SSC CHSL Tier-1 2022: Official Paper (Held On: 13 March, 2023 Shift 2) (Previous Year Paper)

The logic followed here is:

Option 1) 3241-5732 → 3241 - 5732 = -2491.

Option 2) 2354-4835 → 2354 - 4835 = -2481.

Option 3) 1326-3807 → 1326 - 3807 = -2481.

Option 4) 2345-4826 → 2345 - 4826 = -2481.

So, 'Option 1' is odd among the given options.

Hence, the correct answer is "Option 1".

The logic followed here is:

Logic: (Sum of the place value of all numbers)² + 1 = Code of the word.

'BED' is written as '122'

⇒ (2 + 5 + 4)² +1

⇒ 11² + 1 = 122.

'CAB' is written as '37'

⇒ (3 + 1 + 2)2 +1

⇒ 62 + 1 = 37.

Similarly, for 'ADD'

⇒ (1 + 4 + 4)2 +1

⇒ 92 + 1 = 82.

So, 'ADD' will be written as '82'.

Hence, the correct answer is "82".

The logic followed here is:

So, '47' will complete the series,

Hence, the correct answer is "Option 3".

The paper when unfolded will appear as shown below:

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: (1st number)² = 2nd number,

(1st number)3 = 3rd number.

Now,

for, (12, 144, 1728)

⇒ (12)² = 144,

⇒ (12)3 = 1728.

for, (6, 36, 216)

⇒ (6)2 = 36,

⇒ (6)3 = 216.

Similarly, for (10, 100, 1000)

⇒ (10)2 = 100,

⇒ (10)3 = 1000.

Hence, the correct answer is "Option 3".

The triangles are:

The triangles in the figure can be counted by breaking the figure down into its components.

1. The number of single, smallest triangles is 8.
   
2. The number of triangles formed by combining 2 components is 4.
   
3. The number of triangles formed by combining 3 components is 4.
   
4. The number of triangles formed by combining 4 or more components is 4.
   

Total triangles = 8 + 4 + 4 + 4 = 20.

So, there are 20 triangles in the given figure.

Hence, the correct answer is "20".

The logic followed here is:

Consider R as '-' then divide by 2.

Given,

For, 739 R 635 = 52,

⇒ (739 - 635) ÷ 2

⇒ 104 ÷ 2 = 52. 

For, 814 R 122 = 346,

⇒ (814 - 122) ÷ 2

⇒ 692 ÷ 2 = 346.

Similarly, for 532 R 220 = ?

⇒ (532 - 220) ÷ 2

⇒ 312 ÷ 2 = 156.

Hence, the correct answer is "156".

The correct mirror image of the given figure when the mirror is placed at line AB will be: 

 

Hence, "Option 1" is the correct answer.

BODMAS Table: 

Given equation I. 45 + 15 × 30 ÷ 10 − 25

Now, if '+ and -' are interchanged, then:

⇒ 45 - 15 × 30 ÷ 10 + 25

⇒ 45 - 15 × 3 + 25

⇒ 45 - 45 + 25

⇒ 70 - 45 = 25.

Given equation II: 6 × 9 + 5 − 8 ÷ 4

Now, if '+ and -' are interchanged, then:

⇒ 6 × 9 - 5 + 8 ÷ 4

⇒ 6 × 9 - 5 + 2

⇒ 54 - 5 + 2

⇒ 56 - 5 = 51.

Here, the correct values are '25 and 51'.

Hence, the correct answer is "Option 1".

The pattern followed here is:

Logic: The first word is a profession and the second word is a tool commonly used in that profession.

Farmer : Plough → Plough is a tool used by Farmer.

Similarly,

Surgeon: Scalpel → Scalpel is a tool used by the Surgeon.

Hence, the correct answer is "Option 2".

According to the sequence in the dictionary:

5. Wrack
6. Wrangler
7. Wrap
8. Wrasse
9. Wrath

According to the arrangement, "Wrath" will come at 'Fifth' position.

Hence, the correct answer is "Option 3".

The logic followed here is:

Option 1) (Car, Truck, Road) → Here, Car and Truck are types of vehicles, and Road is where these vehicles are used.

Option 2) (Chair, Table, Stool) → All three are types of furniture. They all belong to the same category.

Option 3) (Choreographer, Editor, Carpenter) → These are all professional roles or jobs. They all belong to the same category.

Option 4) (Shirt, Trouser, Saree) → These are all types of clothing. They all belong to the same category.

So, 'Option 1' odd among the options.

Hence, the correct answer is "Option 1".

The logic followed here is:

Given Sequence: WX _ WW _ _ Y _ W _ WXX _ Y _ Y

Now, putting the letters in the blank spaces given in the option one by one:

Option 1) WXXYXWW → WXW / WWXXYY / WXWXXWYWY

Option 2) YXYYWXX → WXY / WWXYYY / WWWXXXYXY

Option 3) YXXYWXY → WXY / WWXXYY / WWWXXXYYY

Here, 'Option 3' followed a pattern.

Option 4) WYXYWXY → WXW /WWYXYY / WWWXXXYYY

Hence, the correct answer is "Option 3".

According to the given Venn diagram:

The shaded area shows the "total number of pink are neither green nor yellow".

So, the total number of pink are neither green nor yellow = 10.

Hence, the correct answer is "10".

The logic followed here is:

For, 'ISLAND' is written as 'HTKBME',

For, 'TABLET' is written as 'SBAMDU',

Similarly, for 'BANGLE'

So, 'BANGLE' is coded as 'ABMHKF'.

Hence, the correct answer is "Option 3".

The logic followed here is:

Step I: Symbol  

rotated 90 degree and shifted one place in anticlockwise direction.

Step II: Symbol  

flipped 180 degree in alternate image.

Step III: Symbol  

rotated 90 degree and shifted one place in anticlockwise direction.

Step IV: Symbol 

 rotated 90 degree and shifted one place in clockwise direction.

So, the complete series is:

Hence, the correct answer is "Option 1".

Family Chart:

Given: 

Aman is the brother of Baman and Chaman.

Baman is Emily's mother.

Farhan is Aman's father.

 

Now, checking the options:

Option 1) Baman is sister of Chaman - True

Option 2) Aman and Emily are siblings - False

Option 3) Chaman is brother of Aman - False

Option 4) Chaman is male - False

Hence, the correct answer is "Option 1".

The correct mirror image of the given figure when the mirror is placed at line AB will be: 

 

Hence, "Option 2" is the correct answer.

The logic followed here is:

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

Now,

For, (8, 5, 39)

⇒ (8 + 5) × 3

⇒ 13 × 3 = 39.

For, (14, 11, 75)

⇒ (14 + 11) × 3

⇒ 25 × 3 = 75.

Similarly, for (7, 4, 33)

⇒ (7 + 4) × 3

⇒ 11 × 3 = 33.

Hence, the correct answer is "Option 4".

Additional Information

The logic followed here is:

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

Now,

For, (8, 5, 39)

⇒ 8² - 5² 

⇒ 64 - 25 = 39.

For, (14, 11, 75)

⇒ (14)² - (11)² 

⇒ 196 - 121 = 75.

Similarly, for (7, 4, 33)

⇒ 7² - 4²

⇒ 49 - 16 = 33.

Hence, the correct answer is "Option 4".

The logic followed here is:

For, ATXJ : BVAN

Similarly, for YMOU : 

So, 'YMOU' will be coded as 'ZORY'.

Hence, the correct answer is "Option 1".

Statements:

I. No mobile is an electronic item.

II. All electronic items are costly.

The least possible Venn diagram for the given statement is:

Conclusion:

I. No costly is a mobile - False (No definite relation given between costly and mobile, so it can be possible only).

II. Some costly are mobile - False (No definite relation given between costly and mobile, so it can be possible only).

Here, Conclusion I and III forms complementary pair for either-or.

So, Either conclusion I or II follow.

Hence, the correct answer is "Option 3".

Additional Information 

Conditions of Either-or case:

1. The elements should be the same in both the statements.
2. Both the conclusions should be false individually.
3. One conclusion should be positive and one conclusion should be negative (Complementary pair)

• The two complementary pairs are:

1. All + Some not

2. No + Some

Note: Some + Some not is not  considered under Either -or case.

The pattern followed here is:

Tadpole : Frog → A tadpole is the juvenile form of a frog.

Similarly,

Caterpillar : Butterfly → A caterpillar is the juvenile form of a butterfly.

Hence, the correct answer is "Option 3".

The logic followed here is:

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

Now,

For, 33 : 121

⇒ (33 ÷ 3)² = (11)² = 121.

For, 27 : 81

⇒ (27 ÷ 3)2 = (9)2 = 81.

Similarly, for 45 : ?

⇒ (45 ÷ 3)2 = (15)2 = 225.

Hence, the correct answer is "Option 4".

For find the adjacent faces of '4', we need to compare the common surface in the given dices,

Now,

From Dice 2 and Dice 3,

Here, 3, 5, and 6 is the adjacent surfaces of 4.

So, according to the options '6 and 5' will be the adjacent surfaces of 4.

Hence, the correct answer is "Option 4".

The logic followed here is:

Option 1) UTS

Option 2) ONM

Option 3) GHI

Option 4) WVU

Here, All the options except 'GHI' followed a pattern.

Hence, the correct answer is "Option 3".

The correct answer is Option 4. 

Key Points

• In the context of the Reserve Bank of India (RBI) defining M1, "DD" stands for Demand Deposits.
• Demand Deposits represent the net demand deposits held by commercial banks.
• Demand Deposits are a type of bank account from which deposited funds can be withdrawn at any time without any notice to the bank.
• These types of accounts include checking accounts, savings accounts, or any other type of bank account that allows for the immediate withdrawal of funds.
• They are considered to be highly liquid assets and are included in the calculation of the M1 money supply.
• Net Demand Deposits would account for the total of these deposits held by a bank, minus any amounts that the bank has itself deposited with other banks.
• This gives a more accurate view of a bank's liquidity and the amount of money readily available in the economy.

Additional Information

• The Reserve Bank of India (RBI) defines various monetary aggregates to measure the amount of money in circulation in the Indian economy.
• M1 money supply includes components such as:
• Currency (notes and coins in circulation with the public and vault cash of banks) - denoted as CU.
• Demand Deposits of the public (DD) with commercial banks.

The correct answer is Option 4. 

Key Points

• FTP stands for File Transfer Protocol.
• It's a standard network protocol used for the transfer of computer files between a client and server on a computer network.
• FTP is built on a client-server model architecture using separate control and data connections between the client and the server.

Additional Information

• There are many protocols used in computer networking, each serving different functions and purposes. Some of the most commonly used protocols are:
• Internet Protocol (IP): It's primarily used to route packets of data from the source to the destination based on their IP addresses.
• Transmission Control Protocol (TCP): Works with IP to ensure that packets are reliably delivered. It manages error checking and retransmission of lost packets.
• User Datagram Protocol (UDP): A simpler, faster alternative to TCP that doesn't provide error checking or packet sequencing.
• Hypertext Transfer Protocol (HTTP): The protocol used for transferring web pages and other content over the internet.
• Hypertext Transfer Protocol Secure (HTTPS): A secure version of HTTP that provides encrypted communication and secure identification of network servers.
• File Transfer Protocol (FTP): A protocol for transferring files between systems.
• Simple Mail Transfer Protocol (SMTP): Used for sending email messages between servers.
• Post Office Protocol 3 (POP3) and Internet Message Access Protocol (IMAP): These are used to retrieve emails from a server.
• Domain Name System (DNS): Translates domain names into IP addresses.
• Simple Network Management Protocol (SNMP): Used for managing and monitoring network devices.
• Dynamic Host Configuration Protocol (DHCP): Assigns IP addresses to devices on a network.
• Network Time Protocol (NTP): Used to synchronize the clocks of computers over a network.
• Secure Shell (SSH): Allows for secure remote login from one computer to another.
• Telnet: An older protocol used for remote login. It's less secure than SSH.
• Internet Control Message Protocol (ICMP): Mainly used by network devices to send error messages.
• Address Resolution Protocol (ARP): Resolves IP addresses to MAC addresses.
• Link Layer Discovery Protocol (LLDP): Used by network devices for advertising their identities, capabilities, and neighbors on a local network.

The correct answer is Option 2.

Key Points

• "Loess" is the term for wind-deposited sediment that is composed predominantly of silt-sized particles.
• It's typically pale yellow or buff, loosely compacted, and often calcareous.
• Loess deposits can be very thick, even hundreds of meters, and can blanket very large areas.
• It is derived from the German term "Löss," which means loose or crumbly.
• It's found in many parts of the world, including the American Midwest, Europe, and China. The Loess Plateau in China, for example, is a well-known area of loess deposits.

Additional Information

• In geographical terms, a "stack" is a geological landform consisting of a steep and often vertical column or columns of rock in the sea near a coast, formed by wave erosion.
• Stacks are formed over time by wind and water, processes of coastal geomorphology.
• They are most commonly found in chalk or limestone areas, where the rock is softer and more prone to erosion.
• This process begins when the sea attacks small cracks in a headland and opens them into larger caves.
• If the caves are on both sides of a headland and eventually break through, they form an arch.
• Over time, the arch will collapse due to the force of gravity, leaving the pillar of hard rock standing away from the coast—the stack.
• Eventually, erosion will cause the stack to collapse, leaving a stump.Famous examples of stacks include the Twelve Apostles in Victoria, Australia, and Old Harry Rocks in Dorset, England.
• ​A moraine is a mass of rocks and sediment carried down and deposited by a glacier, typically as ridges at its edges or extremity.
• There are several types of moraines, and they can give us important clues about the glacier's past behavior.
• Here are the main types of moraines:
• Lateral Moraines: These are formed at the side of the ice flow and are usually a result of frost shattering of the valley sides.
• Medial Moraines: These are formed when two glaciers merge, and lateral moraines combine to form a moraine in the middle of the glacier.
• Terminal Moraines: These mark the maximum advance of the glacier. They usually reflect the shape of the glacier's terminus.
• Recessional Moraines: These are often observed as a series of transverse ridges running across a valley behind a terminal moraine. They mark the pauses in the retreat of a glacier, where it remained stationary for enough time to produce a mound of material.
• Ground Moraines: Also called till, these are unsorted material left beneath the glacier as it melts.

The correct answer is Option 3. 

Key Points

• The International Space Station (ISS) completes an orbit around the Earth approximately every 90 to 93 minutes.
• This high speed means the crew members aboard the ISS witness about 15-16 sunrises and sunsets every day.
• The International Space Station (ISS) is a multi-nation construction project that is the largest single structure humans have ever put into space.
• Its main construction was completed between 1998 and 2011, although the station continually evolves to include new missions and experiments.

Additional Information

• The orbit of the ISS is inclined at about 51.6 degrees to the equator, which allows it to be reached by the launch vehicles of all the international partners to provide a fair amount of coverage of the Earth's surface.
• It is a 'low Earth orbit', which means it's in the lowest part of Earth's outermost atmosphere.
• The ISS doesn't stay in a fixed orbit.
• It is gradually pulled back towards Earth due to atmospheric drag, so it needs occasional 'reboosts' to maintain its altitude.
• These reboosts are usually done by docked spacecraft like the Russian Progress cargo ships.

The correct answer is Option 1. 

Key Points

• "Betting and Gambling" is indeed listed under the State List in the Seventh Schedule of the Indian Constitution.
• This implies that individual state governments have the jurisdiction to make laws related to betting and gambling.
• However, it's important to note that while states can regulate this area, many forms of gambling are generally restricted or regulated in India.

Additional Information

• The Seventh Schedule of the Indian Constitution includes three lists:
• The Union List: This includes subjects on which only the central government can make laws. These subjects are of national importance, such as defense, foreign affairs, atomic energy, railways, etc.
• The State List: This includes subjects on which only the state governments can make laws. These subjects are of local or regional importance, such as police, agriculture, health, etc.
• The Concurrent List: This includes subjects on which both the central and state governments can make laws. Examples include bankruptcy and insolvency, marriage and divorce, bankruptcy and insolvency, education, etc.

The correct answer is Option 4. 

Key Points

• Mahendragiri is the highest peak in the Eastern Ghats mountain range.
• It is located in the Indian state of Odisha and has an elevation of 1,501 meters (4,925 feet) above sea level.
• Mahendragiri is also considered a sacred site in Hindu mythology and is believed to be the place where Lord Parashurama, a Hindu deity, performed penance.
• The mountain is also known for its beautiful natural surroundings and is a popular trekking destination for adventure enthusiasts.

Additional Information

• The Eastern Ghats is a mountain range that runs parallel to the eastern coast of India, stretching over 1,750 kilometers (1,087 miles) from West Bengal in the north to Tamil Nadu in the south.
• The range is lower in elevation compared to the Western Ghats and has an average height of around 600 meters (1,969 feet) above sea level, with some peaks reaching up to 1,500 meters (4,921 feet).
• The Eastern Ghats is a complex and diverse mountain range, consisting of several hills, plateaus, valleys, and forests, with a variety of flora and fauna.
• The range is home to many tribal communities, and several rivers originate from the Eastern Ghats.
• The Eastern Ghats is an important region for biodiversity conservation, with several protected areas and wildlife reserves, such as the Simlipal National Park and Biosphere Reserve in Odisha, the Papikonda Wildlife Sanctuary in Andhra Pradesh, and the Kambalakonda Wildlife Sanctuary in Visakhapatnam.

The correct answer is Option 3. 

Key Points

• The fourth edition of the Khelo India Youth Games was actually hosted by the state of Haryana, India.
• The event was held from January 10 to January 20, 2020, and took place across various venues in the cities of Panchkula, Ambala, and Chandigarh.
• Over 6,800 athletes from 37 states and union territories participated in 20 different sports disciplines in the games.
• The Khelo India Youth Games is an annual national-level multi-sport event organized by the Ministry of Youth Affairs and Sports, Government of India, to identify young talent and promote a sports culture in the country.

Additional Information

• Khelo India Youth Games is a national level multi-sport event organized by the Ministry of Youth Affairs and Sports, Government of India.
• The aim of the games is to identify young talent in various sports disciplines and provide them with a platform to showcase their skills at the national level.
• The Khelo India Youth Games is held annually and features competitions in multiple sports disciplines, including athletics, boxing, swimming, wrestling, shooting, archery, and gymnastics.
• The Khelo India Youth Games were launched in 2018 and have since then become one of the largest sporting events in the country.
• The games are organized in two categories - Under-17 and Under-21 - and are held in different parts of the country each year.
• The Khelo India Youth Games provides a platform for young athletes from all parts of India to compete against each other and showcase their talent at the national level.

The correct answer is Option 2. 

Key Points

• The Government of India issues Treasury Bills in three tenors: 91 days, 182 days, and 364 days.
• These Treasury Bills are short-term money market instruments issued by the Reserve Bank of India (RBI) on behalf of the Government of India to finance its short-term borrowing requirements.
• The correct combinations of tenors of Treasury Bills issued by the Government of India are:
• 91-day Treasury Bills
• 182-day Treasury Bills
• 364-day Treasury Bills
• These Treasury Bills are issued at a discount to face value and redeemed at face value upon maturity.
• The difference between the issue price and the redemption price is the interest earned by the investor, which represents the return on investment.
• Treasury Bills are considered to be very safe investments as they are backed by the full faith and credit of the Government of India.

The correct answer is Option 2. 

Key Points

• Neither of the pairs is correct.
• Eagle is not a term used in hockey. Hockey uses terms such as forward, defenseman, goal, power play, penalty kill, etc.
• Penalty kick is not a term used in volleyball. Volleyball uses terms such as serve, spike, block, dig, set, rotation, etc.
• A penalty kick is a term used in soccer, where it refers to a free kick taken from the penalty spot after a foul has been committed inside the penalty area.

Additional Information

• Some important terms related to sports are listed here-
• Football: Corner kick, direct free kick, indirect free kick, dribble, goal kick, penalty, hat triick, off side, tripping etc.
• Volleyboll: Blocking, Doubling, heave, holding, love service, volley
• Basket ball: Ball, basket, blocking, dribbling, free throw, held ball, holding, jump ball, multiple throws, pivot, etc.
• Hockey: Bully, carry, corner, dribble, hat trick, off-side, scoop, short corner, long corner, penalty stroke, etc.
• Cricket: Power-play, boundary, bowling, wicket, l.b.w, leg-bye, maiden over, no ball, off break, out, over, pitch, run out, sixer, straight drive, stumped, yorker etc.
• Tennis: Ace, Backhand, Stroke, deuce, deep volley, double fault, fault, ground stroke, half volley, let, lov, slice, smash, volley etc.
• Table tennis: Anti loop, Backspin, chop, loop, penhold grip, twiddle etc.

The correct answer is Option 1. 

Key Points

• On Tuesday, Prime Minister Narendra Modi inaugurated the Mahakal Lok corridor at the Mahakaleshwar temple in Ujjain.
• The corridor is 900 metres long and has been built at a cost of Rs 856 crore.
• The first phase of the project was developed at a cost of Rs 351 crore.

​

Additional Information

• The Mahakaleshwar temple is one of the most famous and important Shiva temples in India.
• It is located in the ancient city of Ujjain in the state of Madhya Pradesh.
• The temple is dedicated to Lord Shiva, who is worshipped there in the form of a lingam, which is believed to be one of the twelve Jyotirlingas in India.
• The temple has a long and rich history, with some parts of it dating back to the 4th century BCE.
• The temple has been destroyed and rebuilt several times throughout its history, with the current structure dating back to the 18th century.
• The Mahakaleshwar temple is considered to be one of the most sacred places in Hinduism and attracts thousands of pilgrims every year.

The correct answer is Droupadi Murmu

Key Points 

The President of India is called first citizen of India.

• He is also commander-in-chief of the Indian Armed Forces.
• The president is indirectly elected by a college of electors comprising the Indian Parliament (both houses) and the legislative assemblies of each of India's states and territories, all directly elected.
• He is the nation's legislative Head.
• As a citizen of India, a common man ranks in 27th place.
• The President of India is called the Nominal head.
• The President resides in an estate known as the Rashtrapati Bhavan (President's House) situated in Raisina Hill in New Delhi.

Droupadi Murmu 

• ​Droupadi Murmu was elected the 15th President of India.
• Since July 25, 2022, Droupadi Murmu, also known as Puti Biranchi Tudu, has held the office of India's 15th president.
• She was born on June 20, 1958. After Pratibha Patil, she is the second woman to hold the position and the first member of a tribal community to do so.
• Along with being the first President born in Independent India, she is also the youngest person to hold the position.

Additional Information Citizen of India as per the Order of Precedence of the Republic of India:

• Citizen No.1: President.
• Citizen No. 2: Vice-President.
• Citizen No. 3: Prime Minister.
• Citizen No.4: Governors (within their respective states).
• Citizen No.5: Former Presidents.
• Citizen No. 5A: Deputy Prime Minister.
• Citizen No.6: Chief Justice of India, Speaker of Lok Sabha

​The correct answer is Spread sheet software

• An Excel spreadsheet helps in Sorting data, Arranging data easily, and Calculating numerical data.

Key Points:

• Microsoft Excel is part of the Microsoft Office suite of programs and was developed by Microsoft in 1987.
• Microsoft Excel is a spreadsheet program used to record and analyze numerical and statistical data.
• Microsoft Excel provides multiple features to perform various operations like calculations, pivot tables, graph tools, macro programming, etc.
• An Excel spreadsheet can be understood as a collection of columns and rows that form a table.
• A worksheet is made of rows and columns that intersect each other to form cells where data is entered.
• Alphabetical letters are usually assigned to columns, and numbers are usually assigned to rows.
• The point where a column and a row meet is called a cell.
• The address of a cell is given by the letter representing the column and the number representing a row.
• The main features of MS Excel are:
• AutoFormat: It allows Excel users to use predefined table formatting options.
• AutoSum: AutoSum feature helps us to calculate the sum of a row or column automatically by inserting an addition formula for a range of cells.
• List AutoFill: It automatically develops cell formatting when a new component is added to the end of a list.
• AutoFill: This feature allows us to quickly fill cells with a repetitive or sequential record such as chronological dates or numbers and repeated documents. AutoFill can also be used to copy functions. We can also alter text and numbers with this feature.
• AutoShapes: AutoShapes toolbar will allow us to draw some geometrical shapes, arrows, flowchart items, stars, and more. With these shapes, we can draw our graphs.
• Wizard: It guides us to work effectively while we work by displaying several helpful tips and techniques based on what we are doing. The drag and Drop feature will help us to reposition the record and text by simply dragging the data with the help of the mouse.
• Charts: This feature will help you to present the data in graphical form by using Pie, Bar, Line charts, and more.
• PivotTable: It flips and sums data in seconds and allows us to execute data analysis and generating documents like periodic financial statements, statistical documents, etc. We can also analyze complex data relationships graphically.
• Shortcut Menu: The shortcut menu helps users to make the work done through shortcut commands that need a lengthy process.

Additional Information System software:

• System software is a type of computer program that is designed to run a computer's hardware and application programs.
• The system software is the interface between the hardware and user applications.
• The operating system is the best-known example of system software.
• The OS manages all the other programs on a computer.
• System software is used to manage the computer itself. It runs in the background, maintaining the computer's basic functions so users can run higher-level application software to perform certain tasks.
• Essentially, system software provides a platform for application software to be run on top of.

Operating system software:

• An operating system is the most important software that runs on a computer.
• It manages the computer's memory and processes, as well as all of its software and hardware.
• It also allows you to communicate with the computer without knowing how to speak the computer's language.
• Without an operating system, a computer is useless.

Correct Answer Rs 202

Key Points

• Economic Survey 2020-21, the wages per day under the Mahatma Gandhi National Rural Employment Guarantee Act (MGNREGA) were ₹202, effective from 1st April 2020.
• It's important to note that the wages under MGNREGA can vary across different regions and states, so it's always best to consult official government sources for the most up-to-date and accurate information.

MGNREGA:

• The scheme was introduced as a social measure that guarantees “the right to work”.
• The key tenet of this social measure and labour law is that the local government will have to legally provide at least 100 days of wage employment in rural India to enhance their quality of life.
• The Mahatma Gandhi National Rural Employment Guarantee Act (MGNREGA) was passed in 2005.
• The Acts guarantees the "Right To Work" and aims at enhancing the livelihood security of rural peoples.
• The Mahatma Gandhi National Rural Employment Guarantee Act, 2005 (MGNREGA) was notified on September 7, 2005.

The correct answer is Droupadi Murmu

Key PointsPresident Droupadi Murmu

• ​President Droupadi Murmu was elected the 15th President of India.
• Since July 25, 2022, President Droupadi Murmu, also known as Puti Biranchi Tudu, has held the office of India's 15th president.
• She was born on June 20, 1958. After Pratibha Patil, she is the second woman to hold the position and the first member of a tribal community to do so.
• Along with being the first President born in Independent India, she is also the youngest person to hold the position.

Additional Information జరిగాయి.

• On June 20, 1958, Droupadi Murmu was born to a Santali family in the village of Uparbeda in the Rairangpur, Odisha, neighborhood of Baidaposi.  Biranchi Narayan Tudu, her father, was a farmer.
• Her father and grandfather served as the local council's traditional leaders, or Sarpanch (Gram Panchayat).
• They gave her the name Puti Tudu.
• Her teacher changed her name from Durpadi to Droupadi, and she had previously gone by the names Dorpdi and   Durpadi.
• Ram Nath Kovind is the 14th President of India.
• That presidential election was held on 17th July 2017.
• He was earlier the Governor of Jharkhand.
• Pratibha Devi Singh Patil was the first woman president of India.
• She was born on 19 December 1934.
• She is an Indian politician who served as the 12th President of India from 2007 to 2012.

The correct answer is Sub tropical high-pressure

Key Points:

• The subtropical high-pressure belt region is also known as the horse latitude. These latitudes are characterized by calm winds and little precipitation.
• These ships often encountered areas of high pressure and calm winds, making them unable to sail and resupply for days or even weeks. The crews often ran out of drinking water. To conserve water for their own survival, the sailors would throw the horses into the sea, hence the name horse latitudes.
• A horse latitude is a belt of calm air and sea in both the northern and southern hemispheres between the trade winds and the westerlies.

Additional Information:

• The "doldrums" is a popular nautical term that refers to the belt around the Earth near the equator where sailing ships sometimes get stuck on windless waters. This NASA satellite image shows the Inter-Tropical Convergence Zone, known to sailors around the world as the doldrums.
• Polar Highs: At the North and South Poles, between 700 to 900 North and South, the temperatures are always extremely low. The cold descending air gives rise to high pressures over the Poles. These areas of high pressure are known as the Polar Highs.
• the equatorial low: Near the equator the sea level pressure is low and the area is known as the equatorial low. Along 30° N and 30° S are found the high-pressure areas known as the subtropical highs. Further pole wards along 60° N and 60° S, the low-pressure belts are termed as the subpolar lows.

Thus, Sub tropical high-pressure belt on the globe is otherwise known as the Horse Latitude.

Correct Answer Underweight

Key Points BMI stands for Body mass index which is the measure of body fat based on the height and weight of men and women.

• Increased BMI is usually associated with an increased risk of metabolic diseases such as type II diabetes mellitus, hypertension & dyslipidemia.
• BMI is widely used to know whether a person has a healthy weight equivalent to height or not.
• BMI categories: Underweight < 18.5, Normal Weight: 18.5 - 24.9, Overweight: 25 - 29.9, Obesity > 30.
• We can find the BMI of a person by using the given formula:
• BMI = (Weight in kg)/(Height in meters)2

 Additional Information

• ​A healthy weight is associated with a low risk of weight-related diseases and health issues. If BMI is 18.5 to 24.9, it falls within the normal or Healthy Weight range.
• Obesity: It is a disorder of excessive body fat that increases the risk of various diseases like Hypertension, cardiac arrest, diabetes, etc. It is characterized by a BMI of more than 30.
• Overweight is a BMI greater than or equal to 25-29.9. Overweight is defined as abnormal or excessive fat accumulation that may impair health.

The correct answer is Ugadi.

Key Points:

• Ugadi is one of the famous festivals celebrated among the Hindus with great pomp and fanfare. Ugadi is celebrated as the New Year of the Telugu and Kannada people.
• The festival of Ugadi is celebrated on the first day of Chaitra month according to the Hindu calendar.
• On the other hand, according to the Gregorian calendar, this festival falls in March or April.
• With the arrival of spring, this festival also marks the arrival of a new crop for the farmers.
• On the day of Ugadi, Lord Brahma, the creator of the universe, is worshipped.
• This festival brings us very close to nature and on this day a drink called Pachadi is made which is very healthy.
• On this auspicious day, people in South India also start new work, such as starting a new business, home entry etc.

Additional InformationMonpa Tribe:

• The Losar Festivals are celebrated in Arunachal Pradesh.
• It is celebrated by the people of the Monpa Tribe who are said to be inhabitants of Arunachal Pradesh.
• Losar is a 3-day festival, which is celebrated with great pomp and show in Tawang.
• The festival is observed to ward off evil spirits and welcome the new year that shall be filled with happiness and prosperity.

Vishu:

• Vishu marks the beginning of the New Year for the people of Kerala.
• The festival is celebrated in the month of Medam of the Malayalam calendar with much pomp and vigour.
• The most important part of the festival is the Vishukani.
• Apart from Kerala, the festival is celebrated in neighbouring regions like Mangalore, Tulunadu, and Udupi.
• Vishu is also called the festival of fireworks and light as the celebration includes the bursting of firecrackers. It is said that Krishna killed the demon Narakasur on the day of Vishu.

Dasara or Mahanavani:

• Dasara is observed as a State festival - Nadahabba in Karnataka.
• It's a 10-day festival, the last day being Vijayadashami.
• It is a day when Hindu Goddess Chamundeshwari killed the demon Mahishasura.
• After the fall of the Vijayanagar kingdom Raja Wodiyar, 1 continued the festival in 1610 at Srirangapattana.
• During the reign of Krishnaraja Wodeyar III, in 1805, the tradition of having a special durbar (royal assembly) in the Mysore Palace during Dasara was started.

The correct answer is Robert Clive.

Key Points:

• The East India Company forces led by Robert Clive engaged Siraj-Ud-Daulah in the Battle of Plassey.
• Siraj-Ud-Daulah was the Nawab of Bengal.
• Siraj was enraged by the widespread abuse of trade privileges by EIC authorities.
• The battle of Plassey in 1757 was brought on by EIC's continued wrongdoing against Siraj-Ud-Daulah.
• About 160 kilometres north of Calcutta, close to the little settlement of Plassey (Palashi), the forces came together on the banks of the Bhagirathi-Hooghly River.
• On June 23, 1757, the Battle of Plassey was fought.
• Robert Clive's army of 3,000 troops destroyed Siraj-Ud-army Daulah's of 50,000 warriors, 40 cannons, and 10 war elephants.
• In 11 hours, the battle was over, and Siraj-Ud-Daulah fled after losing.

Additional Information:

• The Battle of Plassey was fought in north-eastern India on 23 June 1757.
• Troops of the British East India Company, led by Robert Clive, came up against the forces of Siraj-ud-Daulah, the last Nawab of Bengal, and his French allies.
• Clive's victory eventually led to the British becoming the greatest economic and military power in India.
• The Battle of Plassey had political significance for it laid the foundation of the British Empire in India.; it has been rightly regarded as the starting point of British rule in India.
• Result of Battle of Plassey-
• As a result of this victory, Mir Jafar became the Nawab of Bengal. He gave large sums of money plus the zamindari of 24 Parganas to the English.
• English rivals, the French were ousted.

The correct answer is 'Australia'.

Key Points

• A memorandum of understanding was inked between India and Australia to use artificial intelligence and machine learning in aerospace, on the final day of the Bengaluru Space Expo (BSX), 2022.
• The MoU was signed between Bengaluru-based aerospace company Valdel Advanced Technologies and Australian artificial intelligence company AICRAFT.
• The MoU, which was signed in the presence of Indian Space Research Organisation (ISRO) scientific secretary Shantanu Bhatawdekar and Australian Space Agency head Enrico Palermo, will work towards using the AI capabilities of AICRAFT to help Valdel with simulation and manufacturing capabilities through the use of advanced AI and machine learning.
• Both parties have agreed to utilize AICRAFT’s advanced artificial intelligence and machine learning capability and products to support Valdel’s modelling, simulation and manufacturing capabilities.
• Valdel’s facilities will also be used to test AICRAFT’s systems and platforms.

Additional Information

• The seventh edition of Bengaluru Space Expo (BSX) was hosted from September 5 to 7 in Bengaluru.
• Australia’s Space Machines Company, an aerospace company, opened a new research and development office in Bengaluru on September 6.

The correct answer is Arundhati Roy

Key Points

• Arundhati Roy is a Political Activist and Writer.
• Her debut Novel is the "God of Small Things" has won the Booker Prize in 1997.
• The Novel depicts  Corruption, Political Violence, and Capitalism.

**Additional Information:**Sunita Narian has written the book 'Conflicts of Interest; My journey through India's Green Movement" in 2017.

• India's foremost environmentalist, Sunita Narain gives a personal account of her battles as part of the country's Green Movement.
• While outlining the enormous environmental challenges that India faces today.
• Narain talks about how corporate lobbies and political interests often scuttle their effective resolution.
• Sunita Narain is an Indian environmentalist and political activist as well as a major proponent of the Green concept of sustainable development.
• Movies: - Before the Flood, River blue, Flow: For Love of Water, Weather Report
• Awards: - Stockholm Water Prize, Padma Shri
• Books: - Excreta Matters, Capitan America: US Climate Goals: a Reckoning, Not in My Backyard: Solid Waste Management in Indian Cities.

The correct answer is Chhatrapati Shivaji Maharaj.

Key Points

• Chhatrapati Shivaji Maharaj
• Shivaji was named Chhatrapati in 1674 and the Maratha empire came to an end in 1818 after the defeat of Peshwa Bajirao II by the British East India company.
• This initially began by freeing the people from the Sultanate of Bijapur when he won Fort Torna in 1645 and after this, it continued by winning other forts.
• His aim was to establish an empire of self-rule for the Hindu people.
• He kept Raigad as his capital and they gave tough fights to the Mughals to defend his kingdom.

Additional Information

• Prithviraj Chauhan
• Prithvirāja III, popularly known as Prithviraj Chauhan, was an Indian king from the Chahamana (Chauhan) dynasty.
• From his very early years, Prithvi Raj showed his sharpness and brilliance by learning all military skills.
• It was believed he mastered the skills of aiming the target based on its sound, known as the “Shabdbhedi” technique.
• He succeeded to the throne of Ajmer at the age of thirteen, in 1179, after the demise of his father in a battle.
• Prithviraj’s grandfather Angam, the ruler of Delhi, declared Prithviraj Chauhan the heir to the throne of Delhi.
• Man Singh ​
• Man Singh was the Kachwaha Rajput Raja of Amer, a state later known as Jaipur in Rajputana.
• He was a trusted general of the Mughal emperor Akbar, who included him among the Navaratnas of the royal court of Akbar.
• Porus
• In 326 BC, Alexander invaded India, after crossing the river Indus he advanced towards Taxila.
• He then challenged King Porus, ruler of the kingdom between the rivers Jhelum and Chenab.
• The Battle is called the “Battle of Hydaspes” named after the Hydaspes River (now Jhelum).
• The Porus were defeated in the fierce battle, even though they fought with elephants, which the Macedonians had never before seen.
• Alexander captured Porus and, like the other local rulers he had defeated, allowed him to continue to govern his territory.

The correct answer is 8th march.

Key Points

• International Women's Day is celebrated on 8th March.
• International Women's Day is a global day celebrating  the social, economic, cultural, and political achievements of women.
• The day also marks a call to action for accelerating gender parity.
• This year's theme for International Day is "Women in leadership: Achieving an equal future in a COVID-19 world".​

Important Points

• National Women's Day- 13 February
• National Girl Child Day- 24 January
• International Day of the Girl Child- 11 October​

Additional Information

The correct answer is Bansuri.

Key Points

• Pandit Hariprasad Chaurasia
• Pandit Hariprasad Chaurasia is a world-renowned exponent of the bansuri or bamboo flute.
• He is one of those rare classical musicians who expanded the peripheries of classical music by taking it to the common masses.
• Pandit Hariprasad Chaurasia is an internationally renowned exponent of the 'bansuri', or the bamboo flute and is the recipient of the Padma Vibhushan and Padma Bhushan awards, which are among the three highest civilian awards in India.
• This musician has donned many hats — of an extraordinary flute artiste, titan of Hindustani classical genre and music director.​

Additional Information

• Tabla
• Tabla is a small drum or  Pair of Drums tuned to different pitches playing with hands.
• It was invented by Amir khusru
• The right side is called the Tabla and the left, the Bayan or Dagga.
• It is type of Avanaddha vadya or  Membranophones​​
• Veena
• The veena is among the oldest of Indian musical instruments.
• From the references to Vedic writings, it can date back to around the first millennium B.C.
• Temple sculptures from the 2nd century B.C. show a type of veena being played.
• The Saraswati veena is the predominant Carnatic music and the Rudra veena is the most played veena in Hindustani music.
• The Saraswati veena has seven strings strung over twenty-four fixed frets.
• It has a large resonator (kudam), a tapering hollow neck (dandi), and a tuning box that curves downwards (yali).
• The Hindu Goddess of Knowledge, Saraswathi, is said to play the Veena. Pictures depict her sitting on a lotus and playing the instrument.
• Muthuswami Dikshitar, Veenai Dhanammal, Veena Sheshanna, etc. are the famous veena players.​
• Drum:-
• The drum is made of wood or brass with drumheads made of calfskin or plastic stretched over both ends of a hollow cylinder.
• It has a set of wire-wrapped strings stretched across the bottom head (the snare), which gives the drum its unique "rattling" sound when the drum is hit. A small switch on the side of the drum allows the player to turn the snare on or off depending on the requirements of the piece.

the correct answer is Human muscle cells.

Key Points

• Human muscle cells
• Aerobic respiration is a process in which the breakdown of glucose occurs in the presence of oxygen. Anaerobic respiration is a process in which food can also be broken down in the absence of oxygen.
• The breakdown of glucose takes place in three ways that are as follows
• The food is broken down to release energy in the presence of oxygen to give carbon dioxide, water, and energy.
• The organisms that can survive in the absence of air are called anaerobes. Through the anaerobic respiration process, they get the energy to survive. In the absence of oxygen, glucose breaks down into alcohol and carbon dioxide.
• When there is a temporary deficiency of oxygen, Our muscle cells respire anaerobically for a short period of time. During heavy exercise, fast running, cycling, walking for many hours, or heavy weight lifting, the demand for energy is high. But the supply of oxygen to produce the energy is limited. The demand for energy in the muscle cells takes place through anaerobic​

Additional Information

• Bacteria
• Bacteria are microscopic prokaryotes (single-celled organisms). They are the sole members of Kingdom Monera.
• Bacteria have variations in their shape, on the basis of their shape bacteria are of different types like : 
• Coccus
• Bacillus
• Spirillum
• Vibrio
• Yeast
• “Yeast is a fungus that grows as a single cell, alternately as a mushroom,” assumes Laura Rusche, associate professor of biological sciences.
• Though every yeast organism is made up of just one cell, yeast cells live jointly in multicellular colonies.
• Yeast cells are classified as fungi as they have some characteristics similar to fungi, such as the   presence of chitin in cell walls, extracellular digestion, saprophytic mode of nutrition, asexual reproduction by budding, and food reserved as glycogen.
• ​Mitochondria
• Mitochondria is a double-layered cell organelle, in which the outer layer is porous and the inner layer is folded upon itself is known to be cristae.
• The number of mitochondria in a single cell may be up to 50 to 5000.
• The inner lumen of mitochondria contains ribosome phosphate particles and DNA molecules.
• It has the potential to synthesize its own protein and the oxidation of carbohydrates and fats are taken place with the help of enzymes in mitochondria.
• This energy is stored in the form of ATP ( Adenosine Triphosphate ) so, these are known as the "Powerhouse of the cell".

The correct answer is Asia.

Key Points

• Asia continent produces more than half of the world's tin.
• In Asia, China is the major producer of tin.
• Tin is found in the ore cassiterite.​

Additional Information

• Asia is the largest continent & It covers about one-third of the total land area of the earth.
• The continent lies in the Eastern Hemisphere. The Tropic of Cancer(23 1/2° N) passes through this continent.
• Asia is separated from Europe by the Ural mountains on the west.
• The combined landmass of Europe and Asia is called Eurasia (Europe + Asia).

Concept Used:

(a + b)² = a² + b² + 2ab

Calculation:

$\frac{4 x^2+9 y^2+12 x y}{144}$

⇒ $\frac{(2x)^2+(3y)^2+2\times 2\times 3\times x y}{(12)^2}$

⇒ $\frac{(2x+3y)^2}{(12)^2}$

⇒ $(\frac{(2x+3y)}{12})^2$

⇒ $(\frac{2x}{12}+\frac{3y}{12})^2$

⇒ $(\frac{x}{6}+\frac{y}{4})^2$

∴ Option 4 is the correct answer.

Calculation:

Statement I:

Number of Pencil sold by A in P and Q together = 150 + 140 = 290

Number of Pencil sold by B in S and T together = 130 + 125 = 255

Percent of number of pencil sold by A in P and Q together to number of pencil sold by B in S and T together = 290 / 255 × 100 = 113.72%

The number of pencil sold by A in P and Q together is 13.72 percent more than the number of pencil sold by B in S and T together.

∴ Statement I is wrong.

Statement II:

Number of Pencil sold by B in Q and R together = 110 + 160 = 270

Number of Pencil sold by A in P and T together = 150 + 105 = 255

Percent of the number of pencil sold by B in Q and R together to the number of pencil sold by A in P and T together = 270/255 × 100 = 105.88%

Statement II is correct.

∴ Option 3 is the correct answer.

Shortcut Trick

Income ratio 4 : 7 → 4 units = ₹2,800 ⇒ 1 unit = ₹700 ⇒ Narendra income = 7 × 700 = ₹4,900.

Jitendra expenditure = 2,800 − 400 = ₹2,400.

Expenditure ratio 6 : 5 → 6 units = ₹2,400 ⇒ 1 unit = ₹400 ⇒ Narendra expenditure = 5 × 400 = ₹2,000.

Narendra savings = 4,900 − 2,000 = ₹2,900.

∴ The correct answer is ₹2,900.

Alternate Method

Given:

Income ratio (Jitendra : Narendra) = 4 : 7

Expenditure ratio (Jitendra : Narendra) = 6 : 5

Jitendra income = ₹2,800 | Jitendra savings = ₹400

Formula Used: Savings = Income − Expenditure

Step-by-step Calculations:

⇒ Jitendra income (4 units) = 2,800

⇒ 1 unit of income = 2,800 ÷ 4 = 700

⇒ Narendra income = 7 × 700 = ₹4,900

⇒ Jitendra expenditure = Income − Savings = 2,800 − 400 = ₹2,400

⇒ Jitendra expenditure ratio (6 units) = 2,400

⇒ 1 unit of expenditure = 2,400 ÷ 6 = 400

⇒ Narendra expenditure = 5 × 400 = ₹2,000

⇒ Narendra savings = 4,900 − 2,000 = ₹2,900

∴ The correct answer is ₹2,900.

Additional Information

Basic Income-Expenditure Relation

Total Income is always the sum of Expenditure and Savings. Income = Expenditure + Savings.

Ratio Unitary Method

When the actual value of one part of a ratio is known, multiply the single unit value by the other ratio parts to find their respective actual values.

Percentage Savings

Savings % = (Savings ÷ Income) × 100. This is useful for comparing saving habits across different income levels.

Variable Method

If incomes are 4x, 7x and expenditures are 6y, 5y, then 4x − 6y = Saving1 and 7x − 5y = Saving2.

Given

m = sec θ - tan θ

n = cosec θ + cot θ

Calculation:

m = sec θ - tan θ = (1 - sin θ)/cos θ

n = cosec θ + cot θ = (1 + cos θ)/ sin θ

m + n(m - 1)  = m + nm - n)

(1 - sin θ)/cos θ +  (1 - sin θ)/cos θ ×  (1 + cos θ)/ sin θ - (1 + cos θ)/ sin θ

(sin θ - cos θ - 1 + 1 - sin θ + cos θ - cos θ × sin θ)/sin θ × cos θ 

(- cos θ × sin θ)/sin θ × cos θ 

• 1

∴ Option 4 is the correct answer.

Calculation:

P1 = The total sales of bikes of all the 5 companies = 50 + 25 + 125 + 150 + 200 = 550

P2 = The total sales of cars of the all 5 companies = 300 + 75 + 175 + 250 + 200 = 1000

P2 - P1 = 1000 - 550 = 450

∴ Option 3 is the correct answer.

Given:

Discount on article A = 20%

Discount on article B = 15%

Formula:

Discount = (Marked Price - Selling Price) / Marked Price

Solution:

Let's assume the marked price of Article A as "MA" and the marked price of Article B as "MB".

Calculate the discount amount on Article A.

Discount Amount on A = MA × (20/100) = 0.2 × MA

Calculate the discount amount on Article B.

Discount Amount on B = MB × (15/100) = 0.15 × MB

As per the given information, the discount amount on A is equal to the discount amount on B.

0.2 × MA = 0.15 × MB

Simplify the equation to find the ratio of the marked prices.

MA /MB = (0.15/0.2)

MA/MB = 0.75

Therefore, the ratio of the marked price of Article A to the marked price of Article B is 0.75 or 3:4.

Given:

Side of equilateral triangle = 12 cm

An incircle with center O is drawn inside an equilateral triangle ABC.

Concept Used:

Area of equilateral triangle = √3/4 × side²

Area of circle = πr²

Inradius of equilateral triangle = side/2√3

Calculation:

Given that the side length of the equilateral triangle is 12 cm, we can calculate the radius:

⇒ r = (12 / 2√3)

⇒  6 /(√3)

⇒  2√3 cm

Now, let's find the area of the incircle using the formula:

Area of incircle = π × r² 

Area of incircle = π × (2√3)²

⇒  12π  cm²

Next, we find the area of the equilateral triangle using the formula:

Area of equilateral triangle = (√3 / 4) ×  (side)²

Area of equilateral triangle = (√3 / 4) ×  (12)²

⇒  (√3 / 4) ×  144

⇒ 36√3 cm²

Finally, we can subtract the area of the incircle from the area of the equilateral triangle to find the area outside the incircle:

Area outside incircle = Area of equilateral triangle - Area of incircle

⇒  36√3 cm² - 12π cm²

⇒ 62.32 - 37.68

⇒ 24.64 cm²

∴ Option 1 is the correct answer.

Given:

Quantity of milk purchased: 30 litres

Cost of milk per litre: Rs. 50

Quantity of water added: 20 litres

Selling price of the mixture: Rs. 48 per litre

Formula Used:

Cost Price (CP) = Cost per litre × Quantity

Selling Price (SP) = Selling price per litre × Quantity

Profit = SP - CP

Profit Percentage = (Profit / CP) × 100

Calculation:

The cost price of 30 litres of milk = Rs. 50 × 30 = Rs. 1500.

He mixes 20 litres of water in it.

Total quantity of mixture = 30 + 20 = 50 litres.

The selling price of 50 litres of mixture = Rs. 48 × 50 = Rs. 2400.

Profit = Rs. (2400 - 1500) = Rs. 900.

Profit percentage = (900/1500) × 100 = 60%.

Therefore, the profit percentage is 60%.

Given:

30% of P = 15% of Q

20% of Q = 10% of R

To find:

(R-P)/P × 100

Solution: 

30% of P = 15% of Q

20% of Q = 10% of R

(30/100)P = (15/100)Q

(20/100)Q = (10/100)R

P = (1/2)Q

Q = (1/2)R

P = (1/4)R

R = 4P

R is 300% more than P.

Shortcut Trick

If x² + 1/x² = a, then x + 1/x = √(a + 2).

Here, x + 1/x = √(7 + 2) = √9 = 3.

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

Required value = 3³ − (3 × 3) = 27 − 9 = 18.

∴ The correct answer is 18.

Alternate Method

Given: x² + 1/x² = 7

Formula Used: (x + 1/x)² = x² + 1/x² + 2 and (x + 1/x)³ = x³ + 1/x³ + 3(x + 1/x)

⇒ x² + 1/x² = 7

⇒ Adding 2 to both sides: x² + 1/x² + 2 = 7 + 2

⇒ (x + 1/x)² = 9

⇒ x + 1/x = 3

⇒ Now, cubing both sides: (x + 1/x)³ = 3³

⇒ x³ + 1/x³ + 3(x)(1/x)(x + 1/x) = 27

⇒ x³ + 1/x³ + 3(3) = 27

⇒ x³ + 1/x³ = 27 − 9 = 18

∴ The correct answer is 18.

Additional Information

Algebraic Identity for Square

(a + b)² = a² + b² + 2ab. For reciprocals, (x + 1/x)² = x² + 1/x² + 2.

Algebraic Identity for Cube

(a + b)³ = a³ + b³ + 3ab(a + b). For reciprocals, x³ + 1/x³ = (x + 1/x)³ − 3(x + 1/x).

Negative Reciprocal Relation

If x − 1/x = k, then x² + 1/x² = k² + 2 and x³ − 1/x³ = k³ + 3k.

Power Transition Rule

To find higher powers like x⁴ + 1/x⁴, square the result of x² + 1/x² and subtract 2.

Shortcut Trick

Total capacity (Total Work) = LCM(5, 10, 20) = 20 units.

Efficiency of P = 20 ÷ 5 = +4 units/hr

Efficiency of Q = 20 ÷ 10 = +2 units/hr

Efficiency of R = 20 ÷ 20 = −1 units/hr (negative work)

Combined efficiency = 4 + 2 − 1 = 5 units/hr

Time taken = Total Work ÷ Combined Efficiency = 20 ÷ 5 = 4 hours.

∴ The correct answer is 4 hours.

Alternate Method

Given:

Time taken by pipe P to fill the tank = 5 hours

Time taken by pipe Q to fill the tank = 10 hours

Time taken by pipe R to empty the tank = 20 hours

Formula Used:

Total Work = Efficiency × Time

Note: Work done by an emptying pipe is considered negative.

Calculations:

⇒ Total Efficiency of P, Q, and R working together = (+4) + (+2) + (−1)

⇒ Total Efficiency = 6 − 1 = 5 units/hour

⇒ Total time taken = Total Work ÷ Total Efficiency

⇒ Total time taken = 20 ÷ 5

⇒ Total time taken = 4 hours

∴ The correct answer is 4 hours.

Additional Information

Pipes & Cisterns vs Time & Work

The underlying concept is exactly identical to standard Time & Work. The only difference is that an outlet pipe or a leak is assigned negative efficiency.

Combined Efficiency Rule

If two pipes A and B can fill a tank in x and y hours, and pipe C empties it in z hours, their combined 1-hour work = (1/x) + (1/y) − (1/z).

Tank Capacity Formula

If the absolute flow rate (liters/min or liters/hour) of any pipe is known, then Tank Capacity = Total filling/emptying time of that pipe × Flow rate.

Calculation:

Loss on article L = 600 - 500 = 100

Loss on article M = 800 - 750 = 50

Loss on article N = 700 - 500 = 200

Loss on article O = 1000 - 700 = 300

Sequence according to loss = O > N > L > M

∴ Option 1 is the correct answer.

Given:

The ratio of the speed of the boat in still water to the speed of the stream is 8 : 3.

The boat can travel 22 km downstream in 24 minutes.

Formula:

Speed = Distance/Time

Calculation:

The ratio of the speed of the boat in still water to the speed of the stream is 8 : 3. Let the speed of the boat in still water be 8x and the speed of the stream be 3x.

The boat can travel 22 km downstream in 24 minutes. The speed of the boat downstream is 22/24 = 11/12 km/min = 11/12 × 60 = 55 km/hr.

The speed of the boat downstream is 8x + 3x = 11x.

So, 11x = 55 km/hr

x = 5 km/hr

The speed of the boat in still water is 8x = 40 km/hr.

The speed of the boat upstream is 8x - 3x = 5x = 25 km/hr.

The time taken by the boat to cover 50 km upstream is 50/25 = 2 hours.

Therefore, the boat will take 2 hours to cover 50 km upstream.

Given:

sin 2θ = √3/2

Formula used:

sin 60°  = √3/2

tan 30°  = 1/√3

Calculation:

sin 2θ = √3/2

sin 2θ = sin 60° 

2θ = 60° 

θ = 30° 

so, tan θ = tan 30°  = 1/√3

∴ Option 3 is the correct answer.

Shortcut Trick

The maximum length of a stick that can be placed in a cuboid is equal to its diagonal.

Direct Trick: Diagonal = √((Sum of dimensions)² − Total Surface Area)

⇒ Diagonal = √(20² − 256)

⇒ Diagonal = √(400 − 256)

⇒ Diagonal = √144 = 12 cm

∴ The correct answer is 12 cm.

Alternate Method

Given:

Sum of length, breadth, and height (l + b + h) = 20 cm

Total Surface Area = 2(lb + bh + hl) = 256 cm²

Formula Used:

Maximum stick length = length of the diagonal = √(l² + b² + h²)

Algebraic Identity: (l + b + h)² = l² + b² + h² + 2(lb + bh + hl)

Diagonal (Max Stick) Length (l) Breadth (b) Height (h)

Calculation:

⇒ Substituting the given values into the algebraic identity:

⇒ (20)² = l² + b² + h² + 256

⇒ 400 = l² + b² + h² + 256

⇒ l² + b² + h² = 400 − 256

⇒ l² + b² + h² = 144

⇒ Taking the square root on both sides:

⇒ √(l² + b² + h²) = √144

⇒ Maximum length of the stick = 12 cm

∴ The correct answer is 12 cm.

Additional Information

Maximum Length in a Cuboid

The maximum length of an object (like a rod or stick) that can fit completely inside a cuboidal box is precisely the length of its main diagonal. Formula: Diagonal = √(l² + b² + h²).

Cube Diagonal

For a perfect cube where all dimensions are identical (l = b = h = a), the length of the maximum stick that can fit inside is given directly by √3 × a.

Lateral Surface Area

The area covering only the 4 standing walls of a cuboidal room (excluding the base floor and the top ceiling) is known as the Lateral Surface Area. Formula: LSA = 2h(l + b).

Concept used:

Calculation:

⇒ $\frac{25}{100}\times 720 + \frac{57}{19} \times \frac{1}{3}\times \frac{100}{11}\times \frac{33}{25}-\frac{15}{100}\times 300$

⇒ $180 + 3 \times \frac{1}{3}\times 4\times 3-45$

⇒ $180 + 1\times 4\times 3-45$

⇒ $147$

Given:

A + B = -5

AB = 6

Formula Used:

A³ + B³ = (A + B)³ - 3AB(A + B)

Solution:

A3 + B3 = (A + B)3 - 3AB(A + B)

Now substitute the values into the formula

A3 + B3 = (-5)3 - 3 × 6(-5)

A3 + B3 = -125 + 90

A3 + B3 = -35

Therefore, the value of A3 + B3 = -35.

Given:

3 tan 20°.tan 45°.tan 70°

Formula used:

tan θ = cot (90° - θ)

tan θ × cot θ = 1

tan 45° = 1

Calculation:

3 tan 20°.tan 45°.tan 70°

⇒ 3 tan 20°.tan 45°. cot (90° - 70°)  ...........Using tan θ = cot (90° - θ)

⇒ 3 tan 20°.tan 45°. cot (20°)

⇒ 3 × tan 45°

⇒ 3 × 1

3

∴ Option 2 is the correct answer.

Given:

Principal = Rs. 6000

Rate = 20%

Time = 18 months

Concept Used:

A = P ×  (1 + r/n)^(nt)

Where:

A = Amount

P = Principal

r = Annual interest rate 

n = Number of times the interest is compounded per year

t = Time period (in years)

Calculation:

The interest is compounded half-yearly, so n = 2 (twice a year).

The time period (t) is 18 months, which is equivalent to 1.5 years.

Rate, r = 20% = 0.20

Let's substitute these values into the formula:

A = 6000 ×  (1 + 0.20/2)^{(2 × 1.5)}

⇒ 6000 ×  (1 + 0.10)³

⇒  6000 ×  1.10³

⇒  6000 ×  1.331

⇒ A = Rs. 7986

Compound interest = A - P

⇒  7986 - 6000

⇒  Rs. 1986

Therefore, the compound interest for 18 months at a rate of 20% per annum, compounded half-yearly, would be Rs. 1986.

∴ Option 2 is the correct answer.

Shortcut Trick

Double the average of two values is always equal to their sum.

Age 3 years from now = (Current age) + (Age 8 years ago)

Current age + 3 = Current age + (Current age − 8)

3 = Current age − 8 ⇒ Current age = 11 years.

Jitin's age 5 years ago = 11 − 5 = 6 years.

∴ The correct answer is 6 years.

Alternate Method

Given:

Let Jitin's current age be J.

Age 3 years from now = J + 3

Age 8 years ago = J − 8

Formula Used:

Average of two numbers A and B = (A + B) ÷ 2

Calculations:

⇒ Average of current age and age 8 years ago = [J + (J − 8)] ÷ 2

⇒ Average = (2J − 8) ÷ 2 = J − 4

⇒ According to the question: (J + 3) = 2 × (J − 4)

⇒ J + 3 = 2J − 8

⇒ 2J − J = 8 + 3

⇒ J = 11 years

⇒ Jitin's age 5 years ago = J − 5 = 11 − 5 = 6 years.

∴ The correct answer is 6 years.

Additional Information

Algebraic Representation of Ages

If the current age is x, then age after n years is (x + n) and age n years ago was (x − n).

Average of Ages

The average of ages of n people is the sum of their individual ages divided by n.

Ratio and Proportions in Ages

The difference between the ages of two people remains constant throughout their lives, which is a key property for solving ratio-based age problems.

Given: 

X, Y and Z are three equilateral triangles.

The side of X = 6 cm

The side of Y = 8 cm

Concept used:

Area of equilateral triangle = $\frac{√3}{{4}}$a2

Calculation:

Area of equilateral triangle = $\frac{√3}{{4}}$a2

According to the question

AX + AY = AZ

⇒ ($\frac{√3}{{4}}$ × 62) + ($\frac{√3}{{4}}$ × 82) = ($\frac{\sqrt3}{{4}}$ × x2)

⇒ 36 + 64 = x2

⇒ 100 = x2

⇒ x = 10

∴ The side length of Z is 10 cm.

Shortcut Trick

The Radius of the circle is half of the diameter, which is 10 cm.

The Chord length is given as 10 cm.

In the triangle formed by the center and the chord, the sides are Radius, Radius, and Chord (10 cm, 10 cm, 10 cm).

Since all three sides are equal, it forms an Equilateral Triangle.

All angles of an equilateral triangle are 60°.

∴ The correct answer is 60 degree.

Alternate Method

Given:

Diameter of the circle = 20 cm

Length of Chord AB = 10 cm

Formula Used:

Radius (r) = Diameter ÷ 2

In any ΔOAB (where O is the center), if OA = OB = AB, then ∠AOB = 60°.

Calculations:

⇒ Radius (r) = 20 ÷ 2 = 10 cm

⇒ Let O be the center of the circle. The radii joining the ends of the chord AB are OA and OB.

⇒ OA = 10 cm and OB = 10 cm

⇒ Length of Chord AB = 10 cm

⇒ In ΔOAB, OA = OB = AB = 10 cm

⇒ This implies that ΔOAB is an Equilateral Triangle.

⇒ ∠AOB = 60° (Angle subtended by the chord at the center).

∴ The correct answer is 60 degree.

Additional Information

Angle at Center and Circumference

The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle. Here, the angle at the circumference would be 30°.

Chord and Radius Relationship

If the chord length equals r√2, the angle at the center is 90°. If the chord length equals r√3, the angle at the center is 120°.

Equilateral Triangle

A triangle in which all three sides are equal is equilateral, and each of its internal angles measures exactly 60°.

Shortcut Trick

First three-digit number divisible by 15 = 105 and Last = 990.

Number of terms (n) = [(990 − 105) ÷ 15] + 1 = 59 + 1 = 60.

Average of terms = (105 + 990) ÷ 2 = 547.5.

Sum = Average × n = 547.5 × 60 = 32850.

∴ The correct answer is 32850.

Alternate Method

Given:

Range: 100 to 999 (three-digit numbers)

Divisor: 15

Formula Used:

Last term (l) = a + (n − 1)d

Sum (S_n) = (n ÷ 2) × (a + l)

Calculations:

⇒ First term (a) = 15 × 7 = 105

⇒ Last term (l) = 15 × 66 = 990

⇒ Common difference (d) = 15

⇒ 990 = 105 + (n − 1) × 15

⇒ 885 = (n − 1) × 15

⇒ n − 1 = 885 ÷ 15 = 59

⇒ n = 60

⇒ Sum = (60 ÷ 2) × (105 + 990)

⇒ Sum = 30 × 1095

⇒ Sum = 32850

∴ The correct answer is 32850.

Additional Information

Arithmetic Progression (AP)

A sequence of numbers where the difference between consecutive terms is constant. General term T_n = a + (n − 1)d.

Sum of AP

The sum of first n terms is given by S_n = n/2 × [2a + (n − 1)d] or S_n = n/2 × [First term + Last term].

Sum of first n natural numbers

The sum of first n natural numbers is Σn = n(n + 1) ÷ 2.

Given:

A total of 1000 kg of vegetables were sold in a day

Calculation:

The percentage of tomatoes sold in a day is 40%

So according to the question:

Number of tomatoes = 40% of 1000 = 400.

∴ Option 1 is the correct answer.

Shortcut Trick

The length of an arc is a direct fraction of the circle's total circumference.

Fraction of the circle = 150° ÷ 360° = 5/12

Total circumference = 2 × (22/7) × 42 = 264 cm

Length of the arc = (5/12) × 264 = 110 cm

∴ The correct answer is 110 cm.

Alternate Method

150° r = 42 cm L = ?

O

Given:

Radius of the circle (r) = 42 cm

Angle formed by the arc at the centre (θ) = 150°

Formula Used:

Length of arc = (θ ÷ 360°) × 2πr

Calculation:

⇒ Length of arc = (150° ÷ 360°) × 2 × (22 / 7) × 42

⇒ Length of arc = (5 / 12) × 2 × 22 × 6

⇒ Length of arc = (5 / 12) × 264

⇒ Length of arc = 5 × 22

⇒ Length of arc = 110 cm

∴ The correct answer is 110 cm.

Additional Information

Area of a Sector

The area enclosed by an arc and two radii is called a sector. It is calculated using the formula: Area = (θ ÷ 360°) × πr².

Circumference of a Circle

The total perimeter or boundary length of a complete circle is known as its circumference, given by the formula 2πr.

Arc vs Chord

An arc is a curved, continuous segment of the circle's outer edge, whereas a chord is a straight line drawn inside the circle connecting two points on its circumference.

The correct answer is 1) Copious.

Key Points

• The word "restricted" means limited, confined, or restrained. It implies a lack of freedom or a limitation on something.
• For example, if someone has restricted access to a certain area, it means their access is limited or controlled.
• On the other hand, "copious" means abundant, plentiful, or extensive. It refers to a large quantity or amount of something. For instance, if there is a copious amount of rainfall, it means there is a significant and abundant rainfall.
• Example sentence using "restricted" - The company has restricted the use of social media during working hours.
• Therefore, the correct answer is 1) Copious, which represents the opposite meaning of "restricted."

Additional Information

• Option 2) Circumscribed is similar in meaning to "restricted" as it also implies something being limited or restricted. It means to confine within limits or boundaries.
• For example: The project's budget was circumscribed, leaving no room for additional expenses.
• Option 3) Capped means to set a limit or put a maximum restriction on something. While it shares some similarity with "restricted," it specifically refers to imposing a maximum limit.
• For example: The maximum number of participants for the workshop is capped at 50.
• Option 4) Finite means having a definite or limited duration, extent, or quantity. It indicates something having an endpoint or being bounded. Although it is related to limitation, it is not the opposite of "restricted."
• For example: Our resources are finite, so we need to use them wisely.

Here the correct answer is She requested her to pay attention to the details.

Key Points

• The given sentence is in Direct Speech and is in an imperative sentence. As per the given instructions, we have to change it into Indirect Speech.
• The process of transformation is as follows:
• The conjunction 'to' will be added and comma and inverted commas will be removed.
• In the Indirect speech 'said to' will be changed into 'requested' because the person is making a request.
• The indirect speech will begin like 'She requested her to.'
• Now we have to change the reported speech.
• According to the rules of grammar, after 'to' we have to use 'V1 (pay).'
• Finally, the indirect speech is 'She requested her to pay attention to the details.'
• So, the correct answer is option 4.

 

Correct Sentence: She requested her to pay attention to the details.

The correct answer is 2) Efficiency.

Key Points

• The word "efficacy" refers to the ability or effectiveness of achieving a desired result or producing a desired effect. It suggests the capability or power of something to bring about a successful outcome.
• For example, if a medicine has high efficacy, it means it is effective in treating a particular condition.
• On the other hand, "efficiency" is the quality or state of being efficient, which means achieving maximum productivity with minimum wasted effort or resources. It implies the ability to accomplish tasks or goals in a timely and effective manner. For instance, if a process or system is efficient, it means it is well-organized and optimized for productivity.
• Example sentence using "efficacy":
• The efficacy of the new cleaning product in removing stains was impressive.
• Therefore, the correct answer is 2) Efficiency, which is a synonym of "efficacy" as it implies effectiveness, productivity, and accomplishing tasks with minimal wastage.

Additional Information

• Option 1) Impotence means powerlessness or inability to take action or achieve results. It is the opposite of efficacy and does not have a similar meaning.
• Option 3) Ineptness refers to a lack of skill or competence. It is not synonymous with efficacy as it suggests incompetence or inability rather than effectiveness.
• Option 4) Futility means the state of being pointless, useless, or ineffective. It is opposite in meaning to efficacy and does not share a similar meaning.

The correct answer is 2) Everyone without distinction.

Key Points

• The idiom "all and sundry" is used to refer to everyone or every single person without any exception or distinction. It implies inclusivity, encompassing all individuals without leaving anyone out.
• For example:
• The announcement was made to all and sundry, ensuring that no one was left uninformed.
• The company's new policy applies to all and sundry, regardless of their position or seniority.
• In both examples, "all and sundry" is used to emphasize that the information or policy is meant for everyone, without any exceptions or exclusions.
• Therefore, the correct answer is 2) Everyone without distinction, as it best captures the meaning of the idiom/phrase.

The correct answer is indeed 1) QPRS.

Key Points

• Here is the correct order of the parts of the sentence:
• Q. typified by dishonesty, exploitation or the: This part introduces the concept of corruption and highlights its key characteristics, which include dishonesty and exploitation.
• P. misuse and abuse of public office, either directly: This part provides further elaboration on corruption by specifying that it involves the misuse and abuse of public office. It emphasizes that corruption can occur directly within the public office itself.
• R. or indirectly, for personal gains or unjust enrichment: This part expands on the previous point by explaining that corruption can also occur indirectly, with individuals seeking personal gains or unjust enrichment through their actions. It highlights the motive behind corrupt practices.
• S. in negation of due process or established protocol: This part adds an important aspect of corruption, stating that it goes against due process or established protocols. It implies that corruption disregards legal and ethical procedures.
• When rearranged, the sentence reads:
• Corruption is typified by dishonesty, exploitation or the misuse and abuse of public office, either directly or indirectly, for personal gains or unjust enrichment, in negation of due process or established protocol.
• This arrangement presents a coherent and logical flow of the sentence, providing a definition of corruption and describing its characteristics and consequences.

The error is in option 3: Fashion might not be first.

Key Points

• The correct form should be "Fashion might not be the first" instead of "Fashion might not be first."
• The definite article "the" is needed before "first" to indicate a specific ranking or order.
• Explanation:
• The definite article "the" is used to specify a particular item in a group or a specific ranking. In this case, it emphasizes that fashion might not be the initial or primary thing that comes to mind when thinking about isolation strategies.
• Example:
• The cat is sitting on the mat. (correct)
• Cat is sitting on the mat. (incorrect)
• In the example, the definite article "the" is necessary to specify which cat is being referred to.
• Therefore, the correct answer is 3) Fashion might not be first.
  

Here's the corrected sentence: "Fashion might not be the first thing that comes to mind when we think of isolation strategies."

The correct answer is 1) Ophthalmologist.

Key Points

• An ophthalmologist is a medical doctor who specializes in the diagnosis and treatment of eye diseases and disorders.
• They are trained to provide comprehensive eye care, including performing eye exams, prescribing corrective lenses, and performing surgeries related to the eyes.
• Example: I visited an ophthalmologist to get my eyes checked and receive treatment for my vision problems.
• Therefore, the correct answer is 1.

Additional Information

• The other options are not related to the field of eye disease and do not accurately describe a healthcare professional who treats eye diseases:
• Prologist: This term does not exist in the field of medicine or ophthalmology.
• Phonologist: A phonologist is a linguist who studies the sound patterns of languages and speech sounds. This term is not related to eye diseases.
• Biologist: A biologist is a scientist who studies living organisms and their interactions. While biology may include the study of eye diseases, it is not specific to the field of curing eye diseases.

The correct answer is: Option 1 i.e. Malcontent.

Key Points

• The word "Malcontent" refers to a person who is dissatisfied and rebellious. (असंतुष्ट व्यक्ति)
• Example: He was known as a malcontent constantly complaining about everything at work.
• Hence, a malcontent is someone who is never happy with what he has.

Therefore, the correct answer is: Option 1 i.e. Malcontent.

Additional Information

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

• Heresy (धर्म-विरोधी मत): Belief or opinion contrary to orthodox religious doctrine.
• Example: He was burned at the stake for heresy in medieval times.
• Malleable (लचीला): Easily influenced or pliable.
• Example: Gold is a malleable metal that can be shaped into different forms.
• Miser (कंजूस): A person who hoards wealth and spends as little money as possible.
• Example: The old miser would not even part with a single penny for charity.

The incorrectly spelt word is: BENIDICTION.

Key Points

• The correct spelling of the word is "BENEDICTION," not "BENIDICTION."
• A benediction is a prayer or blessing, often given at the end of a religious service or ceremony.
• Example sentence: The priest offered a benediction to conclude the wedding ceremony.
• Other options:
• MOCKERY: This word is correctly spelled. It refers to the act of ridiculing or making fun of someone or something.
• Example sentence: The comedian's mockery of politicians was met with laughter from the audience.
• CROCKERY: This word is correctly spelled. It refers to dishes, plates, bowls, or other pottery used for cooking, serving, and eating.
• Example sentence: She carefully arranged the delicate crockery in the china cabinet.
• RELIGIOUS: This word is correctly spelled. It relates to religion or the belief in and worship of a higher power or spiritual being.
• Example sentence: The temple is an important religious center for the local community.

The correctly spelt word is: SABOTAGE.

Key Points

• "SABOTAGE" is the correct spelling of the word. It refers to the act of intentionally destroying, damaging, or obstructing something, especially for disruptive purposes.
• Example sentence: The company suspected an inside job when important files went missing, pointing to possible sabotage.
• Other options:
• MEALIGN: This word is misspelled. The correct spelling is "MALIGN," which means to speak ill of someone or to criticize them unfairly.
• Example sentence: The tabloid published an article maligning the actor's reputation without any evidence.
• PRECISSION: This word is misspelled. The correct spelling is "PRECISION," which refers to the quality of being accurate, exact, or meticulous.
• Example sentence: The surgeon performed the delicate procedure with great precision, ensuring minimal risk.
• MISSIONERY: This word is misspelled. The correct spelling is "MISSIONARY," which refers to a person who is sent on a religious mission, typically to spread a particular faith or provide charitable work.
• Example sentence: The missionary traveled to remote villages to provide medical assistance and teach the local community about their beliefs.

The correct answer is 3) To permit something to proceed.

Key Points

• The idiom "green light" is commonly used to indicate permission or approval for something to proceed. When someone gives the "green light" to a project or action, it means they are granting permission for it to move forward or proceed.
• For example:
• The manager gave the green light for the new marketing campaign to begin.
• After weeks of negotiation, the city council finally gave the green light for the construction of the new stadium.
• In both examples, the phrase "green light" is used to signify that permission or approval has been granted, allowing the respective projects to proceed.
• Therefore, the correct answer is 3) To permit something to proceed.