SSC CHSL Tier-1 2022: Official Paper (Held On: 09 March, 2023 Shift 2) (Previous Year Paper)

The logic followed here is:

So, 'MZJ' will complete the series.

Hence the correct answer is "MZJ".

The logic followed here is:

Logic: The first term is a place or enclosure where the second term lives or is kept.

Now,

Aquarium : Fish → An aquarium is a place where fish are kept.

Similarly,

Hive : Honeybee →  hive is a place where honeybees live.

Hence, the correct answer is "Option 1".

Additional Information

Aeroplane : Hangar → A hangar is a place where aeroplanes are stored, not where they live.

Wine : Cellar → A cellar is a place where wine is stored, not where it lives.

Animals : Zoo → A zoo is a place where animals are kept.

The logic followed here is:

‘PROTEINS’ is coded as ‘119127591419’.

‘REFLECTS’ is coded as ‘9222115532019’.

Similarly, for SCENARIO:

So, 'SCENARIO' is coded as '8242213118915'.

Hence, the correct answer is "Option 2".

The quadrilaterals are:

So, there are '12' quadrilaterals in the given figure.

Hence, the correct answer is "Option 2".

The logic followed here is:

Option 1) OSX

Option 2) IMQ

Option 3) FJN

Option 4) NRV

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

Hence, the correct answer is "Option 1".

The logic followed here is:

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

Now,

11 : 81

→ (11 - 2)² ⇒ 9² = 81.

22 : 400

→ (22 - 2)2 ⇒ 202 = 400.

Similarly, for ? : 225

→ (17 - 2)2 ⇒ 152 = 225.

Hence, the correct answer is "Option 3".

The correct mirror image of the given figure when the mirror is held at the right side is:

Hence, "Option 4" is the correct answer.

Additional InformationIn Mirror image left side and right side changed vice-versa where top and bottom remain same.

Reflection of an object into the water is its water image. It appears by inverting an object vertically i.e. upside down.

The water image of the figure looks like the mirror image of the figure in case the mirror is horizontally at the bottom of the figure.

Water image is just a reflection where top and bottom part of the images changed where left and right side of the image remain same.

The embedded image is:

Hence, the correct answer is "Option 4".

From the given dice:

L is the common letter in both Dice,

So, 7 is the opposite surface of 8.

and, F and 9 is the opposite surface.

 

Therefore, among the given options, 8 and L will be the adjacent surface of 'F'.

Hence, the correct answer is "Option 1".

The logic followed here is:

Consider A as Plus.

Then,

14 A 13 A 3 = 30

→ 14 + 13 + 3 = 30.

and,

39 A 14 A 3 = 56

→ 39 + 14 + 3 = 56.

Similarly,

28 A 11 A 4 = ?

→ 28 + 11 + 4 = 43.

Hence, the correct answer is "43".

Given Statements:

I. All N are Q.

II. Some H are Q.

The least possible Venn diagram for the given statement:

Conclusion:

I. Some Q are N - True (Because All N are Q, so some Q are also N).

II. Some Q are H - True (Because Some H are Q, it means Some Q are also H).

III. Some N are H - False (Because there is no direct relation given between N and H, so it can be possible only).

So, Both conclusions I and II follows.

Hence, the correct answer is "Option 2".

The logic followed here is:

Step I: The line with triangle is shifting in previous place and changed vertically in alternate place.

Step II: The line with circle is shifting in previous place and changed vertically in alternate place.

Step III: The line with square box is shifting in previous place and changed vertically in alternate place.

Step IV: The line with triangle is shifting in previous place and changed vertically in alternate place.

So, the complete series will be:

So, 'Option 4' will replace the question mark.

Hence, the correct answer is "Option 4".

The logic followed here is:

Logic: The given numbers are in Prime number order.

Series are: 2, 3, 5, 7, 11 and the next Prime number is 13.

So, 13 will complete the given series.

Hence, the correct answer is "Option 4".

Additional Information Prime numbers 1 to 100:

The logic followed here is:

Logic: 1^st number × 3 - 9 = 2^nd number,

2^nd number + 7 = 3^rd number.

Here,

(36, 99, 106)

⇒ 36 × 3 - 9 = 108 - 9 = 99,

⇒ 99 + 7 = 106.

(72, 207, 214)

⇒ 72 × 3 - 9 = 216 - 9 = 207,

⇒ 207 + 7 = 214.

Similarly,

(24, 63, 70)

⇒ 24 × 3 - 9 = 72 - 9 = 63,

⇒ 63 + 7 = 70.

Hence, the correct answer is "Option 3".

The logic followed here is:

Dog : Four → A dog has four legs.

Similarly,

Parrot → A parrot has two legs.

Hence, the correct answer is "Option 3".

According to the given Venn diagram:

The shaded area shows "the reptiles are neither mammals nor amphibians".

So, there are 14 reptiles are neither mammals nor amphibians.

Hence, the correct answer is "14".

The correct order according to the English dictionary is:

3. Tackle
4. Tactful 2. Tactless
5. Taken
6. Talent

Here, the correct sequence will be: '34215'.

Hence, the correct answer is "Option 3".

Family Chart:

Given: H is the sister of I. B is the mother of H. J is the daughter of R. I is the sister of J.

So, R is Father of H.

Hence, the correct answer is "Option 3".

The logic followed here is:

Logic:  (1^st number)³ = 2^nd number.

Option 1) 108 – 1257912

→ 108³ = 1259712 ≠ 1257912.

Option 2) 102 – 1061208

(102)3  = 1061208

Option 3) 106 – 1191016

 (106)³ = 1191016.

Option 4) 104 – 1124864

 (104)³ =1124864.

So, '108 – 1257912' odd among the options.

Hence, the correct answer is "Option 1".

The logic followed here is:

‘MANAGE’ is coded as ‘HJDQDP’.

Similarly, for LATTER:

So, LATTER will be coded as UHWWDO.

Hence, the correct answer is "Option 1".

The logic followed here is:

Logic: The first word is the person responsible for producing or overseeing the creation of the second word.

Editor : Newspaper → An editor is responsible for overseeing the creation of a newspaper.

Similarly,

Farmer : Crop → A farmer is responsible for growing crops.

Hence, the correct answer is "Option 4".

Additional Information

Design : Architect → An architect is responsible for creating a design.

Food : Chef → A chef is responsible for preparing food.

Poem : Poet → A poet is responsible for creating a poem.

The logic followed here is:

Logic: 1^st number × 4 = 2^nd number.

Option 1) 638 – 2552

→ 638 × 4 = 2552.

Option 2) 618 – 2472

→ 618 × 4 = 2472.

Option 3) 1074 – 4396

→ 1074 × 4 = 4296 ≠ 4396.

Option 4) 508 – 2032

→ 508 × 4 = 2032.

So, '1074 – 4396' odd among the options.

Hence, the correct answer is "Option 3".

The figure embedded is:

Hence, the correct answer is "Option 4".

BODMAS Table:

Given: By Interchanging '4 and 3' and checking the option:

Option 1) 3 × 4 ÷ 2 + 7 = 17

After interchanging '4 and 3':

⇒ 4 × 3 ÷ 2 + 7 = 17

⇒ 4 × 1.5 + 7 = 17

⇒ 6 + 7 = 17

⇒ 13 ≠ 17.

Option 2) 7 × 4 + 3 ÷ 1 = 30

'4 and 3'

⇒ 7 × 3 + 4 ÷ 1 = 30

⇒ 7 × 3 + 4 = 30

⇒ 21 + 4 = 30

⇒ 25 ≠ 30.

Option 3) 4 + 3 × 7 – 2 = 29

'4 and 3'

⇒ 3 + 4 × 7 – 2 = 29

⇒ 3 + 28 – 2 = 29

⇒ 31 - 2 = 29

⇒ 29 = 29.

Option 4) 4 × 3 + 7 – 5 = 16

'4 and 3'

⇒ 3 × 4 + 7 – 5 = 16

⇒ 12 + 7 – 5 = 16

⇒ 19 - 5 = 16

⇒ 14 ≠ 16.

Hence, the correct answer is "Option 3".

The logic followed here is:

Logic: The first term in each pair is the capital city of the country represented by the second term.

Option 1) New Delhi – India → New Delhi is the capital of India.

Option 2) Beijing – China → Beijing is the capital of China.

Option 3) Dhaka – Bangladesh → Dhaka is the capital of Bangladesh.

Option 4) Lahore – Pakistan → Lahore is not the capital of Pakistan, The capital of Pakistan is Islamabad.

Hence, the correct answer is "Option 4".

The correct answer is 2) Both I and II.

Key PointsUnderstanding the statements in relation to large dams

• Social Problems
• Large dams have significant social impacts, particularly on the lives of peasants and tribal communities.
• The construction of large dams often necessitates the displacement of large populations from their ancestral lands.
• Many affected individuals and communities face inadequate compensation and lack proper rehabilitation plans. Hence statement I is correct.
• Environmental Problems
• The construction and operation of large dams can have profound environmental consequences.
• They often lead to extensive deforestation, which in turn reduces biodiversity by destroying habitats.
• This loss of forests and biological diversity can disrupt local ecosystems and contribute to larger environmental issues. Hence statement II is correct.

Additional Information

• Impacts on Local Communities
• The construction of large dams can disrupt local economies that are dependent on traditional practices and occupations.
• The disruption can lead to long-term socio-economic challenges for the displaced populations.
• Hydrological Changes
• Large dams alter the natural flow of rivers, which can impact the water availability downstream.
• These hydrological changes can negatively affect agriculture, fisheries, and the natural sediment transport, leading to further environmental degradation.

The correct answer is Option 3. 

Key Points

• Wipro fired 300 employees for moonlighting.
• The IT company could have sacked these employees after finding out about their second job through UAN  numbers.
• Wipro chairman Rishad Premji said the company has no place for employees working with rivals.

Additional Information

• Wipro Limited is a multinational corporation headquartered in Bangalore, India.
• It is a global information technology, consulting, and business process services company that provides solutions to various industries, including banking, finance, insurance, healthcare, manufacturing, retail, and telecommunications.
• Wipro was founded in 1945 by M.H. Premji as a manufacturer of vegetable and refined oils. In the 1980s, Wipro shifted its focus to IT services and software development.
• Mindtree Limited is a global technology consulting and services company headquartered in Bangalore, India.
• The company provides end-to-end services in the areas of cloud, data analytics, digital transformation, enterprise application development, testing, infrastructure management, and engineering services to clients across various industries, including banking, financial services, insurance, retail, consumer packaged goods, and manufacturing.
• Mindtree was founded in 1999 by ten industry professionals, including Ashok Soota, Subroto Bagchi, and Krishnakumar Natarajan, with an initial focus on the software development services market.
• Amazon India is a subsidiary of Amazon.com, Inc., the world's largest online retailer.
• Amazon launched its operations in India in 2013, and since then, it has grown rapidly to become one of the largest e-commerce platforms in the country.
• Amazon India offers a wide range of products, including books, electronics, clothing, beauty products, and household items, among others. The company has also introduced various services, such as Amazon Prime, which offers free and fast delivery, streaming of movies and TV shows, and exclusive deals and discounts to its subscribers.
• Microsoft India is a subsidiary of Microsoft Corporation, a multinational technology company headquartered in Redmond, Washington, USA.
• Microsoft India was established in 1990.
• Microsoft India has established various innovation centers and labs to support research and development in emerging technologies such as artificial intelligence, machine learning, and the internet of things.
• The company has also launched various initiatives to promote digital literacy and skills development in India, including the Microsoft India AI School, which offers free online courses in artificial intelligence and machine learning.

The correct answer is Option 1.

Key Points

• Dabang Delhi pulled off a coup on Friday as it beat Patna Pirates 37-36 to clinch its maiden Pro Kabaddi League (PKL) title.
• Delhi was narrowly beaten by Bengal Warriors in last season's final, but coach Krishan Hooda’s men dazzled on the second time of asking.
• Naveen Kumar and Vijay's raiding brilliance came to the side's aid once more as the duo bagged Super 10s and scored a total of 27 points - 73 per cent of their team’s total points.
• The defence managed all of four points, Sandeep Narwal and Manjeet Chhillar managed two each.

Additional Information

• PKL stands for Pro Kabaddi League, which is a professional league for the sport of Kabaddi in India.
• The league was founded in 2014, and since then, it has grown rapidly in popularity, making it one of the most-watched sports leagues in India.
• The Pro Kabaddi League consists of teams representing various cities in India, and the league follows a franchise model similar to other professional sports leagues.
• The league features both men's and women's teams, and the teams compete in a round-robin format followed by playoffs.
• The Pro Kabaddi League has been instrumental in the growth of Kabaddi as a sport in India.
• The league has helped to popularize the sport beyond its traditional strongholds and has attracted a new generation of fans to the sport.
• The league has also helped to create opportunities for professional Kabaddi players in India and has provided a platform for them to showcase their skills.
• The Pro Kabaddi League has also been a major commercial success, with major corporate sponsors and advertisers supporting the league.
• The league has also attracted investment from prominent Indian and international investors, including Bollywood actor Abhishek Bachchan and Ratan Tata, the former chairman of Tata Sons.
• The Pro Kabaddi League has also been recognized for its commitment to social responsibility and sustainability.

The correct answer is Option 1. 

Key Points

• Roger Federer is the latest star to retire from the sport.
• The Swiss maestro announced his decision to call time on his career a few weeks ago, and the 2022 Laver Cup was the scene where he played the final match of his career.
• Roger Federer is a professional tennis player from Switzerland, widely regarded as one of the greatest players of all time.
• He has won a record 20 Grand Slam singles titles, including eight Wimbledon titles, and has spent over 300 weeks as the world No. 1 ranked player.
• Federer has also won a gold medal in doubles at the 2008 Beijing Olympics and a silver medal in singles at the 2012 London Olympics.
• He is known for his elegant playing style, exceptional shot-making ability, and sportsmanship on and off the court.

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Additional Information

• Rafael Nadal is a professional tennis player from Spain and is widely regarded as one of the greatest tennis players of all time.

• He has won 20 Grand Slam singles titles, tied with Roger Federer for the most in men's tennis history, and has won the French Open a record 13 times.

• Nadal has also won two Olympic gold medals, one in singles at the 2008 Beijing Olympics and the other in doubles at the 2016 Rio Olympics. Known for his tenacious play, Nadal is considered one of the best clay court players of all time and has had success on all surfaces.

• Off the court, he is known for his philanthropic work, particularly with his foundation which focuses on education and social integration for disadvantaged youth.

• Novak Djokovic is a professional tennis player from Serbia and is currently ranked as the world No. 1 in men's singles tennis by the Association of Tennis Professionals (ATP).

• He has won 20 Grand Slam singles titles, tied with Rafael Nadal and Roger Federer for the most in men's tennis history. Djokovic has won all four Grand Slam tournaments at least twice, including nine Australian Open titles, five Wimbledon titles, three US Open titles, and two French Open titles.

• He is also a five-time ATP Finals champion and has won a total of 84 career ATP singles titles.

• Djokovic is known for his exceptional flexibility, court coverage, and return of serve.

• He is considered one of the best returners in the history of the game and has a strong all-court game that allows him to succeed on all surfaces.

• Carlos Alcaraz is a young professional tennis player from Spain.

• He was born on May 5, 2003, and has quickly established himself as one of the most promising talents in the sport.

• Alcaraz turned professional in 2018 and has since won two ATP Challenger titles, as well as his first ATP Tour title at the age of 18 in Umag, Croatia, in July 2021.

• He is known for his aggressive playing style and powerful groundstrokes, particularly his forehand. Alcaraz has been compared to his fellow Spaniard Rafael Nadal, and many tennis experts consider him to be one of the future stars of the sport.

The correct answer is Option 3. 

Key Points

• The total length of the coastline of India's mainland, including the coastlines of the Andaman and Nicobar Islands and Lakshadweep Islands, is approximately 11098.81km according to the Ministry of Environment, Forests and Climate Change, Government of India.
• This coastline stretches along the Arabian Sea to the west, the Bay of Bengal to the east, and the Indian Ocean to the south.
• It is important to note that the exact length of the coastline can vary depending on the method used to measure it, as coastlines are often complex and irregular.

Additional Information

• The Andaman and Nicobar Islands are located in the Bay of Bengal, on the southeastern coast of India.
• They are a group of islands consisting of 572 islands, of which only 38 are inhabited.
• The Andaman Islands are to the north of the Nicobar Islands and are separated by the Ten Degree Channel.
• The capital city of the Andaman and Nicobar Islands is Port Blair, located on the Andaman Islands.
• The islands are known for their pristine beaches, crystal-clear waters, and diverse flora and fauna.

The correct answer is Option 2. 

Key Points

• Ravi Shankar is famously known as the sitar maestro in India.
• He was a legendary musician and composer who was born in Varanasi, India in 1920 and passed away in 2012.
• Shankar was known for popularizing Indian classical music in the West and was a major influence on the "psychedelic" rock music of the 1960s.
• He collaborated with a number of Western musicians, including George Harrison of The Beatles, and was awarded several prestigious awards during his lifetime, including the Bharat Ratna, India's highest civilian award.
• Shankar is regarded as one of the most important figures in the history of Indian classical music and his legacy continues to influence musicians around the world.

Additional Information

• Maharshi Patanjali was a revered ancient Indian sage who is believed to have compiled the Yoga Sutras, a collection of 196 aphorisms that provide guidance on the practice and philosophy of yoga.
• The exact date of Patanjali's birth and death is not known, but he is believed to have lived in India during the 2^nd century BCE or earlier.
• Patanjali is also revered as the founder of classical Ayurveda, a system of traditional medicine that emphasizes the balance of body, mind, and spirit.
• In addition to his contributions to yoga and Ayurveda, Patanjali is also known for his commentary on the Sanskrit grammar of Panini, known as the Mahabhashya.
• Patanjali's teachings have had a profound impact on the spiritual and philosophical traditions of India, and his legacy continues to influence millions of people around the world today.
• Ustad Bismillah Khan was a legendary Indian musician who is widely regarded as one of the finest shehnai players of all time.
• He was born in 1916 in the small town of Dumraon in Bihar, India, and grew up in the city of Varanasi, which is known for its rich musical heritage.
• Khan began playing the shehnai, a traditional Indian wind instrument, at a young age and quickly gained a reputation for his skill and virtuosity.
• He went on to become one of the most celebrated musicians in India, performing for audiences around the world and receiving numerous awards and accolades for his contributions to music.
• Khan was also known for his dedication to preserving and promoting traditional Indian music, and he played a key role in popularizing the shehnai as a solo instrument.
• He passed away in 2006 at the age of 90, but his legacy continues to inspire and influence musicians around the world.
• Sitara Devi was a renowned Indian classical dancer who specialized in Kathak, a North Indian dance form that emphasizes footwork, facial expressions, and storytelling.
• She was born in 1920 in Kolkata, India, and was raised in a family of musicians and dancers.
• Devi began performing as a child and quickly gained a reputation as a talented and charismatic dancer.
• She went on to become one of the most famous and respected dancers in India, performing for audiences around the world and receiving numerous awards and accolades for her contributions to dance.
• Devi was known for her dynamic and expressive performances, as well as her tireless efforts to promote and preserve traditional Indian dance forms.
• She passed away in 2014 at the age of 94, but her legacy as a pioneer of Indian classical dance continues to inspire generations of dancers and dance enthusiasts.

The correct answer is Option 3. 

Key Points

• In India, the primary financial institution that protects investors in the stock market is the Securities and Exchange Board of India (SEBI).
• SEBI is a regulatory body that was established in 1988 to protect the interests of investors in the Indian securities market and to promote the development of the securities market.
• SEBI regulates and supervises the activities of various market participants, including stock exchanges, brokers, mutual funds, and other intermediaries, and it also enforces rules and regulations related to trading, disclosure, and transparency in the securities market.
• SEBI plays a critical role in maintaining the integrity and stability of the Indian securities market and in safeguarding the interests of investors by ensuring fair and transparent trading practices, promoting investor education and awareness, and enforcing laws and regulations to prevent fraud and malpractice.

Additional Information

• The Bombay Stock Exchange (BSE) is a major stock exchange located in Mumbai, India.
• It was established in 1875, making it one of the oldest stock exchanges in Asia.
• The BSE is a popular platform for trading in stocks, bonds, and other financial instruments, and it is known for its role in shaping the Indian capital market.
• The BSE has a market capitalization of over $2 trillion, making it one of the largest stock exchanges in the world.
• The BSE also serves as an important source of financing for Indian companies, allowing them to raise capital by issuing stocks and bonds to investors.
• The BSE is regulated by the Securities and Exchange Board of India (SEBI), which is responsible for ensuring fair and transparent trading practices in the Indian securities market.
• The BSE has played a significant role in the growth and development of the Indian economy, and it continues to be a major hub for investment and trading activity in India.
• The Reserve Bank of India (RBI) is the central bank of India, responsible for regulating the monetary policy of the country and supervising the banking system.
• The RBI was established in 1935 and is headquartered in Mumbai. Its main functions include formulating and implementing monetary policy, regulating and supervising banks and other financial institutions, managing the foreign exchange market, and issuing currency.
• The RBI is governed by a central board of directors, headed by a Governor who is appointed by the Indian government.
• The RBI plays a crucial role in maintaining financial stability and promoting economic growth in India.
• Its policies and decisions have a significant impact on the banking and financial sectors in the country, as well as on the broader economy.
• The RBI also serves as a lender of last resort, providing liquidity to banks and other financial institutions in times of crisis.
• The National Stock Exchange (NSE) is one of the major stock exchanges in India, located in Mumbai.
• It was established in 1992 and has since become one of the largest stock exchanges in the world by market capitalization.
• The NSE provides a platform for trading in a wide range of financial instruments, including equities, futures and options, currencies, and debt securities. It is known for its advanced electronic trading platform and has been a pioneer in introducing technology-driven innovations in the Indian securities market.
• The NSE is regulated by the Securities and Exchange Board of India (SEBI) and operates under strict rules and regulations to ensure fair and transparent trading practices.
• The NSE has played a significant role in the development of the Indian capital market, providing investors with access to a wide range of investment opportunities and contributing to the growth and development of Indian businesses.
• The NSE has also been a driving force behind the growth of the Indian economy and has helped to promote economic stability and growth by facilitating the flow of capital to businesses and entrepreneurs$.

The correct answer is Option 4. 

Key Points

• Kanchipuram was the capital of the Pallava dynasty.
• The Pallavas were a powerful dynasty that ruled a large part of southern India from the 3^rd to the 9^th century CE.
• Kanchipuram, also known as Kanchi, is located in the state of Tamil Nadu and is renowned for its temples, silk sarees, and rich cultural heritage.

Additional Information

• The Pallavas were one of the earliest dynasties to emerge in southern India, and their capital was Kanchipuram, located in present-day Tamil Nadu.
• The Pallavas were patrons of art, architecture, literature, and religion, and their influence can still be seen in many parts of southern India today.
• They were responsible for building many famous temples and monuments, including the Shore Temple in Mahabalipuram and the Kailasanatha Temple in Kanchipuram.
• The Pallava dynasty declined in the 9^th century CE, with the rise of the Chola dynasty, but their legacy continued to shape the culture and history of southern India for centuries to come.

The correct answer is Option 2. 

Key Points

• The Industrial Policy Resolution of 1956 was an important policy document in India's economic history and played a key role in shaping the country's economic development trajectory.
• It was adopted by the Indian government under the leadership of Prime Minister Jawaharlal Nehru with the aim of promoting industrialization and economic growth in the country.
• The policy was closely linked to India's Second Five Year Plan (1956-61), which was the country's second major economic development plan after independence.
• The Second Five Year Plan was heavily influenced by the principles laid out in the Industrial Policy Resolution of 1956, which emphasized the importance of state-led development and the establishment of a mixed economy in which the private sector and public sector would both have a role to play.
• The Second Five Year Plan focused on promoting industrialization, particularly in key sectors such as steel, power, and heavy engineering, and on developing the country's infrastructure.
• The plan was also aimed at promoting social welfare and reducing poverty by creating employment opportunities and improving access to essential goods and services for the people of India.

Additional Information

• A Five Year Plan is a strategic planning framework used by organizations, governments, and individuals to set long-term goals and objectives over a five-year period. The plan typically includes specific targets and timelines for achieving those goals.
• The Fifth Five Year Plan was a period of economic planning in India that covered the period from 1974 to 1979.
• The plan was introduced during a period of economic crisis, marked by high inflation and slow economic growth.
• The main focus of the Fifth Five Year Plan was on increasing agricultural production, promoting rural development, and reducing poverty.
• The plan also emphasized the need to increase industrial production and promote exports to earn foreign exchange.
• The Fourth Five-Year Plan was a period of economic planning in India that covered the period from 1969 to 1974.
• The main focus of the Fourth Five-Year Plan was on achieving self-sufficiency in food production and reducing poverty.
• The plan also emphasized the need to increase industrial production and to promote exports to earn foreign exchange.
• The Third Five-Year Plan was a period of economic planning in India that covered the period from 1961 to 1966.
• The main objective of the Third Five-Year Plan was to achieve self-sustaining growth and to reduce poverty.
• This plan was introduced after a brief period of stability following the Indo-China war in 1962.

The correct answer is Option 1. 

Key Points

• Sponge is a type of colloid in which gas is dispersed in a solid, rather than in a liquid.
• In a sponge, a solid material (such as cellulose or polyurethane) forms a network of pores that trap gas.
• When a sponge is soaked in water, the pores fill with water and create a stable suspension.
• This is different from a foam, where gas is dispersed in a liquid.
• An example of a sponge colloid is the polyurethane foam used in mattresses, cushions, and insulation, in which air is dispersed within a solid polyurethane matrix.

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Additional Information

• Butter is a complex mixture of many different chemical compounds, including fats, proteins, water, and various other substances.
• The major chemical components of butter are the fatty acids, which are long chains of carbon and hydrogen atoms.
• The fatty acids in butter can vary depending on the source and processing of the butter, but they are typically a mixture of saturated and unsaturated fatty acids.
• Cheese is a complex mixture of proteins, fats, and water, as well as various vitamins, minerals, and flavor compounds. The specific chemical form of cheese can vary depending on the type of cheese, but some of the key components include:
• Proteins: Cheese contains a variety of proteins, including casein and whey proteins. These proteins are made up of amino acids, which are the building blocks of proteins. The specific amino acid composition of cheese can vary depending on the type of cheese and how it is made.
• Fats: Cheese is also high in fat, which is an important source of flavor and texture. The fats in cheese are mostly in the form of triglycerides, which are made up of fatty acids and glycerol.
• Water: Cheese contains varying amounts of water, depending on the type of cheese and how it is made. The water content can range from less than 40% for hard, aged cheeses to over 70% for soft, fresh cheeses.
• Minerals: Cheese is a good source of calcium, phosphorus, and other minerals that are important for bone health and other bodily functions.
• Flavor compounds: Cheese contains a wide variety of flavor compounds, including volatile compounds like esters, aldehydes, and ketones, as well as non-volatile compounds like amino acids and peptides. The specific flavor profile of cheese can vary depending on the type of cheese and how it is made.

The correct answer is Ctrl + Alt + I.

Key Points

• Other important computer shortcut keys
• Ctrl + M -- Indent the paragraph.
• Ctrl + B -- Bold highlighted selection.
• Ctrl + D -- Font options.
• Alt + F--File menu options in the current program.
• Alt + E--Edits options in the current program.
• F1--Universal help (for any sort of program).
• Ctrl + A--Selects all text.
• Ctrl + X--Cuts the selected item.
• Ctrl + Del--Delete the next word.
• Ctrl + C--Copy any selected item.
• Ctrl + Ins-- Copies any highlighted text into the clipboard.
• Ctrl + V--Paste the selected item.
• Shift + Ins -- Paste the selected item.
• Home -- Takes the user to the beginning of the current line.
• Ctrl + Home--Go to the beginning of the document.
• End -- Go to the end of the current line.
• Ctrl + End -- Go to the end of a document.
• Shift + Home -- Highlight from the current position to the beginning of the line.
• Shift + End -- Highlight from the current position to the end of the line.
• Ctrl + (Left arrow) -- Move one word to the left at a time.
• Ctrl + (Right arrow) -- Move one word to the right at a time.

The correct answer is Bihar.

Key Points

• As per National Mineral Inventory data, the total reserves/resources of gold ore (primary) in the country have been estimated at 501.83 million tonnes.
• In India, largest resources of gold ore (primary) are located in Bihar (44%) followed by Rajasthan (25%), Karnataka (21%), West Bengal (3%), Andhra Pradesh (3% ), Jharkhand (2 %).
• The remaining 2% resources of ore are located in Chhattisgarh, Madhya Pradesh, Kerala, Maharashtra, and Tamil Nadu.
• Cost of extraction of any mineral including gold vary from mine to mine.

Additional Information

• Karnataka is the largest producer of gold in India.
• Karnataka was the leading producer of primary gold accounting for 99% of the total production.
• The remaining production was reported from Jharkhand.
• Kolar gold fields and Hutti goldfields are the two major goldfields located in Karnataka.
• Karnataka has the only operational gold mine in India.
• Hutti Gold Mines is the only producer of primary gold in the country.
• Hutti Gold Mines has the capacity to produce 5,50,000 tonnes per annum.
• Hutti Gold Mine is one of the most ancient metal mines in the world.
• Kolar gold fields closed on 28 February 2001 due to a fall in gold prices.

The correct answer is Godavari.

Key Points

• Godavari
• The Godavari is India's largest peninsular river.
• It is the second-longest river in India after the Ganga.
• It rises from Maharashtra's Thriambak hill.
• Its length is about 1465 km.
• Due to its length and the area it covers, it is also known as the ‘Dakshin Ganga’.
• Flows through the states of Maharashtra, Chhattisgarh, Telangana, and Andhra Pradesh.​

Additional Information

• Mahi
• ​It originates in the Mahi Kanta hills, from the northern slopes of Vindhyas at an altitude of 500 m near village Bhopawar, Sardarpur Tehsil in the Dhar district of Madhya Pradesh.
• It flows through the Vagad region of Rajasthan, enters Gujarat, and flows into the Arabian Sea.
• ​Narmada
• The Narmada river originates from the Narmada Kund located in Amarkantak, Anuppur district in Madhya Pradesh.
• Amarkantak is located on the Maikal mountain.
• The Narmada river forms the unmarked boundary between North and South India.
• The major tributaries of the Narmada are Barna, Tawa, Kanar, Kolar, Man, Hatni, Uri, Shakkar, etc.
• It flows westwards (1, 312 km) before falling into the Gulf of Khambhat.
• The Narmada river is the longest river in Madhya Pradesh and it's called "The Lifeline of Madhya Pradesh".
• The waterfalls created by the Narmada River include Kapil Dhara and Dudh Dhara Falls (Anuppur), Dhuandhar Falls (Bhedaghat, Jabalpur), Sahasradhara Falls (Maheshwar, Khargone), Dardhi Falls, Manadhata Falls, etc.
• Tapi
• The Tapti River  (aka Tapi river )is a river in central India located to the south of the Narmada river which flows westwards before draining into the Arabian Sea.
• The river has a length of around 724 kms and flows through the states of Maharashtra, Gujarat, and Madhya Pradesh.
• Tapti river originates from Multai Betul district Madhya Pradesh. And also from the Satpura range.

The correct answer is ROM.

Key Points

• ROM
• Read-Only Memory is a ROM in a computer.
• Read-only memory is a storage medium that permanently stores data on computers and electronic devices.
• The data stored in these chips is nonvolatile i.e. it is not lost when power is removed.
• There are five basic ROM types:
• ROM: Read-Only Memory.
• PROM: Programmable read-only memory.
• EPROM: Erasable programmable read-only memory.
• EEPROM: Electrically erasable programmable read-only memory.
• Flash memory: Flash memory, a type of EEPROM that uses in-circuit wiring.
• BIOS uses Flash memory.

Additional Information

• Register
• The smallest and fastest memory of a computer is registered memory located in the computer's central processing unit(CPU).
• It generally stores the most used instructions, data, etc. which are to be used by CPU.
• Control Unit is part of the CPU.
• It advises the input and output devices, and computer memory on how to respond to the instructions sent to the processor.
• RAM
• It stores data that the computer needs to use temporarily. So it is faster than the secondary storage devices. It is a volatile memory i.e. the data disappear from it when the power is off.
• It is known as the Read-Write Memory. i.e. the user can write information into RAM and read information from it.
• It is called random access since any memory location can be accessed randomly for reading and writing. The access time is the same for each memory location.
• It is usually called “temporary” memory, which means that when the system is shut down, the memory is lost.
• Cache
• A cache memory is used by the central processing unit of a computer to reduce the average cost time or energy to access data from the main memory.
• Generally Cache memory is logically positioned between CPU and main memory.

The correct answer is Uttar Pradesh.

 Key Points

• Aaram Bagh ​
• Aaram Bagh was originally built by the Mughal Emperor Babur in 1528.
• The Aaram Bagh is the oldest Mughal Garden in India, located in Agra, five kilometres northeast of the Taj Mahal.
• Before being interred in Kabul, Babur was temporarily buried there.
• The garden is a Persian garden, where the garden is divided by paths and canals to represent the Islamic ideal of paradise, a plentiful garden through which rivers flow.
• Two viewing pavilions face the Jamuna river and include an underground 'tahkhana' that was used to provide visitors with relief during the hot summers. There are numerous watercourses and fountains in the garden.

Additional Information

• Mughals:
• The Mughals were descendants of two great lineages of rulers.
• From their mother’s side, they were descendants of Genghis Khan (died 1227), the Mongol ruler who ruled over parts of China and Central Asia.
• From their father’s side, they were the successors of Timur (died 1404), the ruler of Iran, Iraq and modern-day Turkey.
• However, the Mughals did not like to be called Mughal or Mongol. This was because Genghis Khan’s memory was associated with the massacre of innumerable people.
• It was also linked with the Uzbeks, their Mongol competitors.
• On the other hand, the Mughals were proud of their Timurid ancestry, not least of all because their great ancestor had captured Delhi in 1398.

The correct answer is Himachal Pradesh.

Key Points

• Bulk Drug Park
• The Prime Minister, Shri Narendra Modi laid the foundation stone of Bulk Drug Park and dedicated the Indian Institute of Information Technology (IIIT) Una to the nation.
• work is beginning on the second bulk drug park of the country at Una here.
• “Being chosen as one of the only three states for a bulk drug park is a momentous decision for the state and is a result of our affection and dedication for the state”.
• Three bulk drug parks have received ‘in principle approval from the Central government of India.
• The bulk drug parks in Gujarat, Himachal Pradesh, and Andhra Pradesh will provide a consistent supply of bulk drug active components and will ensure India’s drug security.

Additional Information

• The state of Himachal Pradesh was formed in the year 1971.
• It was established as the 18^th state with Shimla as its capital.
• In 1950, it was created after a merger of 30 princely states and in 1956 it was declared a union territory.

The correct answer is Establishment of standards of weight and measure.

Key Points

• The Seventh schedule of the Indian Constitution deals with the division of powers between the union and the states in terms of the list.
• The Seventh Schedule to the Constitution of India defines and specifies the allocation of powers and functions between Union & States.
• It contains three lists:

1. Union List,
2. State List and
3. Concurrent List

• 7^th Schedule of Indian Constitution – Union List had 97 subjects. Now, it has 100 subjects.
• 88^th Amendment added a new subject in the Union List called ‘taxes on services.’
• The state list has 61 subjects. Earlier, it had 66 items.
• The 69^th Constitutional Amendment Act of 1991 made special provisions in relation to National Capital. Laws cannot be made by the Delhi government on three subjects under State List named as – Public Order, Police & Land.
• The concurrent list has 52 subjects enumerated under it.

The correct answer is Robert Clive.

Key Points

• Battle of Plassey:
• It was fought in 1757 in the Plassey region of West Bengal, on the east of the Bhagirathi river.
• Troops of the British East India Company, led by Robert Clive, came up against the forces of Siraj-ud-Daulah, the last independent Nawab of Bengal, and his French allies.
• The victory of the British East India Company in the Battle of Plassey is one of the important landmarks in India History.
• The Battle of Plassey paved the way for the beginning of the British empire in India.
• The British enjoyed the tax benefits, had to compete with no rival foreign merchants, and began to use the revenue of Bengal for protecting their military and trade interests.
• So much wealth was drained from Bengal that the economy was completely shattered. This is known as the Plassey Plunder.
• With the wealth of Bengal, the British secured their business and political supremacy.

Additional Information

• The Governor and company of merchants of London trading into the East Indies, popularly known as the English East India Company, were formed in 1600 AD.
• Captain William Hawkins arrived at Jahangir’s court in 1609 AD to seek permission to open a factory in Surat.
• A Farman was issued by Jahangir, permitting the English to build a factory in Surat.
• In 1613, a permanent factory of East India Company was established at Surat.
• In 1611, the company established its first factory in the south in Masulipattanam.

the correct answer is Premchand.

Key Points

• Premchand
• Premchand, also known as Dhanpat Rai Srivastava, was an Indian author best known for his contemporary Hindustani writing.
• He was born on July 31, 1880, and died on October 8, 1936.
• Hindi and Urdu social fiction were invented by Premchand.
• He was one of the first writers to discuss caste systems, the suffering of working women, and other issues that were prevalent in late 1880s culture.
• He is one of the most well-known authors on the Indian continent and is recognised as one of the greatest Hindi authors of the first half of the 20^th century.
• He has written various novels, including, Godaan, Karmabhoomi, Gaban, Mansarovar, and Idgah.
• In a book titled Soz-e-Watan, he released his first collection of five short stories.

The correct answer is Radiation therapy.

Key Points

• Radiotherapy to treat cancer:
• High doses of radiation are used in radiation therapy, also known as radiotherapy, as a cancer treatment to eradicate cancer cells and reduce tumour size.
• As with X-rays of your teeth or shattered bones, radiation is utilised at low doses in x-rays to see inside your body.
• Radiation therapy damages cancer cells' DNA, which either kills them or limits their growth at high dosages.
• Cancer cells that have DNA damage that cannot be repaired either cease proliferating or die.
• When the injured cells expire, the body degrades and eliminates them.
• But too much radiation can damage tissues by changing cell structure and damaging DNA.
• This can cause serious health problems.

Additional Information

• Chemotherapy 
• Chemotherapy is the use of any drug to treat any disease.
• But to most people, the word chemotherapy means drugs used for cancer treatment.
• It's often shortened to “chemo.” Surgery and radiation therapy remove, kill, or damage cancer cells in a certain area, but chemo can work throughout the whole body.
• Surgery:
• Surgery is a medical speciality that employs operative manual and instrumental techniques on a patient to examine or treat a pathological condition.
• Such as a disease or injury, to enhance bodily function or appearance, or to repair unwelcome ruptured areas
• Physiotherapy
• ​Physiotherapy is a healthcare profession that aims to help people restore and maintain movement and function when affected by injury, illness or disability.
• Physiotherapists use a combination of manual therapy, exercise, and education.

The correct answer is 226.

Key Points 

• Under Article 226, a writ petition can be filed in a High court for issuing one of the five writs as per the case.
• A High Court is empowered to issue directions, orders, or writs for the enforcement of a Fundamental Right and for any other purpose those include:
• Habeas corpus
• Mandamus
• Prohibition
• Quo warranto
• Certiorari.
• The Supreme Court is considered the protector and guarantor of fundamental rights(Article 32).

Additional Information

• Article 32  of the Indian Constitution has been described as the ‘heart and soul’ of the Indian Constitution by Dr B. R. Ambedkar.
• It gives a citizen the right to approach the Supreme Court to get resorted to any of the fundamental rights in case of their violation.
• It is also known as the Right to Constitutional Remedies.

The correct answer is Banas.

Key Points

• Banas river originates from the state of Rajasthan.
• The river originates from the Khamnor hills of the Aravali range near Kumbhalgarh.
• It is also known as 'Van ki Asha' (Hope of forest).
• It flows northeast through the Mewar region of Rajasthan and meets the Chambal near the village of Rameshwar in Sawai Madhopur district.
• Berach and Menali are the right bank tributaries of the Banas river.
• Kothari, Khari, Dai, Dheel River, Sohadara River, Morel, and Kalisil are the left bank tributaries of Banas river.​

Additional Information

• Chambal River
• It is the tributary of the Yamuna River.
• It rises in the Vindhyachal range South of Mhow, the western state of Madhya Pradesh.
• It flows from the north into the southeastern state of Rajasthan.
• It ends on the confluence of five rivers which includes the Chambal, Kwari, Yamuna, Sind, Pahuj, at Pachnada near Bhareh in Uttar Pradesh, at the border of Bhind and Etawah districts.
• Major Tributary - Kshipra, Kalisindh, Parvati, Bansa, Newaj, Kwari, Sindh, etc.
• Narmada River
• It originates from the Narmada Kund located in Amarkantak, Anuppur district in Madhya Pradesh.
• The major tributaries of the Narmada are Barna, Tawa, Kanar, Kolar, Man, Hatni, Uri, Shakkar, etc.
• It flows westwards before falling into the Gulf of Khambhat.
• The Narmada river is the longest river in Madhya Pradesh and it's called "The Lifeline of Madhya Pradesh".
• The waterfalls created by the Narmada River include Kapil Dhara and Dudh Dhara Falls (Anuppur), Dhuandhar Falls (Bhedaghat, Jabalpur), Sahasradhara Falls (Maheshwar, Khargone), Dardhi Falls, Manadhata Falls, etc.
• Mahi River
• It rises in Madhya Pradesh and, after flowing through the Vagad region of Rajasthan, enters Gujarat and flows into the Arabian Sea.
• It is one of Five west-flowing rivers in India, along with Tapti River, Sabarmati River, Luni River (Endorheic river) and the Narmada River.
• Tributaries- Som, Anas, and Panam.

The correct answer is Gokulam Kerala.

Key Points

• Gokulam Kerala won the I-League title as it defeated TRAU 4-1 in the final match of the season in Kolkata.
• Gokulam as an I-League champion has qualified for the group stage of the AFC Cup next season, Asia's second-tier club competition.
• They also became the first club from the Kerala side to win the I-League title.

Additional Information Hero I-League:

• it was founded in the year 1996 as National Football League.
• The league was established in the year 2007 as I-League.
• It is organized by the All India Football Federation (AIFF).
• A total of 13 teams participates in the tournament.

The correct answer is National Commission for Protection of Child Rights.

Key Points

• E-Baal Nidan is an online complaint mechanism launched in 2015 to enable individuals to report violations committed against a child and track them.
• It was revamped in September 2022.

Additional Information

• The National Commission for Protection of Child Rights (NCPCR) was set up in March 2007 under the Commissions for Protection of Child Rights (CPCR) Act, 2005, an Act of Parliament (December 2005).
• The National Commission for Protection of Child Rights (NCPCR) is a statutory body under the Commissions for Protection of Child Rights (CPCR) Act, 2005 under the administrative control of the Ministry of Women & Child Development, Government of India.
• The Commission's Mandate is to ensure that all Laws, Policies, Programmes, and Administrative Mechanisms are in consonance with the Child Rights perspective as enshrined in the Constitution of India and also the UN Convention on the Rights of the Child.
• The Child is defined as a person in the 0 to 18 years age group.
• The National Commission for Protection of Child Rights (NCPCR) works at State, Central and Local bodies.
• Independent monitoring of the implementation of the Act is assigned to the National Council of Protection of Child Rights (NCPCR), the main responsibilities are:
• examine and review safeguards for rights under this Act, and recommend measures for effective implementation
• inquire into complaints relating to child’s right to free and compulsory education
• conduct periodic social audits of the status of implementation and review
• Hence, the National Commission for Protection of Child Rights (NCPCR) works at ​State, Central and Local bodies.

The correct answer is Homi J. Bhabha.

Key Points

• Homi Jehangir Bhabha is called as father of Indian nuclear program.
• He is also called as Architect of the nuclear Age and Architect of the atomic bomb.
• He was founding director of Atomic energy establishment, Trombay (AEET) which is now named the Bhabha atomic research centre in his honor.
• He was the founding chairman of Atomic Energy Commission (AEC), which was established in 1948.
• He was awarded the Adam prize and Padma Bhushan.
• He was also nominated for Noble prize for physics in 1951 and 1953-56.

Additional Information

• Vikram Sarabhai initiated space research and helped to develop nuclear power in India.
• He is internationally regarded as father of Indian space program.
• He was the founder of Indian Space Research Organization(ISRO).
• APJ Abdul Kalam was an Indian aerospace scientist and known as Missile Man of India.
• He was intimately involved in civil space program and military missile development efforts.
• U.R.Rao was an Indian space scientist and former chairman of ISRO.
• He is known as The Satellite Man of India.
• C.V. Raman discovered the Raman effect, which occurs when light scatters and changes wavelength as it passes through a material. This phenomenon is now known as Raman scattering.
• Venkatraman Radhakrishnan was a physicist and radio astronomer who contributed to many areas of study, including the magnetic field of Jupiter, the rotation of Jupiter's interior, and pulsar astronomy.

Calculation:

Total number of people = 8 + 2 + 1 + 6 + 10 + 8 + 12 + 3 = 50

Total number of people who like black colour = 10

Now, the required % = $\frac {10}{50} \times 100\%$ = 20%

∴ 20% of the total number of people like black colour.

Given:

In ΔSTU, X and Y are the points on sides ST and SU respectively.

XY is parallel to TU. If SX ∶ XT = 2 ∶ 5 and UY = 20 cm

Concept used:

Thales' Theorem states if a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio.

Calculation:

According to the concept,

SX ∶ XT = 2 ∶ 5

⇒ SY : YU = 2 : 5

So, SY = $\frac {20}{5} \times 2$ = 8 cm

Now, the length of SU

⇒ SY + YU

⇒ 20 + 8

⇒ 28 cm

∴ The value of SU is 28 cm.

Calculation:

Rohit and Raju scored 15% and 20% of the total marks respectively.

Now, the required % = $\frac {20 - 15}{20} \times 100\%$ = 25%

∴ The marks of Rohit is 25% less than that of Raju.

Given:

Circumference of the base of the cone = 88 cm

Height of the cone = 28 cm

Formula:

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

Solution:

Let's first find the radius of the base of the cone.

Circumference of the base of the cone = 2πr, where r is the radius

88 = 2πr

r = 88/2π = 14 cm

Now, we can use the Pythagorean theorem to find the slant height of the cone.

The slant height (ℓ) of the cone is given by:

ℓ² = r² + h²

ℓ² = 14² + 28²

ℓ² = 980

ℓ = √980 = 14√5 cm

Now, we can use the formula for the curved surface area of a cone:

The curved surface area of the cone = πrℓ

= 22\7 × (14)(14√5)

= 616√5 

Therefore, the curved surface area of the cone is 616√5 cm².

Shortcut Trick When two circles of equal radius (r) pass through each other's centre, the length of their common chord is given directly by the formula √3r. Given, radius (r) = 6 cm. Length of common chord = 6√3 cm. ∴ The correct answer is 6√3 cm.

Alternate Method

A B P Q M

6 cm 6 cm 3 3

Length of Common Chord PQ

Given: Radius of both circles = r = 6 cm The circles pass through each other's centre, implying the distance between their centres is exactly equal to their radius. Distance between centres (AB) = 6 cm Concept Used: The line joining the centres of two intersecting circles acts as a perpendicular bisector to their common chord. Calculation: ⇒ Let the centres of the two circles be A and B, and their intersection points be P and Q. ⇒ The distance AP = BP = r = 6 cm. ⇒ The distance AB = r = 6 cm. ⇒ Thus, ΔAPB is an equilateral triangle with a side length of 6 cm. ⇒ Let M be the point of intersection of the common chord PQ and the line AB. ⇒ Since PQ is perpendicularly bisected by AB, AM = AB ÷ 2 = 6 ÷ 2 = 3 cm. ⇒ In right-angled triangle ΔAMP, using the Pythagoras theorem: ⇒ AP2 = AM2 + PM2 ⇒ 62 = 32 + PM2 ⇒ 36 = 9 + PM2 ⇒ PM2 = 36 − 9 = 27 ⇒ PM = √27 = 3√3 cm ⇒ The common chord PQ is exactly twice the length of PM. ⇒ PQ = 2 × PM = 2 × 3√3 = 6√3 cm ∴ The correct answer is 6√3 cm.

Additional Information Properties of Common Chord The common chord of two intersecting circles is perpendicularly bisected by the straight line joining their centres. The maximum length of a common chord equals the diameter of the smaller circle. Distance Between Centres of Intersecting Circles If two circles with radii r1 and r2 intersect at two distinct points, the distance 'd' between their centres will always satisfy the strict inequality: |r1 − r2| < d < r1 + r2. Number of Common Tangents When two circles intersect each other at exactly two distinct points, exactly 2 direct common tangents can be drawn touching both circles, and no transverse common tangents exist.

Given:

Number of pens bought = 80

Cost price of each pen = Rs. 80

Number of pens sold at a loss = 40

Loss percentage = 20%

Profit percentage on all pens = 20%

Formula:

Selling price (S.P.) = Cost price (C.P.) × (100% + Profit %)/100

Selling price (S.P.) = Cost price (C.P.) × (100% - Loss %)/100

Profit/Loss = Selling Price (S.P.) - Cost Price (C.P.)

Solution:

Cost price of 80 pens = 80 × 80 = Rs. 6400

Cost price of 40 pens = 40 × 80 = Rs. 3200

Selling price of 40 pens sold at a loss of 20%:

S.P. = C.P. × (100% - Loss%)/100

S.P. = 3200 × (100% - 20%)/100

S.P. = 3200 × 0.8 = 2560

Selling price of all 80 pens at a profit of 20%:

S.P. = C.P. × (100% + Profit %)/100

S.P. = 6400 × (100% + 20%)/100

S.P. = 6400 × 1.2 = Rs. 7680

SP of the remaining 40 pens = 7680 - 2560 = Rs. 5120

Profit = SP - CP

Profit = 5120 - 3200

Profit = 1920

Profit% = Profit/CP × 100

⇒ 1920/3200 × 100

⇒ 60%

The profit percentage on the remaining 40 pens is 60%.

Calculation:

Let us assume that the total work to be done is 100 units.

Given that P and Q together can complete the work in 20 days.

Hence, in 1 day, P and Q can complete 100/20 = 5 units of work.

Let the efficiency of P be x units/day.

Therefore, the efficiency of Q will be (5-x) units/day.

Given that Q alone can complete the work in 25 days.

Hence, the efficiency of Q is (100/25) = 4 units/day.

Therefore, (5-x) = 4

x = 1

Hence, the efficiency of P is 1 unit/day.

Therefore, P alone can complete the work in 100/1 = 100 days.

Therefore, P alone can complete the work in 100 days.

Calculation:

Checking Statement I:

The sales of bikes of company L and M together = 500 + 450 = 950

The sales of cars of company P and Q together = 900 + 800 = 1700

Now, % = $\frac {950}{1700} \times 100\%$ ≈ 55.88%

Hence, the sales of bikes of company L and M together is NOT 45.88% of the sales of cars of company P and Q together.

Checking Statement II:

Total sales of bikes = 500 + 450 + 650 + 700 + 800 = 3100

Total sales of cars = 1000 + 550 + 750 + 900 + 800 = 4000

Now, % = $\frac {3100}{4000} \times 100\%$ = 77.5%

Hence, the total sales of bikes is 77.5% of the total sales of cars

∴ Only II is correct.

Given:

The circumference of a circle is 88 cm.

Chord XY makes an angle of 90 degrees at the circumference of this circle.

Concept used:

1. Only the diameter of a circle subtends an angle of 90° at the circumference of the circle. 2. The diameter is the largest chord of a circle.
2. Circumference of the circle = 2πR (R = Radius and π = 22/7)
3. Diameter = Radius × 2

Calculation:

Let the radius of the circle be R cm.

According to the concept,

2πR = 88

⇒ 2 × 22/7 × R = 88

⇒ R = 7 × 2

⇒ R = 14

So, Diameter = 14 × 2 = 28 cm

According to the question,

XY chord subtends an angle of 90° at the circumference of this circle.

But according to the concept, only the diameter of a circle subtends an angle of 90° at the circumference of the circle.

Hence, XY has to be the diameter of the circle.

Now, XY = Diameter of the circle = 28 cm

∴ The length of XY is 28 cm.

Shortcut Trick

Each pair of terms (1 − 2), (3 − 4), (5 − 6) results in −1.

Total number of terms = 100.

Total number of pairs = 100 ÷ 2 = 50 pairs.

Value of expression = 50 × (−1) = −50.

∴ The correct answer is -50.

Alternate Method

Given: 1 − 2 + 3 − 4 + 5 − 6 ..... to 100 terms.

Formula Used: Sum of Arithmetic Progression (AP) = (n÷2)[2a + (n−1)d]

Calculations:

Separate the positive and negative terms into two series:

⇒ Sum = (1 + 3 + 5 + ... to 50 terms) − (2 + 4 + 6 + ... to 50 terms)

⇒ Positive series: n = 50, a = 1, d = 2

⇒ Sum_pos = (50÷2)[2(1) + (50−1)2] = 25[2 + 98] = 25 × 100 = 2500

⇒ Negative series: n = 50, a = 2, d = 2

⇒ Sum_neg = (50÷2)[2(2) + (50−1)2] = 25[4 + 98] = 25 × 102 = 2550

⇒ Total Sum = 2500 − 2550 = −50

∴ The correct answer is -50.

Additional Information

Sum of First n Odd Numbers

The sum of the first n odd natural numbers is always given by the formula n².

Sum of First n Even Numbers

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

Alternating Sum of first n terms

For an alternating series 1 − 2 + 3 − 4 ..., if n is even, the sum is −n/2. If n is odd, the sum is (n+1)/2.

Given:

$\rm \frac{\frac{1}{1}\div \frac{1}{2}\times \frac{1}{2}+\frac{1}{2}\times \frac{1}{2}\div\frac{1}{2}}{\frac{1}{4}\times\frac{1}{4}\div\frac{1}{2}+\frac{1}{4}\div \frac{1}{4}\times \frac{1}{2}-\frac{1}{4}\div \frac{1}{2}\times \frac{1}{2}}$

Concept used:

Calculation:

According to the concept,

$\rm \frac{\frac{1}{1}\div \frac{1}{2}\times \frac{1}{2}+\frac{1}{2}\times \frac{1}{2}\div\frac{1}{2}}{\frac{1}{4}\times\frac{1}{4}\div\frac{1}{2}+\frac{1}{4}\div \frac{1}{4}\times \frac{1}{2}-\frac{1}{4}\div \frac{1}{2}\times \frac{1}{2}}$

⇒ $\rm \frac{1 \times \frac{2}{1}\times \frac{1}{2}+\frac{1}{2}\times \frac{1}{2}\times\frac{2}{1}}{\frac{1}{4}\times\frac{1}{4}\times\frac{2}{1}+\frac{1}{4}\times\frac{4}{1}\times \frac{1}{2}-\frac{1}{4}\times\frac{2}{1}\times \frac{1}{2}}$

⇒ $\rm \frac{1 +\frac{1}{2}}{\frac{1}{8}+ \frac{1}{2}-\frac{1}{4}}$

⇒ $\rm \frac{\frac{3}{2}}{\frac{3}{8}}$

⇒ $\frac {3 \times 8}{3 \times 2}$

⇒ 4

∴ The simplified value is 4.

Given:

The angle subtended by a chord on the major arc of a circle is 55 degrees.

Concept used:

The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

Calculation:

Let O, R, and PQ be the centre, a point on the major arc, and the aforementioned chord respectively.

So, the major arc for the PQ chord is PRQ.

Hence, ∠PRQ = 55°

Here, ∠POQ is the angle subtended by the same chord, PQ on the centre of the circle.

According to the concept,

∠POQ = 2 × ∠PRQ

⇒ ∠POQ = 2 × 55°

⇒ ∠POQ = 110°

∴ The angle subtended by the same chord on the centre of the circle is 110°.

Given:

20% of A's income = 10% of B's income

A's income = Rs. 2550

Let B's income be x.

Formula:

To find the percentage, we can use the formula:

Part/Whole = Percentage/100

Solution:

According to the given information, we can write the equation:

(20/100) × 2550 = (10/100) × x

Simplifying this equation, we get:

(2/10) × 2550 = (1/10) × x

Multiplying both sides by 10, we get:

5100 = x

Therefore, B's income is Rs. 5100.

Given:

$\rm \frac{\tan A-\sin A}{\tan A+\sin A}$

Concept used:

1. tanα = sinα/cosα
2. secα = 1/cosα

Calculation:

According to the concept,

$\rm \frac{\tan A-\sin A}{\tan A+\sin A}$

⇒ $\rm \frac{\frac {\sin A}{\cos A}-\sin A}{\frac {\sin A}{\cos A}+\sin A}$

⇒ $\rm \frac{\frac {1}{\cos A}-1}{\frac {1}{\cos A}+1}$ (Cancelling sin A from both numerator and denominator)

⇒ $\rm\frac{\sec A-1}{\sec A+1}$

∴ The value of $\rm \frac{\tan A-\sin A}{\tan A+\sin A}$ is $\rm\frac{\sec A-1}{\sec A+1}$.

Given:

The cost price of the ball is Rs. 700.

Two successive discounts of 20% and 40% are given.

Formula:

To calculate the selling price after applying successive discounts, we can use the formula:

Selling price = Cost price × (1 - d1/100) × (1 - d2/100)

where d1 and d2 are the percentages of the first and second discounts, respectively.

Solution:

Here, d1 = 20 and d2 = 40, as discounts of 20% and 40% are given successively.

Substituting the values in the formula, we get:

Selling price = 700 × (1 - 20/100) × (1 - 40/100)

Selling price = 700 × 0.8 × 0.6

Selling price = Rs. 336

Therefore, the selling price of the ball after applying the two successive discounts is Rs. 336.

Given:

The average age of 120 members of a society is 62.5 years.

30 new members are added to the society.

The average age of all the members becomes 58.2 years.

Formula:

To find the average, we can use the formula:

Average = (Sum of all values) / (Total number of values)

Solution:

Let the average age of the 30 new members be x.

According to the given information, we can write the following equations:

The average age of 120 members = 62.5

Total number of members after addition = 120 + 30 = 150

The average age of all 150 members = 58.2

Using equations (1) and (3), we can write:

(120 × 62.5 + 30x)/150 = 58.2

Simplifying this equation, we get:

7500 + 30x = 8730

30x = 1230

x = 41

Therefore, the average age of the newly joined members is 41 years.

Alternate Method 

Calculate the total sum of ages before and after the new members arrived:

Total sum before = 120 × 62.5 = 7500 years

Total sum after = 150 × 58.2 = 8730 years

Total age of new members = Total sum after - Total sum before = 8730 - 7500 = 1230 years

The average age of new members = Total age of new members / Number of new members = 1230 / 30 = 41 years.

So, the average age of the newly joined members is 41 years.

**Shortcut TrickWe can solved this from given ratio:**Income   =   Expenditure +  Saving

     9         =         5           :         4

Then, 

Rahul's Income        9   →  36,000 ( given income)

Rahul's Expenditure  5  →   20,000 

∴ Rahul's Expenditure is Rs. 20,000

 

Given:

The ratio of Rahul's expenditure and savings is 5: 4.

Rahul's income is Rs. 36000.

Solution:

Let the expenditure and savings of Rahul be 5x and 4x, respectively, where x is a common factor.

We know that the sum of the parts in a ratio is equal to the total number of parts. Therefore, the total parts in the ratio 5:4 are 5+4=9.

So, 5x is the part that represents the expenditure and 4x is the part that represents the savings.

We are given that Rahul's income is Rs. 36000. Therefore, we can write:

5x + 4x = 9x = 36000

Solving for x, we get:

x = 36000/9 = 4000

Hence, Rahul's expenditure is 5x = 5 × 4000 = Rs. 20,000.

Given:

$\rm \cos B=\frac{5}{9}$

Concept used:

1. cosecα = 1/sinα 2. $\sin^2\alpha + \cos^2\alpha = 1$

Calculation:

According to the concept,

$\rm \cos B=\frac{5}{9}$

⇒ $\rm \cos^2 B=(\frac{5}{9})^2$

⇒ $\rm \cos^2 B=\frac{25}{81}$

⇒ $\rm (1 - \cos^2 B)=(1 - \frac{25}{81})$

⇒ $\rm \sin^2 B=\frac{56}{81}$

⇒ $\rm cosec^2 B=\frac{81}{56}$

⇒ $\rm cosec B=\sqrt {\frac{81}{4 \times 14}}$

⇒ $\rm cosec B={\frac{9}{2 \sqrt {14}}}$

∴ The value of cosec B is ${\frac{9}{2 \sqrt {14}}}$.

Shortcut Trick

Total simple interest percentage for 3 years = 3 × 10% = 30%.

The total Amount becomes 100% (Principal) + 30% (Interest) = 130%.

Given 130% of Principal = Rs. 403

Principal (100%) = (403 ÷ 130) × 100 = 31 × 10 = 310

∴ The correct answer is Rs. 310.

Alternate Method

Given:

Amount (A) = Rs. 403

Time (T) = 3 years

Rate (R) = 10% per annum

Year 0 Year 1 Year 2 Year 3

+10%

+10%

+10%

P = ?

A = 403

Total Interest = 3 × 10% = 30%

Formula Used:

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

Amount (A) = P + SI = P × (1 + (R × T) ÷ 100)

Calculations:

⇒ Let the principal sum be P.

⇒ 403 = P × (1 + (10 × 3) ÷ 100)

⇒ 403 = P × (1 + 30 ÷ 100)

⇒ 403 = P × (1 + 0.3)

⇒ 403 = 1.3 × P

⇒ P = 403 ÷ 1.3

⇒ P = 4030 ÷ 13

⇒ P = Rs. 310

∴ The correct answer is Rs. 310.

Additional Information

Principal from Amount Rule

When only the final amount (A) is given in simple interest, the principal (P) can be found directly using: P = (A × 100) ÷ (100 + R × T).

Simple vs Compound Interest

Simple interest is calculated only on the original principal, whereas compound interest is calculated on both the initial principal and the accumulated interest from previous periods.

Effective Rate Concept

For simple interest, the effective rate for multiple years is simply the product of Rate and Time (Effective Rate = R × T %). This allows direct percentage-based calculations without using the standard long formulas.

Given:

$\rm x^4+\frac{1}{x^4}=47$

Concept used:

1. (a + b)² - 2ab = a² + b²
2. (a + b)³ = a³ + b³ + 3ab(a + b)

Calculation:

According to the concept,

$\rm x^4+\frac{1}{x^4}=47$

⇒ $\rm (x^2+\frac{1}{x^2})^2 - 2 × x^2 × \frac{1}{x^2}=47$

⇒ $\rm (x^2+\frac{1}{x^2})^2 - 2 =47$

⇒ $\rm (x^2+\frac{1}{x^2})^2 = 47 + 2$

⇒ $\rm (x^2+\frac{1}{x^2})^2 = 49$

⇒ $\rm (x^2+\frac{1}{x^2}) = 7$

⇒ $\rm (x +\frac{1}{x})^2 - 2 × x × \frac{1}{x} = 7$

⇒ $\rm (x +\frac{1}{x})^2 - 2 = 7$

⇒ $\rm (x +\frac{1}{x})^2 = 7 + 2$

⇒ $\rm (x +\frac{1}{x})^2 = 9$

⇒ $\rm (x +\frac{1}{x}) = 3$      ....(1)

⇒ $\rm (x +\frac{1}{x})^3 = 3^3$

⇒ $\rm x^3 +\frac{1}{x^3} + 3x × \frac {1}{x} (x + \frac {1}{x}) = 3^3$

⇒ $\rm x^3 +\frac{1}{x^3} + 3 × 3 = 3^3$ (From 1)

⇒ $\rm x^3 +\frac{1}{x^3} = 27 - 9$

⇒ $\rm x^3 +\frac{1}{x^3} = 18$

∴ The value of $\rm x^3+\frac{1}{x^3}$ is 18.

Shortcut TrickIfx4 + 1/x4 = P, then x² + 1/x² = √(P + 2) = Q

And x + 1/x = √(Q + 2) = S

x³ + 1/x³ = S³ - 3S 

Now, x⁴ + 1/x⁴ = 47

x2 + 1/x2 = √(47 + 2) = √49 = 7

x + 1/x = √(7 + 2) = √9 = 3

x3 + 1/x3 = 33 - 3 × 3 

⇒ 27 - 9 = 18

∴ x3 + 1/x3 is 18.

Given: 

The average weight of 20 persons = 60 kg

The average weight of 21 persons = 59 kg

Formula:

Average = (Sum of observations) / (Number of observations)

Solution:

Let the weight of the new person be x kg.

According to the given information, we can write the following equations:

(Sum of weights of 20 persons) / 20 = 60

(Sum of weights of 21 persons) / 21 = 59

We can simplify the second equation as:

[(Sum of weights of 20 persons) + x]/21 = 59

Multiplying both sides by 21, we get:

(Sum of weights of 20 persons) + x = 21 × 59

(Sum of weights of 20 persons) + x = 1239

Substituting the value of the sum of weights of 20 persons from the first equation, we get:

20 × 60 + x = 1239

x = 1239 - 1200

x = 39

Therefore, the weight of the new person is 39 kg.

Given:

√(1 - sin A)/√(1 + sin A) 

Concept used:

1. sin² α + cos² α = 1
2. (a + b) (a - b) = (a² - b²)
3. sec α = 1/cos α
4. tan α = sin α/cos α

Calculation:

According to the concept,

√(1 - sin A)/√(1 + sin A) 

⇒ $\sqrt {\frac {1 - \sin A}{1 + \sin A}}$

⇒ $\sqrt {\frac {(1 - \sin A)^2}{(1 + \sin A) \times (1 - \sin A)}}$

⇒ $\sqrt {\frac {(1 - \sin A)^2}{ (1 - \sin^2A)}}$

⇒ $\sqrt {\frac {(1 - \sin A)^2}{\cos^2A}}$

⇒ ${\frac {(1 - \sin A)}{\cos A}}$

⇒ $(\frac {1}{\cos A} - \frac {\sin A}{\cos A})$

⇒ sec A - tan A

∴ The simplified value of $\sqrt {\frac {1 - \sin A}{1 + \sin A}}$ is sec A - tan A.

Given:

$\rm K+\frac{1}{K}-2=0$ and K > 0

Concept used:

$(a^2 + 2ab + b^2) = (a + b)^2$

Calculation:

$(\rm K+\frac{1}{K})=2$

⇒ $k^2 - 2k + 1 = 0$

⇒ (k - 1)² = 0

⇒ (k - 1) = 0

⇒ k = 1

Now,  $\rm K^{17}+\frac{1}{K^{12}}?$

⇒ $\rm (1)^{17}+\frac{1}{(1)^{12}}?$

⇒ 1 + 1

⇒ 2

∴ Option 1 is the correct answer.