

Given:

The sum of the angles made by a chord XY at the centre and on the circumference of the circle is 270 degrees.

The radius of this circle is 24 cm

Concept Used:

The angle formed by the chord at the centre is double the angle formed by the same chord on the circumference.

Calculation:

Let the angle formed by the chord on the circumference be θ.

Then the angle formed by the same chord on the centre is 2θ.

According to the question,

2θ + θ = 270

θ = 90° 

It means the chord is the diameter as the diameter makes the 90° angle on the circumference.

Length of this chord = Diameter = 2 × 24 = 48 cm

∴ Option 4 is the correct answer.

Calculation:

The total number of workers whose daily wages are less than Rs. 450 = 30

Total number of workers whose daily wages are Rs. 650 = 35

Ratio = 30 : 35 = 6 : 7

∴ Option 4 is the correct answer.

Shortcut Trick

Income of C = Expenditure of C + Savings of C.

Given Savings of C = Expenditure of D, so Income of C = Expenditure of C + Expenditure of D = Rs. 12000.

Ratio of Incomes is 3 : 4 ⇒ 3 units = Rs. 12000 ⇒ 1 unit = Rs. 4000.

Total Income (3 + 4 = 7 units) = 7 × 4000 = Rs. 28000.

Total Savings = Total Income − Total Expenditure = 28000 − 12000 = Rs. 16000.

∴ The correct answer is Rs. 16000.

Alternate Method

Given:

Ratio of Incomes of C and D = 3 : 4

Sum of Expenditures (E_C + E_D) = Rs. 12000

Savings of C (S_C) = Expenditure of D (E_D)

Formula:

Income = Expenditure + Savings

Calculations:

⇒ Let Income of C = 3x and Income of D = 4x.

⇒ Savings of C = Income of C − Expenditure of C

⇒ S_C = 3x − E_C

⇒ Since S_C = E_D, then E_D = 3x − E_C

⇒ E_C + E_D = 3x

⇒ Given E_C + E_D = 12000, so 3x = 12000

⇒ x = 12000 ÷ 3 = 4000

⇒ Total Income = 3x + 4x = 7x = 7 × 4000 = Rs. 28000

⇒ Total Savings = Total Income − Total Expenditure

⇒ Total Savings = 28000 − 12000 = 16000

∴ The correct answer is Rs. 16000.

Additional Information

Fundamental Budget Equation

The relationship between income, expenditure, and savings is always Income = Expenditure + Savings. For multiple individuals, Total Income = Total Expenditure + Total Savings.

Ratio Distribution

If a total value V is divided in ratio a : b, then the parts are [a/(a+b)] × V and [b/(a+b)] × V. Here, the units method (1 unit = Total/Total units) is the fastest way to solve.

Savings Equality Cases

When one person's savings equals another's expenditure, it directly links the first person's income to the sum of both people's expenditures.

The correct answer is 'Option 1' i.e. 'Float'.

Key Points

• The term "levitate" refers to the act of rising or floating in the air, especially in seeming defiance of gravity.
• The word "float" refers to remain or move on the surface of a liquid without sinking. (तैरना)

Therefore, the correct answer is: 'Float'.

Additional Information

• Laydown: To put or place something in a particular position. (रखना)
• Rusticate: To send someone away from a university or school as a punishment. (विद्यालय से निष्कासित करना)
• Walk: To move on foot at a regular pace by lifting and setting down each foot in turn. (चलना)

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

Key Points

• Fabricate means to create or invent something, often with the intention of deceiving.
• "Concoct" refers to creating or devising, often something that is not true.

Therefore, the correct answer is: 'Concoct'. 

Additional InformationMimic: To imitate or copy the actions, speech, or appearance of someone. (नकल करना)

Detached: Separated or disconnected from something; not emotionally involved or concerned. (अलग)

Flatten: To make something flat or level by pressing or crushing. (समतल करना)

The correct answer is 'Option 4'.

Key Points

• In the original sentence, there is a subject-verb agreement error.
• The subject "Vijay and Ajay" is plural, so the verb should also be in the plural form "are" instead of the singular form "is."
• This ensures proper subject-verb agreement.

Therefore, the correct sentence is: 'Vijay and Ajay are here to celebrate 7 years of their friendship'.

The correct answer is 'Option 1'.

Key Points

• The sentence discusses the behavior observed in a particular animal group where parents and others teach their young how to find food or water when it becomes scarce due to drought or other environmental changes.
• This order of the sentence provides a logical flow of information, starting with the subject (P) introducing the parents and others, followed by the purpose of teaching through example (Q).
• Then, it describes the specific situation (S) where food or water becomes scarce, and finally, it mentions the cause or reason (R) for the scarcity, which is drought or other environmental change.

Therefore, the correct answer is: 'PQSR'.

The correct answer is 'Option 4'.

Key Points

• When reporting someone's statement in indirect speech, we usually change the verb tense to reflect the shift in time.
• In this case, the original statement is in the present tense ("My parents are getting divorced"), so when we report it indirectly, we need to change the verb tense to past tense.
• 'Option 4' correctly changes the verb tense to past tense, reflecting the shift from the original statement.
• The past progressive tense ("were getting divorced") indicates an ongoing action in the past.

Therefore, the correct sentence is:  "Tina said that her parents were getting divorced".