SSC CGL 2024 Tier-I Official Paper (Held On: 17 Sept, 2024 Shift 2) (Previous Year Paper)

The logic followed here is:

Triangle is added by 1 outside of inner square .

• is increased by 1 inside surface of square.

Hence, the correct answer is "Option 4".

The logic followed here is:

Logic: (1^st number × 5) + 21 = 2^nd number.

Now,

For, 34 : 191

⇒ (34 × 5) + 21 = 170 + 21 = 191.

For, 56 : 301

⇒ (56 × 5) + 21 = 280 + 21 = 301.

Similarly, for 63 ∶ ?

⇒ (63 × 5) + 21 = 315 + 21 = 336.

Hence, the correct answer is "Option 3".

Family Chart:

Decoding the Symbols:

 

Given: 5 ÷ 1 × 3 ÷ 4 − 2

It means: 5 is the father of 1, 1 is the wife of 3, 3 is the father of 4 and 4 is the brother of 2.

So, 5 is the "Mother's father" of 2.

Hence, the correct answer is "Mother's father".

The logic followed here is:

Logic: (1^st number × 4) + 11 = 2^nd number.

Now,

For, 27 : 119

⇒ (27 × 4) + 11 = 108 + 11 = 119.

For, 33 : 143

⇒ (33 × 4) + 11 = 132 + 11 = 143.

Similarly, for 42 ∶ ?

⇒ (42 × 4) + 11 = 168 + 11 = 179.

Hence, the correct answer is "Option 3".

The logic followed here is: 1^st letter + 4 = 2^nd letter; 2^nd letter - 2 = 3^rd letter;

Option 1) HLJ

Option 2) GIK

Option 3) LPN

Option 4) BFD

Hence, the correct answer is "GIK".

BODMAS Table: 

After decoding signs:

 

Given equation: 63 × 9 + 21 – 4 ÷ 5 = ?

After interchanging the signs then:

⇒ 63 ÷ 9 - 21 + 4 × 5 = ?

⇒ ? = 7 - 21 + 4 × 5

⇒ ? = 7 - 21 + 20

⇒ ? = 27 - 21 = 6

Hence, the correct answer is "6".

The logic followed here is:

Line with letter shifts in clockwise and new line with letter is added on the previous position of existing shape.

Hence, the correct answer is "Option 4".

The logic followed here is:

Hence, the correct answer is "1264".

Statements:

All computers are printers.

Some printers are laptops.

All laptops are mobiles.

The least possible Venn diagram:

Conclusions:

I. Some printers are computers. - True (because All computers are printers so, Some printers are computers too)

II. Some laptops are printers. - True (because Some printers are laptops so, Some laptops are printers too)

III. Some mobiles are laptops. - True (because All laptops are mobiles so, Some mobiles are laptops too)

Hence, the correct answer is "All the conclusions follow".

The logic followed here is:

'ACKO' is related to 'ZXPL'

'HIND' is related to 'SRMW'

Similarly, 'PUKE' is related to:

Hence, the correct answer is "KFPV".

According to the given information:

So, 'achieve' will be written as "Te".

Hence, the correct answer is "Te".

The logic followed here is:

Logic: Opposites

Here,

Noise is the opposite of Silence.

Similarly,

Light is the opposite of Darkness.

Hence, the correct answer is "Option 4".

The logic followed here is:

Hence, the correct answer is "IOFW".

BODMAS Table: 

Given equation: 31 ÷ 3 – 186 × 6 + 17 = ?

Now, if ‘+’ and ‘–‘ and ‘×’ and ‘÷’ are interchanged, then:

⇒ 31 × 3 + 186 ÷ 6 – 17 = ?

⇒ 31 × 3 + 186 ÷ 6 – 17 = ?

⇒ 93 + 186 ÷ 6 – 17 = ?

⇒ 93 + 31 – 17 = ?

⇒ 124 – 17 = ?

⇒ 107.

Hence, the correct answer is "Option 4".

Statements:

Some telephones are curtains.

All curtains are lamps.

No lamps is books.

The least possible Venn diagram:

Conclusions:

(I) All lamps are telephones. - False (because Some telephones are curtains and All curtains are lamps. So, All lamps are telephones it is not possible)

(II) No books is lamps. - True (because No lamps is books given. So, No books is lamps it is true)

Hence, the correct answer is "Only conclusion (II) is follow".

Counting of squares:

Thus, squares are there in the given figure = 20

Hence, the correct answer is "20".

The logic followed here is: Numbers ration is 5 : 6.

Option 1) 40 : 52 → This pair will not come in 5 : 6 ratio.

Option 2) 45 : 54 → 45 / 9 : 54 / 9 → 5 : 6

Option 3) 35 : 42 → 35 / 7 : 42 / 7 → 5 : 6

Option 4) 55 : 66 → 55 / 11 : 66 / 11 → 5 : 6

Hence, the correct answer is "40 : 52".

The paper look when unfolded:

Hence, the correct answer is "Option 4".

The logic followed here is:

So, the code for 'N' = '3'.

Hence, the correct answer is "3".

The logic followed here is:

Given word: 'LASTING'

Each of the letters in the word 'LASTING' is arranged in the English alphabetical order.

LASTING → AGILNTS

The letter which is second from the left end = G

The one which is fourth from the right end = L

Thus, Four letters (G, H, I, J, K, L) are there in the English alphabetical series between the letter which is second from the left end and the one which is fourth from the right end in the new letter-cluster thus formed.

Hence, the correct answer is "Four".

Sheet will appear when the transparent sheet is folded at the middle horizontal line:

Hence, the correct answer is "Option 3".

The given figure (X) is embedded:

Hence, the correct answer is "Option 3".

The logic followed here is:

Given Sequence: M N _ O J K M _ Q O J K _ N Q _ J K M N Q O _ K M N

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

Option 1) QMNJO → M N Q O J K / M M Q O J K / N N Q J J K / M N Q O O K M N

Option 2) QNJMO → M N Q O J K / M N Q O J K / J N Q M J K / M N Q O O K M N

Option 3) QNMJO → M N Q O J K / M N Q O J K / M N Q J J K / M N Q O O K M N

Option 4) QNMOJ → M N Q O J K / M N Q O J K / M N Q O J K / M N Q O J K M N

Here, 'M N Q O J K M N' this pattern is followed.

Hence, the correct answer is "QNMOJ".

The logic followed here is:

Logic: (1^st number)² + 15 = 2^nd number.

Now,

For, 8 : 79

⇒ (8²) + 15 = 64 + 15 = 79.

For, 6 : 51

⇒ (6²) + 15 = 36 + 15 = 51.

Similarly, for 9 : ?

⇒ (9²) + 15 = 81 + 15 = 96.

Hence, the correct answer is "Option 1".

The given figure (X) is embedded:

Hence, the correct answer is "Option 3".

The correct answer is Nepal.

Key Points

• Nepal is the country with the highest Hindu population after India.
• Approximately 81.3% of Nepal's population adheres to Hinduism.
• Nepal is the only Hindu countries in the world.
• Hinduism is deeply integrated into Nepalese culture, with numerous festivals, temples, and traditions rooted in the religion.

Additional Information

• Hindu Population
• India: India has the largest Hindu population in the world, with over 79.8% of its population adhering to Hinduism, which translates to around 1.2 billion people.
• Nepal: As mentioned, Nepal has the highest Hindu population after India. The majority religion in Nepal is Hinduism.
• Bangladesh: Bangladesh has a significant Hindu minority, making up about 8-10% of the population, which translates to approximately 12-15 million people.
• Indonesia: Indonesia, primarily a Muslim-majority country, has a Hindu minority, primarily in Bali, constituting about 1.7% of its population.
• Hinduism
• Hinduism is one of the oldest religions in the world, with its origins tracing back more than 4,000 years.
• It is a complex faith characterized by a variety of beliefs, practices, and rituals.
• Key concepts in Hinduism include Dharma (duty/ethics), Karma (action and subsequent reaction), and Moksha (liberation from the cycle of rebirth).
• Hinduism is polytheistic, with a vast array of gods and goddesses, the most prominent being Brahma, Vishnu, and Shiva.

The correct answer is 1, 2 and 3 are correct.

Key Points

• The National Mission for Sustainable Agriculture (NMSA) aims to make agriculture more productive, sustainable, remunerative, and climate-resilient by promoting location-specific integrated/composite farming systems.
• It also focuses on improving soil health and water use efficiency, as well as enhancing seed quality and promoting the use of organic farming practices.
• The NMSA is designed to cover both rainfed and irrigated areas to ensure comprehensive coverage of all agricultural zones.
• It supports the adoption of sustainable agricultural practices that help in conserving natural resources while maintaining agricultural productivity.

Additional Information

• Soil Health Management (SHM)
• SHM is one of the major components of the NMSA. It aims to promote Integrated Nutrient Management (INM) through judicious use of chemical fertilizers, including secondary and micronutrients, in conjunction with organic manure and bio-fertilizers.
• The objective is to improve soil health and its productivity, thus supporting sustainable agriculture.
• Rainfed Area Development (RAD)
• RAD focuses on Integrated Farming Systems (IFS) for enhancing productivity and minimizing risks associated with climatic variability.
• It includes crop diversification, horticulture, livestock, fishery, and agroforestry to make agriculture more resilient to climate change.
• Climate Change and Sustainable Agriculture: Monitoring, Modeling and Networking (CCSAMMN)
• This initiative aims to build and strengthen the capacity of farmers and other stakeholders in addressing climate change impacts on agriculture.
• It involves the development of climate-resilient agricultural practices and technologies, and promoting their adoption.
• Organic Farming
• The NMSA promotes organic farming through the Paramparagat Krishi Vikas Yojana (PKVY). PKVY aims to support and encourage farmers to adopt organic farming practices and certifications.
• It also focuses on marketing organic produce to ensure better returns to farmers.

The correct answer is Deepa Malik.

Key Points

• Deepa Malik is a renowned Indian athlete who has won numerous accolades in para-athletics.
• She is the first Indian woman to win a medal in the Paralympic Games.
• She has been honored with the Padma Shri and Arjuna Award for her contributions to sports.
• As a brand ambassador for the Nikshay Mitra initiative, she plays a crucial role in promoting the eradication of tuberculosis in India.

Additional Information

• Pradhan Mantri TB Mukt Bharat Abhiyan
• The Pradhan Mantri TB Mukt Bharat Abhiyan is a significant initiative by the Ministry of Health and Family Welfare, Government of India, aimed at eliminating tuberculosis (TB) from the country by 2025.
• The campaign emphasizes the need for community involvement, awareness, and support to combat TB effectively.
• The Nikshay Mitra initiative is part of this larger campaign, where individuals, institutions, and corporate entities can adopt TB patients and ensure they receive the necessary nutrition, medical care, and support for complete recovery.
• The initiative aims to provide a holistic approach to TB treatment, focusing not just on medical interventions but also on the social and nutritional needs of patients.
• Mary Kom
• Mary Kom is an Indian Olympic boxer and a multiple-time World Amateur Boxing champion.
• She has received the Padma Bhushan, Padma Shri, and Arjuna Award for her contributions to boxing.
• Though she is an iconic sports figure, she is not the brand ambassador for the Nikshay Mitra initiative.
• Abhinav Bindra
• Abhinav Bindra is an Indian shooter and the first Indian to win an individual gold medal at the Olympic Games.
• He has been awarded the Padma Bhushan, Padma Shri, and Arjuna Award.
• Bindra has significantly contributed to Indian sports but is not associated with the Nikshay Mitra initiative.
• Pullela Gopichand
• Pullela Gopichand is a former Indian badminton player and the chief national coach for the Indian Badminton team.
• He has been awarded the Padma Bhushan, Padma Shri, and Dronacharya Award.
• Gopichand is known for his coaching prowess but is not the brand ambassador for the Nikshay Mitra initiative.

The correct answer is Depreciation.

Key Points

• Depreciation refers to the reduction in the value of assets over time due to wear and tear, obsolescence, or other factors.
• In national accounting, GDP (Gross Domestic Product) measures the total economic output of a country.
• NDP (Net Domestic Product) is derived by subtracting the depreciation of the country's capital assets from its GDP.
• This adjustment is necessary to account for the loss in value of fixed capital and provides a more accurate measure of economic performance.

Additional Information

• Gross Domestic Product (GDP)
• GDP is the total market value of all final goods and services produced within a country's borders in a given time period.
• It is used to gauge the economic performance of a country and make international comparisons.
• GDP can be calculated using three approaches: the production (or output or value added) approach, the income approach, and the expenditure approach.
• Net Domestic Product (NDP)
• NDP is calculated by subtracting depreciation from GDP.
• Depreciation, also known as the consumption of fixed capital, reflects the wear and tear or obsolescence of physical assets.
• NDP provides a clearer picture of the actual economic performance by accounting for the decrease in value of capital goods.
• Subsidies
• Subsidies are financial assistance provided by the government to individuals, businesses, or other entities to promote economic and social policy objectives.
• They can take various forms, including direct cash transfers, tax breaks, or price controls.
• Net Indirect Taxes
• Net Indirect Taxes are calculated as indirect taxes (like sales tax, VAT) minus subsidies.
• They are part of the factor cost adjustment to reach market prices in national accounting.
• Net Factor Income from Abroad
• Net Factor Income from Abroad is the difference between the income residents receive from abroad for factor services (like labor and capital) and the income paid to foreign residents for their factor services within the domestic economy.
• This measure is used to calculate Gross National Product (GNP) from GDP.

The correct answer is Sattriya.

Key Points

• Sattriya is one of the eight major Indian classical dance forms.
• It originated in the 15^th century Assam, attributed to the Vaishnavite saint Sankaradeva.
• This dance form was initially performed in monasteries (Sattras) as a part of the Ankiya Naat (a form of Assamese one-a14ct plays).
• Sattriya was recognized as a classical dance by the Sangeet Natak Akademi in 2000.

Additional Information

• Sattriya Dance
• Sattriya is a combination of music, dance, and drama.
• The dance was traditionally performed by male monks, known as Bhakats, within the confines of the monasteries.
• It includes both nritta (pure dance) and nritya (expressive dance) forms.
• The themes of Sattriya dances are mostly based on the mythological stories of Krishna and Vishnu.
• The costumes used in Sattriya are usually made of white or off-white silk with embroidered patterns.
• Musical instruments used in Sattriya include the Khol (drum), Taals (cymbals), and the Flute.
• Kathak
• Kathak is a North Indian classical dance form known for its intricate footwork and spins.
• It traces its origins to the wandering bards of ancient northern India known as Kathakars or storytellers.
• It is characterized by its rhythmic foot movements, adorned with small bells (Ghungroo).
• Kuchipudi
• Kuchipudi is a classical Indian dance form from Andhra Pradesh.
• It involves a combination of rhythmic footwork, dramatic characterization, and expressive eye movements.
• This dance form is known for its graceful movements and strong narrative/dramatic character.
• Bharatanatyam
• Bharatanatyam is a South Indian classical dance form originating from Tamil Nadu.
• It is known for its fixed upper torso, bent legs, and intricate footwork.
• Bharatanatyam is deeply rooted in Hindu religious themes and mythology.
• It is known for its elaborate costumes, intricate jewelry, and expressive hand gestures (Mudras).

The correct answer is Only Test Matches.

Key Points

• The term Follow On is used exclusively in the format of Test cricket.
• It occurs when a team, batting second, fails to avoid the follow on by scoring a certain percentage of the first team's score, usually 200 runs fewer than the first team in a 5-day test match.
• The captain of the first batting team has the option to enforce the follow on, making the second team bat again immediately.
• This rule is designed to expedite the outcome of a match and is unique to Test cricket, emphasizing the strategic depth of this format.

Additional Information

• Test Cricket
• Test cricket is the longest form of the sport of cricket, where a match is played over five days, with each team having two innings.
• It is considered the ultimate test of playing ability and endurance, with matches often swinging back and forth in momentum.
• Introduced in 1877, Test cricket is the oldest form of the game and is played between international teams that are full members of the International Cricket Council (ICC).
• The follow on rule adds a strategic layer, where teams must decide whether to enforce it based on match conditions, player fitness, and weather forecasts.
• One Day International (ODI) Cricket
• ODI cricket is a limited-overs format where each team faces a set number of overs, usually 50.
• Matches are completed in a single day, making them more dynamic and fast-paced compared to Test matches.
• There is no follow on in ODIs as each team gets only one innings to bat.
• ODIs are part of major international tournaments like the ICC Cricket World Cup.
• T20 Cricket
• T20 cricket is the shortest form of the game, with each team playing a maximum of 20 overs.
• It is designed to be completed in about three hours, providing a quick and entertaining format for spectators.
• There is no follow on in T20 cricket, as each team has only one innings.
• It has led to the creation of several domestic leagues, including the Indian Premier League (IPL), which have greatly increased the game's popularity.

The correct answer is He.

Key Points

• Helium (He) is a noble gas, not a halogen.
• Helium is the second lightest and second most abundant element in the observable universe.
• It is chemically inert and does not form compounds easily.
• Helium is primarily used in applications requiring low temperatures, such as cryogenics and cooling superconducting magnets.

Additional Information

• Halogens
• Halogens are a group of elements in Group 17 of the periodic table, consisting of fluorine (F), chlorine (Cl), bromine (Br), iodine (I), and astatine (At).
• They are highly reactive nonmetals and have seven electrons in their outermost shell, making them eager to gain one more electron to achieve a stable octet configuration.
• Halogens are known for their ability to form salts when they react with metals, hence the name 'halogen' which means 'salt-former'.
• They are used in a wide range of applications, including disinfectants, bleaches, and in the production of various chemical compounds.
• Noble Gases
• Noble gases are elements in Group 18 of the periodic table, consisting of helium (He), neon (Ne), argon (Ar), krypton (Kr), xenon (Xe), and radon (Rn).
• They are characterized by their full valence electron shell, which makes them extremely stable and inert under normal conditions.
• Noble gases are used in applications where non-reactivity is crucial, such as in lighting (neon lights), welding (argon), and in providing a stable environment for chemical reactions.
• Helium, being the lightest noble gas, is also used in balloons and as a lifting gas.

The correct answer is Article 40.

Key Points

• Article 40 of the Indian Constitution directs the State to organize Village Panchayats and endow them with such powers and authority as may be necessary to enable them to function as units of self-government.
• This article is part of the Directive Principles of State Policy (DPSP), which are guidelines for the framing of laws by the government.
• Village Panchayats are a form of decentralized government where each village is responsible for its own affairs, promoting local self-governance.
• The inclusion of Village Panchayats in the Constitution reflects the importance of grassroots democracy and the empowerment of local communities in India.

Additional Information

• Directive Principles of State Policy (DPSP):
• The Directive Principles of State Policy are enumerated in Part IV of the Indian Constitution, from Articles 36 to 51.
• DPSP serve as guidelines for the central and state governments of India, which are intended to be kept in mind while framing laws and policies.
• Though not enforceable by any court, these principles are considered fundamental in the governance of the country and aim to create social and economic conditions under which citizens can lead a good life.
• Examples of DPSP include securing a living wage, ensuring equal pay for equal work, promoting the health and strength of workers, and fostering respect for international law and treaty obligations.
• Village Panchayats:
• Village Panchayats are part of the Panchayati Raj system in India, which is a three-tier system of local self-government in rural areas.
• The three tiers include the Village Panchayat at the village level, the Panchayat Samiti at the block level, and the Zila Parishad at the district level.
• The 73^rd Constitutional Amendment Act of 1992 provided a constitutional status to the Panchayati Raj institutions and brought them under the purview of the justiciable part of the Constitution.
• This amendment aimed at creating a uniform structure of Panchayati Raj throughout India and ensuring more powers and responsibilities to these bodies.

The correct answer is Ustad Amjad Ali Khan Bangash.

Key Points

• Ustad Amjad Ali Khan Bangash is an Indian classical musician known for his virtuosity in playing the Sarod.
• He is popularly known as the 'Sarod Samrat' (Emperor of the Sarod).
• He belongs to the illustrious Bangash lineage, which has significantly contributed to Indian classical music.
• Ustad Amjad Ali Khan has been honored with several prestigious awards, including the Padma Vibhushan, one of India's highest civilian honors.

Additional Information

• Sarod:
• The Sarod is a stringed musical instrument, used mainly in Indian classical music.
• It is known for its deep, weighty, introspective sound, and is a prominent instrument in Hindustani classical music.
• The Sarod is believed to have evolved from the ancient Afghan Rabab, and its current form was given by Ustad Amjad Ali Khan's ancestors.
• The Sarod has a fretless fingerboard and is played with a plectrum called a 'jawa'.
• Ustad Amjad Ali Khan's Contributions:
• Ustad Amjad Ali Khan has redefined the Sarod and its techniques, making it accessible to a global audience.
• He has performed in various prestigious venues worldwide, contributing to the global appreciation of Indian classical music.
• He has also collaborated with several international artists, blending Indian classical music with other genres.
• His efforts in music education, through workshops and lectures, have inspired many young musicians.
• Other Notable Indian Classical Musicians:
• Pandit Ravi Shankar: A legendary Sitar player who popularized Indian classical music in the West.
• Pandit Kishan Maharaj: A renowned Tabla player known for his dexterity and rhythmic innovations.
• Pandit Shivkumar Sharma: A famous Santoor player who brought the instrument to the forefront of Indian classical music.

This source code provides a detailed explanation about Ustad Amjad Ali Khan Bangash, known as 'Sarod Samrat', along with key points and additional information about the Sarod, his contributions, and other notable Indian classical musicians.

The correct answer is Sawai Jaisingh II.

Key Points

• Sawai Jaisingh II was a notable ruler of the Amber kingdom in the early 18^th century.
• He built five astronomical observatories, known as Jantar Mantar, located in Delhi, Jaipur, Ujjain, Mathura, and Varanasi.
• The primary purpose of these observatories was to study the movements of celestial bodies and predict astronomical events.
• These observatories are significant examples of Indian scientific heritage and architectural ingenuity.

Additional Information

• Sawai Jaisingh II
• He was the ruler of Amber (later Jaipur) from 1699 to 1743.
• Jaisingh was a scholar in astronomy, mathematics, and architecture. He was deeply interested in the study of celestial bodies.
• His observatories combined elements of Mughal architecture with traditional Indian styles, reflecting his innovative approach.
• The observatories were equipped with large instruments made of stone and brass, designed for precise astronomical measurements.
• Jantar Mantar Observatories
• These are collections of architectural astronomical instruments, built in the early 18^th century.
• The largest of these observatories is located in Jaipur, which also serves as a UNESCO World Heritage Site.
• The instruments at Jantar Mantar were designed to observe and measure the positions of stars, predict eclipses, and ascertain the declinations of celestial bodies.
• The observatories are a testament to the advanced scientific knowledge and architectural prowess of that era.
• Historical Context
• During the rule of Sawai Jaisingh II, there was significant cultural and scientific exchange between India and other parts of the world.
• Jaisingh's patronage of science and architecture led to advancements in various fields, including astronomy, which was crucial for navigation and timekeeping.
• The construction of the Jantar Mantar observatories marked a significant period in the history of Indian science and demonstrated the ruler's commitment to knowledge and innovation.

The correct answer is Khajuraho Dance Festival.

Key Points

• The Khajuraho Dance Festival is a prestigious annual event held in the state of Madhya Pradesh.
• The festival takes place in the Khajuraho temple complex, which is renowned for its stunning ancient temples and intricate sculptures.
• This festival showcases a variety of classical dance forms of India, including Kathak, Bharatanatyam, Odissi, and Kuchipudi.
• The event attracts numerous tourists and dance enthusiasts from all over the world, celebrating India's rich cultural heritage.

Additional Information

• Thaipusam Festival:
• It is a Hindu festival celebrated mostly by the Tamil community in India and abroad.
• This festival is dedicated to Lord Murugan, the Hindu god of war, and is observed with various rituals and processions.
• Jaisalmer Desert Festival:
• This festival takes place in the city of Jaisalmer in Rajasthan, India.
• It is celebrated with cultural events, including camel races, traditional music, dance performances, and the showcasing of local crafts.
• Bihu Festival:
• The Bihu festival is an important cultural festival of Assam, India.
• There are three types of Bihu: Rongali Bihu, Kongali Bihu, and Bhogali Bihu, each marking different agricultural cycles.
• Rongali Bihu is the most prominent and marks the Assamese New Year, celebrated with dance, music, and traditional feasts.
• Khajuraho Dance Festival:
• The festival is held annually in February in the Khajuraho temple complex in Madhya Pradesh.
• It is organized by the Madhya Pradesh Kala Parishad (MP Department of Culture).
• The festival aims to promote and preserve the rich cultural traditions of India's classical dance forms.
• The Khajuraho temples, a UNESCO World Heritage site, provide a stunning backdrop for the performances.

The correct answer is Bindusara.

Key Points

• Deimachus was a Greek ambassador who came to India during the reign of the Mauryan king Bindusara.
• Bindusara was the second Mauryan emperor, ruling from c. 297 to c. 273 BCE.
• He was the son of Chandragupta Maurya, the founder of the Maurya Dynasty.
• Bindusara maintained diplomatic relations with various Hellenistic states, including the Seleucid Empire.

Additional Information

• Bindusara
• Bindusara, also known as Amitraghata, was the second emperor of the Mauryan dynasty.
• He succeeded his father, Chandragupta Maurya, and ruled from c. 297 BCE to c. 273 BCE.
• Bindusara is known for his administrative skills and the expansion of the Mauryan Empire.
• He maintained friendly relations with the Hellenistic kingdoms, which were established by the successors of Alexander the Great.
• Deimachus
• Deimachus was a Greek envoy sent by Antiochus I, the Seleucid king, to the Mauryan court.
• His visit to India is recorded as part of the diplomatic relations between the Mauryan Empire and the Hellenistic world.
• Deimachus succeeded Megasthenes, another Greek ambassador, at the Mauryan court.
• Mauryan Empire
• The Mauryan Empire was the first large-scale empire in India, founded by Chandragupta Maurya in 322 BCE.
• It is known for its significant achievements in political, military, and cultural fields.
• The empire reached its zenith under Ashoka the Great, who is renowned for his promotion of Buddhism and non-violence.
• Diplomatic Relations
• During the Mauryan period, diplomatic relations were established with several Hellenistic kingdoms, including the Seleucid Empire.
• These relations were crucial for trade, cultural exchange, and political alliances.
• Greek ambassadors like Megasthenes and Deimachus played a key role in these diplomatic efforts.

The correct answer is Hydra.

Key Points

• Hydra is a genus of small, fresh-water organisms of the phylum Cnidaria and class Hydrozoa.
• They are known for their regenerative ability, meaning they can regrow their body parts.
• Hydra is not a member of the phylum Porifera, which consists of sponges.
• Sponges (Porifera) include organisms like Sycon, Spongilla, and Euplectella, which are entirely different from Hydra.

Additional Information

• Phylum Porifera
• Commonly known as sponges, Porifera are simple, multicellular organisms that live in aquatic environments, mostly marine.
• They have a porous body structure with channels that allow water to circulate through them, facilitating feeding, respiration, and waste elimination.
• Sponges have specialized cells called choanocytes that help in water flow and capturing food particles.
• Examples include Sycon, Spongilla, and Euplectella.
• Hydra
• Hydra belongs to the phylum Cnidaria, which includes jellyfish, corals, and sea anemones.
• They are characterized by their simple body structure, radial symmetry, and presence of cnidocytes (stinging cells) used for capturing prey.
• Hydra are known for their remarkable ability to regenerate, meaning they can regrow any lost or damaged parts of their body.
• They primarily reproduce asexually by budding, although sexual reproduction can also occur under certain conditions.
• Sycon (Scypha)
• Sycon is a genus of calcareous sponges belonging to the phylum Porifera.
• They have a tubular body structure with a single central cavity called the spongocoel.
• Sycon species are marine and are found attached to rocks or other surfaces underwater.
• Spongilla
• Spongilla is a genus of freshwater sponges belonging to the family Spongillidae.
• They are found in lakes, rivers, and streams, often attached to submerged objects.
• Spongilla sponges have a soft, porous body that filters small food particles from the water.
• Euplectella
• Euplectella, commonly known as Venus' flower basket, is a genus of glass sponges found in deep ocean environments.
• They have a unique and intricate skeletal structure made of silica, which provides structural support.
• Euplectella species are known for their symbiotic relationship with certain shrimp, which live inside the sponge's body for protection.

The correct answer is Diphtheria.

Key Points

• Diphtheria is a serious bacterial infection that usually affects the mucous membranes of the nose and throat.
• The disease is caused by the bacterium Corynebacterium diphtheriae.
• Diphtheria spreads through respiratory droplets from coughing or sneezing.
• Symptoms include a thick, gray membrane covering the throat and tonsils, sore throat, swollen glands, and difficulty breathing.

Additional Information

• Meningococcal Disease
• Meningococcal disease is caused by the bacterium Neisseria meningitidis.
• It can lead to serious infections such as meningitis (inflammation of the membranes around the brain and spinal cord) and septicemia (blood poisoning).
• The disease spreads through respiratory droplets and close contact with an infected person.
• Symptoms include sudden fever, headache, and a stiff neck, often accompanied by nausea, vomiting, sensitivity to light, and altered mental status.
• Shigellosis
• Shigellosis is an infectious disease caused by a group of bacteria called Shigella.
• It is characterized by diarrhea (often bloody), fever, and stomach cramps.
• The infection spreads through contaminated food, water, or contact with an infected person.
• Good hygiene practices, especially handwashing, are critical for preventing the spread of Shigellosis.
• Chlamydia
• Chlamydia is a common sexually transmitted infection (STI) caused by the bacterium Chlamydia trachomatis.
• It can infect both men and women, causing damage to the reproductive system.
• Symptoms may include abnormal genital discharge and a burning sensation during urination.
• If left untreated, Chlamydia can lead to serious reproductive and other health problems with both short-term and long-term consequences.

The correct answer is Pandit Bhimsen Joshi.

Key Points

• Pandit Bhimsen Joshi was an Indian vocalist in the Hindustani classical tradition, renowned for his khayal form singing as well as for his popular renditions of devotional music.
• He was awarded the Maharashtra Bhushan in 2002, which is one of the highest civilian awards presented by the Government of Maharashtra.
• Pandit Bhimsen Joshi was also the recipient of several other prestigious awards, including the Bharat Ratna in 2008, India's highest civilian honor.
• His unique style and dedication to Indian classical music have earned him a legendary status among music enthusiasts in India and abroad.

Additional Information

• Maharashtra Bhushan Award
• The Maharashtra Bhushan is a prestigious civilian award presented annually by the Government of Maharashtra.
• It was instituted in 1996 to recognize and honor individuals for their outstanding contributions to various fields such as literature, arts, sports, and social work.
• The award includes a citation and a monetary prize, and it is considered one of the highest accolades given by the state.
• Notable recipients of the Maharashtra Bhushan Award include personalities like Lata Mangeshkar, Sachin Tendulkar, and Ratan Tata, among others.
• Bharat Ratna
• The Bharat Ratna is the highest civilian award in India, instituted in 1954.
• It is awarded in recognition of exceptional service or performance of the highest order in any field of human endeavor.
• The award does not carry any monetary grant, but it holds immense prestige and honor.
• Recipients of the Bharat Ratna include prominent figures such as C. Rajagopalachari, S. Radhakrishnan, and Mother Teresa.
• Khayal
• Khayal is a major form of Hindustani classical music, characterized by its flexibility, improvisation, and emotional expression.
• The word 'khayal' means "imagination" in Arabic, and it allows the singer to explore various melodic and rhythmic possibilities.
• It is usually performed in a slow tempo (vilambit) followed by a fast tempo (drut) composition.
• Pandit Bhimsen Joshi was known for his powerful and emotive khayal renditions, which captivated audiences worldwide.
• Hindustani Classical Music
• Hindustani classical music is one of the two main forms of Indian classical music, the other being Carnatic music.
• It originated in North India and has a rich tradition that dates back over a thousand years.
• It includes various forms such as dhrupad, khayal, thumri, and tappa, each with its own unique style and characteristics.
• Prominent exponents of Hindustani classical music include Ustad Amir Khan, Pandit Ravi Shankar, and Ustad Zakir Hussain.

The correct answer is Article 165.

Key Points

• Article 165 of the Indian Constitution specifies the duties of the Advocate-General for the State.
• It mandates that the Advocate-General shall give advice to the State Government upon legal matters referred to him.
• The Advocate-General is the highest law officer in the state and corresponding to the Attorney General of India at the central level.
• Article 165 also allows the Advocate-General to perform any other legal duties assigned to him by the Governor.

Additional Information

• Advocate-General of the State:
• The Advocate-General is appointed by the Governor of the State.
• He must be a person who is qualified to be appointed as a judge of a High Court, which means he must be an Indian citizen and must have been an advocate of a High Court for ten years or a judge of two or more such courts in succession for a similar period.
• The Advocate-General's functions are comparable to those of the Attorney General of India, but he operates at the state level.
• Legal Advice to the Government:
• Article 165(2) mentions that the Advocate-General shall perform duties of a legal character assigned to him by the Governor.
• He has the right to speak and participate in the proceedings of both Houses of the State Legislature, but without the right to vote.
• Other Relevant Articles:
• Article 168: Deals with the Constitution of Legislatures in states.
• Article 166: Specifies the conduct of business of the Government of a State.
• Article 167: Discusses the duties of the Chief Minister as respects the furnishing of information to the Governor.

The correct answer is 6 years or up to the age of 65 years.

Key Points

• The tenure of the Chief Election Commissioner (CEC) is 6 years or up to the age of 65 years, whichever is earlier.
• The Chief Election Commissioner can be removed from office only through impeachment by Parliament for proven misbehavior or incapacity.
• The CEC and other Election Commissioners have the same powers, salary, allowances, and other perquisites as are available to a judge of the Supreme Court of India.
• The concept of an independent Election Commission was introduced to ensure free and fair elections in India, as per the provisions of Article 324 of the Indian Constitution.

Additional Information

• Election Commission of India (ECI)
• The Election Commission of India is an autonomous constitutional authority responsible for administering election processes in India at both the national and state levels.
• The body administers elections to the Lok Sabha, Rajya Sabha, and State Legislative Assemblies, as well as the offices of the President and Vice President in the country.
• The Election Commission operates under the authority of Constitution per Article 324, and subsequently enacted Representation of the People Act.
• The commission has the powers to monitor the election process, including the preparation of electoral rolls, ensuring the model code of conduct, and scrutinizing election expenses of candidates.
• Chief Election Commissioner (CEC)
• The Chief Election Commissioner heads the Election Commission of India and oversees the entire electoral process.
• Appointed by the President of India, the CEC ensures that the election process is conducted in a free, fair, and impartial manner.
• The CEC can only be removed through a process similar to that of a judge of the Supreme Court, which requires a two-thirds majority in Parliament.
• The CEC’s role is critical in maintaining the sanctity of the democratic process in India.

The correct answer is Soil degradation.

Key Points

• The Green Revolution led to the extensive use of chemical fertilizers and pesticides, which resulted in the degradation of soil quality.
• Overuse of these chemicals destroyed beneficial soil microorganisms, making the soil less fertile over time.
• High-yielding varieties of crops required more water and nutrients, leading to the depletion of soil nutrients and increased soil salinity.
• Monocropping practices associated with the Green Revolution reduced the organic matter in the soil, further contributing to soil degradation.

Additional Information

• Green Revolution
• The Green Revolution refers to a set of research, development, and technology transfer initiatives that increased agricultural production worldwide, particularly in developing countries, starting in the 1960s.
• Key components included the development of high-yielding varieties (HYVs) of staple crops, the use of chemical fertilizers and pesticides, and the introduction of modern farming techniques.
• The main aim was to achieve food security and reduce hunger by increasing crop yields.
• Soil Degradation
• Soil degradation is the decline in soil quality caused by its improper use, usually for agricultural, industrial, or urban purposes.
• It involves the loss of soil's physical, chemical, and biological properties, which affects its ability to sustain plant life and provide ecosystem services.
• Factors contributing to soil degradation include erosion, salinization, compaction, loss of soil organic matter, and contamination by toxic substances.
• Chemical Fertilizers and Pesticides
• Chemical fertilizers are substances that supply essential nutrients to plants in the form of compounds like nitrogen, phosphorus, and potassium.
• Pesticides are chemicals used to kill or control pests that can damage crops.
• Excessive use of these chemicals can lead to environmental issues such as soil degradation, water pollution, and harm to non-target organisms.
• Monocropping
• Monocropping is the agricultural practice of growing the same crop on the same piece of land year after year.
• This practice can lead to soil nutrient depletion, increased vulnerability to pests and diseases, and reduced biodiversity.
• It often requires higher inputs of fertilizers and pesticides to maintain crop yields, contributing to soil degradation and environmental pollution.

The correct answer is Sabarmati river.

Key Points

• The Sabarmati river is one of the major rivers in the western part of India and primarily flows through the state of Gujarat.
• It originates from the Aravalli Range in the Udaipur District of Rajasthan.
• The river flows in a south-west direction and eventually falls into the Arabian Sea.
• Sabarmati river is significant for the city of Ahmedabad, which is situated on the banks of this river.

Additional Information

• Mahanadi
• The Mahanadi river is a major river in East Central India.
• It flows through the states of Chhattisgarh and Odisha.
• The river finally empties into the Bay of Bengal.
• Krishna River
• The Krishna river is one of the longest rivers in India, flowing through the states of Maharashtra, Karnataka, Telangana, and Andhra Pradesh.
• It originates near Mahabaleshwar in Maharashtra.
• This river also drains into the Bay of Bengal.
• Godavari River
• The Godavari river is the second longest river in India after the Ganges.
• It flows through the states of Maharashtra, Telangana, Andhra Pradesh, Chhattisgarh, and Odisha.
• The Godavari river also empties into the Bay of Bengal.

The correct answer is Krishna.

Key Points

• The Krishna River is the fourth-largest river in India after the Ganga, Godavari, and Brahmaputra.
• It originates in the Western Ghats near Mahabaleshwar in Maharashtra, at an elevation of approximately 1,300 meters (4,300 ft).
• The river flows through the states of Maharashtra, Karnataka, and Andhra Pradesh before emptying into the Bay of Bengal.
• The Krishna River basin is one of the major agricultural regions in India, supporting a wide range of crops such as rice, sugarcane, and cotton.

Additional Information

• Mahadev Temple, Mahabaleshwar
• The ancient Mahadev temple in Mahabaleshwar is dedicated to Lord Shiva, one of the principal deities in Hinduism.
• The temple is famous for its spout from which the Krishna River is said to emerge, symbolically from the mouth of a cow statue called "Gomukh".
• Mahabaleshwar, located in the Satara district of Maharashtra, is a popular hill station and pilgrimage site.
• Krishna River
• The Krishna River is one of the longest rivers in India, with a total length of about 1,400 kilometers (870 miles).
• Several important tributaries join the Krishna River, including the Bhima, Tungabhadra, and Musi rivers.
• The river basin is a critical water source for irrigation, drinking water, and hydroelectric power generation.
• There are several major dams built on the Krishna River, including the Nagarjuna Sagar Dam, Srisailam Dam, and Almatti Dam.
• Significance of River Basins
• A river basin is the land area drained by a river and its tributaries, playing a crucial role in the hydrological cycle.
• River basins support diverse ecosystems and are vital for the sustenance of human populations, agriculture, and industry.
• Management and conservation of river basins are essential for sustainable water resources and environmental health.
• Integrated River Basin Management (IRBM) is an approach that promotes the coordinated development and management of water, land, and related resources.

The correct answer is Tiger.

Key Points

• The tiger was the emblem of the Chola dynasty, which was one of the longest-ruling dynasties in the history of southern India.
• The Chola dynasty used the tiger emblem to symbolize their strength, courage, and dominance over their territory.
• The emblem can be found on many of the Chola inscriptions, coins, and temple walls, indicating its importance as a royal insignia.
• The tiger emblem not only represented the power of the Chola kings but also their commitment to protecting their kingdom and upholding justice.

Additional Information

• Chola Dynasty
• The Chola dynasty was a Tamil dynasty that ruled primarily in southern India until the 13^th century.They are known for their significant contributions to art, architecture, and literature, especially during the medieval period.
• The Cholas are often credited with the establishment of a well-organized administrative system and the promotion of trade and commerce.
• The dynasty reached its zenith under the rule of Rajaraja Chola I and his son Rajendra Chola I, who expanded the empire to include parts of Southeast Asia.
• Tiger Emblem
• The tiger symbol was chosen by the Cholas to reflect their royal and warrior status.
• The emblem is often depicted in various artistic forms, such as sculptures and carvings, in the temples built by the Chola rulers.
• It served as a unifying symbol for the Chola empire, representing the courage and valor of its people.
• Historical artifacts like coins and inscriptions bearing the tiger emblem provide insights into the cultural and political landscape of the Chola period.
• Influence of the Cholas
• The Cholas played a pivotal role in the spread of Hinduism and the construction of grand temples, such as the Brihadeeswarar Temple in Thanjavur.
• Their naval prowess helped in establishing maritime trade routes with Southeast Asia, contributing to the cultural exchange and economic prosperity of the region.
• The Chola administration is noted for its efficient governance, including the development of a systematic revenue collection mechanism.
• Their patronage of art and architecture left a lasting legacy that continues to be admired and studied for its grandeur and sophistication.

The correct answer is BR Ambedkar.

Key Points

• BR Ambedkar, also known as Dr. Babasaheb Ambedkar, was a prominent Indian jurist, economist, politician, and social reformer.
• He is best known for his efforts in fighting for the rights of the Dalits (formerly known as untouchables) and other socially backward classes in India.
• He played a key role in the drafting of the Indian Constitution and served as the first Law and Justice Minister of independent India.
• The Samata Sainik Dal, formed in 1927, was an organization aimed at providing protection and promoting the social and political rights of the oppressed classes in India.

Additional Information

• Savitribai Phule
• She was an Indian social reformer, educationalist, and poet from Maharashtra.
• She is regarded as the first female teacher in India and played a crucial role in improving women's rights in the country.
• Along with her husband Jyotirao Phule, she founded the first girls' school in Pune in 1848.
• Mahatma Gandhi
• He was an Indian lawyer, anti-colonial nationalist, and political ethicist.
• He employed nonviolent resistance to lead the successful campaign for India's independence from British rule.
• He is internationally recognized for his philosophy of Satyagraha (truth and nonviolent resistance).
• Narayana Guru
• He was a social reformer and spiritual leader from Kerala.
• He led a reform movement against the caste system in the Hindu society.
• He emphasized the significance of education, spirituality, and social equality in the upliftment of the downtrodden sections of society.

The correct answer is To mitigate gender disparity in science and engineering research funding in various academic programmes and laboratories.

Key Points

• The SERB-POWER (Promoting Opportunities for Women in Exploratory Research) Scheme was launched by the Ministry of Science and Technology on 29^th October 2020.
• The primary objective of the scheme is to mitigate gender disparity in science and engineering research funding in various academic programs and laboratories.
• The scheme aims to empower women researchers by providing them with structured support in their research endeavors.
• It focuses on creating a conducive environment for women scientists to excel in their respective fields through grants, fellowships, and other supportive measures.

Additional Information

• Science and Engineering Research Board (SERB)
• SERB is a statutory body under the Department of Science and Technology, Government of India.
• It was established through an Act of Parliament in 2008 and came into existence in 2009.
• The primary mandate of SERB is to promote basic research in emerging areas of science and engineering.
• The board supports research through various programs, grants, and fellowships.
• Gender Disparity in Science and Engineering
• Gender disparity in science and engineering refers to the underrepresentation of women in these fields.
• Several factors contribute to this disparity, including societal biases, lack of role models, and unequal access to resources and opportunities.
• Efforts to address gender disparity include providing scholarships, mentorship programs, and creating inclusive policies.
• Encouraging women's participation in STEM (Science, Technology, Engineering, and Mathematics) is crucial for achieving gender equality and fostering innovation.
• Academic Programs and Laboratories
• Academic programs refer to structured courses and curricula offered by educational institutions to impart knowledge and skills.
• Laboratories are facilities equipped for scientific research, experiments, and measurement, providing hands-on experience and practical training.
• Both academic programs and laboratories play a vital role in advancing scientific knowledge and fostering research and development.
• Ensuring equal access and opportunities in these settings is essential for promoting diversity and inclusion in the scientific community.

The correct answer is Jitu.

Key Points

• Jitu was chosen as the mascot for the Khelo India University Games 2022.
• The mascot represents a tiger, which is symbolic of strength, agility, and the spirit of sportsmanship.
• Khelo India University Games is an initiative to promote university-level sports and to identify and nurture young sporting talent in India.
• The mascot aims to inspire young athletes to pursue excellence in sports with dedication and vigor.

Additional Information

• Khelo India University Games (KIUG)
• The Khelo India University Games is an annual multi-sport event held in India for university athletes.
• It is part of the larger Khelo India initiative, which aims to promote sports at the grassroots level and build a strong sports culture in the country.
• The first edition of the Khelo India University Games was held in 2020 in Bhubaneswar, Odisha.
• The event includes various sports disciplines such as athletics, basketball, boxing, fencing, judo, kabaddi, swimming, weightlifting, wrestling, and more.
• KIUG serves as a platform for university athletes to showcase their talents and compete at a high level, with the objective of identifying potential athletes for national and international competitions.
• Significance of Mascots in Sports Events
• Mascots play a crucial role in sports events by representing the cultural and regional identity of the host location.
• They are designed to be memorable and engaging, often embodying the characteristics and values of the event.
• Mascots help in promoting the event, creating a festive atmosphere, and engaging with the audience, especially children and young fans.
• They also serve as ambassadors for the event, appearing in promotional activities, merchandise, and media campaigns.
• Examples of famous sports mascots include "Wenlock and Mandeville" for the London 2012 Olympics and "Zabivaka" for the 2018 FIFA World Cup in Russia.

The correct answer is 40%.

Key Points

• The chemical formula for glucose is C₆H₁₂O₆.
• The molar mass of glucose can be calculated by summing the molar masses of its constituent elements: Carbon (C), Hydrogen (H), and Oxygen (O).
• To find the percentage of carbon in glucose, the mass of carbon atoms in one mole of glucose is divided by the molar mass of glucose and then multiplied by 100.
• This gives the weight percentage of carbon in glucose as 40%.

Additional Information

• Molecular Formula
• The molecular formula of a compound gives the exact number of atoms of each element in a molecule of the compound.
• For glucose, the molecular formula is C₆H₁₂O₆.
• Molar Mass
• The molar mass is the mass of one mole of a substance (chemical element or chemical compound).
• The molar masses of carbon, hydrogen, and oxygen are approximately 12 g/mol, 1 g/mol, and 16 g/mol, respectively.
• Percentage Composition by Mass
• The percentage composition by mass of an element in a compound is the percentage by mass of that element in the compound.
• It is calculated as (mass of the element in 1 mole of the compound / molar mass of the compound) × 100.
• Calculation of Weight % of Carbon in Glucose
• The molar mass of glucose (C₆H₁₂O₆) = (6 × 12) + (12 × 1) + (6 × 16) = 180 g/mol.
• The mass of carbon in one mole of glucose = 6 × 12 = 72 g.
• Weight % of carbon in glucose = (72 g / 180 g) × 100 = 40%.

Given:

Expenditures of a company from 2010 to 2014 (in Lakh Rupees).

Formula used:

Percentage = (Total Bonus / Total Salary) × 100

Calculations:

Total Bonus = 3.84 + 3.68 + 3.00 + 2.52 + 3.96 = 17 lakh 

Total Salary = 310 + 324 + 338 + 346 + 410 = 1728 Lakh 

Now,

Percentage = (Total Bonus / Total Salary) × 100

⇒ Percentage = (17 / 1728) × 100

⇒ Percentage = 1700/1728 = 

⇒ Percentage = 0.98 ≈ 1%

The total amount of bonus paid is approximately 1% of the total salary paid during this period.

Shortcut Trick

Majority = 70% − 30% = 40% of valid votes.

Total Voters × 80% × 95% × 40% = 36,480

Total Voters × (4/5) × (19/20) × (2/5) = 36,480

Total Voters × (152/500) = 36,480

Total Voters = 36,480 × (500 ÷ 152) = 1,20,000

∴ The correct answer is 1,20,000 voters.

Alternate Method

Given:

Polled votes = 80% of total voters

Valid votes = 95% of polled votes

Winning candidate votes = 70% of valid votes

Majority = 36,480 votes

Calculations:

⇒ Let the total number of voters be 100x.

⇒ Polled votes = 80% of 100x = 80x

⇒ Valid votes = 95% of 80x = 76x

⇒ Winner's share = 70% of 76x

⇒ Loser's share = (100% − 70%) = 30% of 76x

⇒ Majority = Winner's share − Loser's share

⇒ Majority = (70% − 30%) = 40% of 76x

⇒ Majority = 0.40 × 76x = 30.4x

⇒ 30.4x = 36,480

⇒ x = 36,480 ÷ 30.4 = 1,200

⇒ Total voters = 100x = 100 × 1,200 = 1,20,000

∴ The correct answer is 1,20,000 voters.

Additional Information

Successive Percentage Trick

When multiple percentage reductions occur consecutively (e.g., voters → polled → valid), the final value can be found by directly multiplying the base with their equivalent successive fractions: Final Value = Initial Base × (1 − r₁/100) × (1 − r₂/100).

Majority in Elections

The term "majority" exclusively represents the margin or the difference between the winning candidate's votes and the opposing candidate's votes. Majority % = (Winner % − Loser %) calculated out of valid votes only.

Valid vs Invalid Votes

Only the votes that are actively polled in the election can be considered for determining validity. Hence, Valid Votes = Polled Votes − Invalid Votes. Do not subtract invalid votes directly from the total voters list.

Given:

The bar graph provides the actual production and targeted production of cars for the years 2019 to 2022:

To Find:

The ratio of the total targeted production of cars in 2021 and 2022 to the total actual production of cars from 2019 to 2022.

Formula used:

Ratio = (Total Targeted Production in 2021 and 2022) / (Total Actual Production from 2019 to 2022)

Calculations:

Step 1: Calculate the total targeted production in 2021 and 2022:

Targeted production in 2021 = 70

Targeted production in 2022 = 80

Total targeted production = 70 + 80 = 150

Step 2: Calculate the total actual production from 2019 to 2022:

Actual production in 2019 = 36

Actual production in 2020 = 32

Actual production in 2021 = 59

Actual production in 2022 = 65

Total actual production = 36 + 32 + 59 + 65 = 192

Step 3: Calculate the ratio:

Ratio = Total Targeted Production / Total Actual Production

Ratio = 150 / 192

Simplify the ratio:

150 ÷ 6 = 25

192 ÷ 6 = 32

Ratio = 25 : 32

The ratio of the total targeted production in 2021 and 2022 to the total actual production from 2019 to 2022 is 25 : 32.

Shortcut Trick Direct Common Tangent = √[d2 − (R − r)2] Given distance between centres d = 16 cm, R = 12 cm, and r = 8 cm. DCT = √[162 − (12 − 8)2] DCT = √[256 − 16] = √240 = 4√15 cm ∴ The correct answer is 4√15 cm.

Alternate Method

M N Q R P

12 8 16 QR = ?

Given: Radius of first circle (R) = 12 cm Radius of second circle (r) = 8 cm Distance between their centres (d) = MN = 16 cm QR is the Direct Common Tangent (DCT). Formula Used: Length of Direct Common Tangent = √[d2 − (R − r)2] Calculation: ⇒ QR = √[162 − (12 − 8)2] ⇒ QR = √[256 − 42] ⇒ QR = √[256 − 16] ⇒ QR = √240 ⇒ QR = √(16 × 15) ⇒ QR = 4√15 cm ∴ The correct answer is 4√15 cm.

Additional Information Transverse Common Tangent (TCT) Length = √[d2 − (R + r)2]. Applicable only when the distance between centers is greater than the sum of their radii. Number of Common Tangents When two circles intersect (R − r < d < R + r), exactly 2 direct common tangents can be drawn, and 0 transverse common tangents. Intersection of Tangents The direct common tangents meet at a point that divides the line joining the centers externally in the ratio of their radii (R : r).

Given:

$\left( 5 - \frac{15}{16} \right) \times 1 \frac{12}{13}$

Calculation:

⇒ $\left( 5 - \frac{15}{16} \right) \times 1 \frac{12}{13}$

⇒ $\left( \frac{80\ -\ 15}{16} \right) \times 1 \frac{12}{13}$

⇒ $\left( \frac{65}{16} \right) \times \frac{25}{13}$

⇒ $\left( \frac{5}{16} \right) \times \frac{25}{1}$

⇒ $\frac{125}{16} = 7\frac{13}{16}$

∴ The correct answer is $7 \frac{13}{16}$.

Shortcut Trick

Ratio of the number of students = 12 : 18 = 2 : 3.

Let the assumed average be 62.

Net deviation from the assumed average = 3 × (76 − 62) = +42.

Average deviation for all 5 parts = +42 ÷ 5 = +8.4.

Actual average = 62 + 8.4 = 70.4.

∴ The correct answer is 70.4 marks.

Alternate Method

Given:

Total number of students = 30

Average score of 12 students = 62

Average score of the rest (30 − 12 = 18) students = 76

Formula Used:

Average = (Sum of all observations) ÷ (Total number of observations)

12 Students Avg: 62

18 Students Avg: 76

Ratio: 2

Ratio: 3

Overall Average = 70.4

Calculations:

⇒ Sum of scores of 12 students = 12 × 62 = 744

⇒ Sum of scores of 18 students = 18 × 76 = 1368

⇒ Total sum of scores for all 30 students = 744 + 1368 = 2112

⇒ Overall average = 2112 ÷ 30

⇒ Overall average = 70.4

∴ The correct answer is 70.4 marks.

Additional Information

Weighted Average

When two groups have averages A₁ and A₂ with a number of elements N₁ and N₂, the combined average is calculated as (N₁A₁ + N₂A₂) ÷ (N₁ + N₂).

Deviation Method for Averages

Instead of calculating large sums directly, pick an assumed average. The true average is determined by Assumed Average + (Total Deviation ÷ Total Elements).

Shortcut Trick

The half-lengths of the two chords are 24 ÷ 2 = 12 cm and 18 ÷ 2 = 9 cm.

We observe that the distance between the parallel chords is exactly the sum of their half-lengths (12 + 9 = 21 cm).

This implies the perpendicular distances from the centre to the chords are 9 cm and 12 cm.

Using the Pythagorean theorem, the radius r = √(12² + 9²).

r = √(144 + 81) = √225 = 15 cm.

∴ The correct answer is 15 cm.

Alternate Method

O A B C D M N 12 cm 9 cm r r x 21 − x

Given:

⇒ Length of chord AB = 24 cm

⇒ Length of chord CD = 18 cm

⇒ Distance between the chords = 21 cm

Formula and Concept Used:

⇒ The perpendicular drawn from the centre of a circle to a chord bisects the chord.

⇒ Pythagoras Theorem: Hypotenuse² = Base² + Perpendicular²

Calculation:

⇒ Let the radius of the circle be r.

⇒ Let O be the centre, and OM and ON be the perpendiculars drawn from O to the chords AB and CD respectively.

⇒ AM = AB ÷ 2 = 24 ÷ 2 = 12 cm

⇒ CN = CD ÷ 2 = 18 ÷ 2 = 9 cm

⇒ Let OM = x, then ON = 21 − x (since the total distance is 21 cm).

⇒ In right-angled ΔOMA: r² = x² + 12² ... (Equation 1)

⇒ In right-angled ΔONC: r² = (21 − x)² + 9² ... (Equation 2)

⇒ Equating Equation 1 and Equation 2:

⇒ x² + 144 = (21 − x)² + 81

⇒ x² + 144 = 441 + x² − 42x + 81

⇒ 144 = 522 − 42x

⇒ 42x = 522 − 144 = 378

⇒ x = 378 ÷ 42 = 9 cm

⇒ Substituting x = 9 in Equation 1:

⇒ r² = 9² + 12²

⇒ r² = 81 + 144 = 225

⇒ r = √225 = 15 cm

∴ The correct answer is 15 cm.

Additional Information

Perpendicular Bisector Theorem

The perpendicular drawn from the centre of a circle to a chord always bisects the chord into two equal halves.

Distance Between Parallel Chords

If two parallel chords of lengths 2a and 2b are on the opposite sides of the centre, the distance between them is √(r² − a²) + √(r² − b²).

Pythagorean Triplets

A set of three positive integers a, b, and c that satisfy a² + b² = c². The numbers 9, 12, and 15 form a common Pythagorean triplet, representing the sides of a right-angled triangle.

Shortcut Trick

Total Work = LCM(8, 10) = 40 units (A = 5 units/min, B = 4 units/min).

Total obstruction efficiency = 5 × 5/8 + 4 × 3/5 = 25/8 + 12/5 = 221/40 units/min.

Work completed in last 3 mins without obstruction = 3 × 9 = 27 units.

Remaining work done during obstruction = 40 − 27 = 13 units.

Time before full flow = 13 ÷ (221/40) = 40/17 = 2 6/17 minutes.

∴ The correct answer is 2 6/17 minutes.

Alternate Method

Given:

Time taken by Pipe A to fill the cistern = 8 minutes

Time taken by Pipe B to fill the cistern = 10 minutes

Flow during obstruction: Pipe A = 5/8 of full flow, Pipe B = 3/5 of full flow

Time taken to fill the remaining cistern after obstruction removal = 3 minutes

Formula Used:

Total Work = Efficiency × Time

Calculations:

⇒ Total efficiency of A and B without obstruction = 5 + 4 = 9 units/min

⇒ Work done by A and B in the last 3 minutes = 9 × 3 = 27 units

⇒ Remaining work completed during obstruction = 40 − 27 = 13 units

⇒ Efficiency of Pipe A during obstruction = 5 × (5/8) = 25/8 units/min

⇒ Efficiency of Pipe B during obstruction = 4 × (3/5) = 12/5 units/min

⇒ Total efficiency during obstruction = 25/8 + 12/5 = (125 + 96) / 40 = 221/40 units/min

⇒ Time taken during obstruction = Remaining Work ÷ Total efficiency during obstruction

⇒ Time taken = 13 ÷ (221/40) = 13 × 40 / 221

⇒ Time taken = 40 / 17 = 2 6/17 minutes

∴ The correct answer is 2 6/17 minutes.

Additional Information

Pipes and Cisterns Basics

If a pipe can fill a tank in x hours, the part of the tank filled by it in 1 hour is 1/x. If a pipe empties the tank in y hours, its effective work is taken as negative (−1/y).

LCM Method

The total capacity of the cistern is assumed to be the Lowest Common Multiple (LCM) of the time taken by individual pipes. This converts fractional work into easily calculable whole number units.

Reduced Efficiency (Obstruction)

When a pipe is obstructed, its effective efficiency becomes the product of its normal efficiency and the operational fraction of the flow allowed through the obstruction.

Shortcut Trick

Put θ = 0° to quickly find the numerical values of a and b.

⇒ a = xcos(0°) + ysin(0°) = x(1) + 0 = x

⇒ b = xsin(0°) − ycos(0°) = 0 − y(1) = −y

Now, substitute these into the given expression:

⇒ a² + b² = (x)² + (−y)² = x² + y²

∴ The correct answer is x² + y².

Alternate Method

Given:

a = xcosθ + ysinθ

b = xsinθ − ycosθ

Formula Used:

(A + B)² = A² + B² + 2AB

(A − B)² = A² + B² − 2AB

sin²θ + cos²θ = 1

Calculations:

⇒ a² = (xcosθ + ysinθ)²

⇒ a² = x²cos²θ + y²sin²θ + 2xycosθsinθ

⇒ b² = (xsinθ − ycosθ)²

⇒ b² = x²sin²θ + y²cos²θ − 2xycosθsinθ

Adding the expanded equations for a² and b²:

⇒ a² + b² = x²cos²θ + y²sin²θ + 2xycosθsinθ + x²sin²θ + y²cos²θ − 2xycosθsinθ

⇒ a² + b² = x²cos²θ + x²sin²θ + y²sin²θ + y²cos²θ

⇒ a² + b² = x²(cos²θ + sin²θ) + y²(sin²θ + cos²θ)

Using the trigonometric identity sin²θ + cos²θ = 1:

⇒ a² + b² = x²(1) + y²(1)

⇒ a² + b² = x² + y²

∴ The correct answer is x² + y².

Additional Information

Pythagorean Trigonometric Identities

⇒ sin²θ + cos²θ = 1

⇒ 1 + tan²θ = sec²θ

⇒ 1 + cot²θ = cosec²θ

Value Substitution Method

In trigonometric expressions where the final options are independent of the angle θ, substituting standard angles like 0° or 90° instantly simplifies the equation by eliminating multiple terms, serving as an excellent time-saving shortcut.

Algebraic Expansion Rules

When expanding equations with positive and negative symmetric terms, the middle products (like +2AB and −2AB) generally cancel each other out upon addition, effortlessly leaving only the squared terms behind.

Shortcut Trick

For infinite solutions, the ratio of coefficients of x and y must be equal.

4 / 5 = 12 / k

⇒ 4 × k = 12 × 5

⇒ k = 60 ÷ 4 = 15

∴ The correct answer is 15.

Alternate Method

Given:

Equation 1: 4x + 12y + 36 = 0

Equation 2: 5x + ky + 45 = 0

Formula Used:

For a system of linear equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 to have an infinite number of solutions, the condition is:

a₁/a₂ = b₁/b₂ = c₁/c₂

Calculations:

⇒ a₁ = 4, b₁ = 12, c₁ = 36

⇒ a₂ = 5, b₂ = k, c₂ = 45

⇒ 4/5 = 12/k = 36/45

⇒ 4/5 = 12/k = 4/5

⇒ 4/5 = 12/k

⇒ 4k = 60

⇒ k = 15

∴ The correct answer is 15.

Additional Information

Condition for Unique Solution (Intersecting Lines)

The system of equations has exactly one solution if a₁/a₂ ≠ b₁/b₂.

Condition for No Solution (Parallel Lines)

The system of equations has no solution if a₁/a₂ = b₁/b₂ ≠ c₁/c₂.

Consistent vs Inconsistent Systems

If a system has at least one solution (unique or infinite), it is consistent. If it has no solution, it is inconsistent.

Shortcut Trick

When distance is constant, Speed ratio is inverse of Time ratio.

Time Ratio (Downstream : Upstream) = 18 : 36 = 1 : 2 ⇒ Speed Ratio (D : U) = 2 : 1

Let Downstream Speed (D) = 2 and Upstream Speed (U) = 1

Speed of boat (B) = (D + U) ÷ 2 = 3 ÷ 2 = 1.5

Speed of stream (S) = (D − U) ÷ 2 = 1 ÷ 2 = 0.5

Ratio B : S = 1.5 : 0.5 = 3 : 1

∴ The correct answer is 3 : 1.

Alternate Method

Given:

Time taken downstream (T_d) = 18 hours

Time taken upstream (T_u) = 36 hours

Formula Used:

Distance = Speed × Time

Downstream Speed = Speed of Boat in still water (B) + Speed of Stream (S)

Upstream Speed = Speed of Boat in still water (B) − Speed of Stream (S)

Calculations:

⇒ Let the speed of the boat in still water be B and the speed of the stream be S.

⇒ Downstream speed = B + S

⇒ Upstream speed = B − S

⇒ Since the distance is constant in both directions, we equate the distances:

⇒ Distance = Downstream Speed × Downstream Time = Upstream Speed × Upstream Time

⇒ (B + S) × 18 = (B − S) × 36

⇒ Dividing both sides by 18, we get:

⇒ B + S = (B − S) × 2

⇒ B + S = 2B − 2S

⇒ 2S + S = 2B − B

⇒ 3S = B

⇒ Ratio of B to S = 3 : 1

∴ The correct answer is 3 : 1.

Additional Information

Speed of Boat in Still Water

If Downstream Speed is D and Upstream Speed is U, then the Speed of the Boat in still water B = (D + U) ÷ 2.

Speed of Stream

If Downstream Speed is D and Upstream Speed is U, then the Speed of the Stream S = (D − U) ÷ 2.

Average Speed

When traveling equal distances downstream and upstream, the Average Speed = (2 × D × U) ÷ (D + U).

Shortcut Trick

In a right-angled triangle, the square of the altitude drawn to the hypotenuse equals the product of the two segments of the hypotenuse.

By Geometric Mean Theorem: CM² = AM × BM

Given AB = 18 cm and BM = 6 cm, we can find AM = 18 − 6 = 12 cm.

CM² = 12 × 6 = 72

CM = √72 = 6√2 cm

∴ The correct answer is 6√2 cm.

Alternate Method

Given:

∠C = 90°

CM ⊥ AB

AB = 18 cm

BM = 6 cm

  A B C M AM = 12 cm BM = 6 cm CM = ?    AB = 18 cm

Formula Used:

When an altitude is drawn from the right angle to the hypotenuse, the square of its length is the product of the lengths of the two segments it creates on the hypotenuse.

CM² = AM × BM

Calculations:

⇒ AB = AM + BM

⇒ 18 = AM + 6

⇒ AM = 18 − 6 = 12 cm

Now, substitute the values of AM and BM into the geometric mean formula:

⇒ CM² = 12 × 6

⇒ CM² = 72

⇒ CM = √72

⇒ CM = 6√2 cm

∴ The correct answer is 6√2 cm.

Additional Information

Altitude Rule

The altitude drawn to the hypotenuse is the geometric mean of the two hypotenuse segments (h² = x × y).

Leg Rule

Each leg of the right triangle is the geometric mean of the entire hypotenuse and the segment adjacent to that leg (a² = c × x and b² = c × y).

Area Equivalency

The product of the two legs equals the product of the hypotenuse and the altitude to the hypotenuse (a × b = c × h).

Shortcut Trick

A number is divisible by 9 if the sum of its digits is a multiple of 9.

Sum of digits = 5 + 7 + x + 7 + 1 + 6 = 26 + x.

The nearest multiple of 9 greater than 26 is 27.

26 + x = 27 ⇒ x = 1.

∴ The correct answer is 1.

Alternate Method

Given:

The number is 57x716, which is completely divisible by 9.

Concept Used:

For a number to be perfectly divisible by 9, the sum of all its digits must be a multiple of 9.

Calculations:

⇒ Sum of the digits of 57x716 = 5 + 7 + x + 7 + 1 + 6

⇒ Sum = 26 + x

⇒ Possible values for (26 + x) that are multiples of 9 are 27, 36, 45, etc.

⇒ Since x is a single-digit positive integer (from 0 to 9), the maximum possible sum can be 26 + 9 = 35.

⇒ Therefore, the only possible multiple of 9 in this range is 27.

⇒ 26 + x = 27

⇒ x = 27 − 26 = 1

∴ The correct answer is 1.

Additional Information

Divisibility Rule of 3

A number is completely divisible by 3 if the sum of its digits is divisible by 3.

Divisibility Rule of 4

A number is divisible by 4 if the number formed by its last two digits is perfectly divisible by 4.

Divisibility Rule of 11

A number is divisible by 11 if the difference between the sum of digits at odd positions and the sum of digits at even positions is 0 or a multiple of 11.

Divisibility Rule of 8

A number is divisible by 8 if the number formed by its last three digits is perfectly divisible by 8.

Shortcut Trick

The locus of a point equidistant from two vertices (P and R) is their perpendicular bisector.

In a rhombus, the diagonal SQ is the perpendicular bisector of the diagonal PR.

Since OP = OR, the point O must lie exactly on the diagonal SQ.

Because O is an interior point, S, O, and Q lie on the same straight line.

A straight line always forms an angle of 180°.

∴ The correct answer is 180°.

Alternate Method

Given:

PQRS is a rhombus.

O is an interior point such that OP = OR.

Formula / Concept Used:

The diagonals of a rhombus bisect each other at 90°.

The set of all points equidistant from two given points forms the perpendicular bisector of the segment connecting them.

M

O P S R Q OP OR

Calculations:

⇒ Let the diagonals PR and SQ intersect at point M.

⇒ In rhombus PQRS, SQ ⊥ PR and PM = MR.

⇒ This implies that the diagonal SQ acts as the perpendicular bisector of the diagonal PR.

⇒ We are given that OP = OR, which means O is perfectly equidistant from the endpoints P and R.

⇒ By the locus theorem, any point equidistant from P and R must lie exactly on the perpendicular bisector of PR.

⇒ Therefore, the point O must lie completely on the line segment SQ.

⇒ Since O is placed strictly inside the rhombus on the diagonal SQ, the points S, O, and Q are collinear.

⇒ A collinear arrangement forms a straight angle.

⇒ ∠SOQ = 180°

∴ The correct answer is 180°.

Additional Information

Properties of a Rhombus

All four sides are equal in length. The diagonals bisect each other at right angles (90°) and also perfectly bisect the opposite interior angles.

Locus of Equidistant Point

The locus of a point that is completely equidistant from two given points A and B is the perpendicular bisector of the line segment AB.

Collinear Points

Three or more points that lie directly on the same straight line are termed collinear points. The angle formed by three collinear points with the middle point acting as the vertex is exactly 180°.

Shortcut Trick

For two successive discounts of a% and b%, the single equivalent discount is given by the formula:

Equivalent Discount = a + b − (a × b) ÷ 100

Here, a = 40 and b = 20

⇒ Equivalent Discount = 40 + 20 − (40 × 20) ÷ 100

⇒ Equivalent Discount = 60 − 8 = 52%

∴ The correct answer is 52%.

Alternate Method

Given:

First discount = 40%

Second discount = 20%

Calculations:

Let the Marked Price (MP) of the goods be 100.

⇒ Price after 1^st discount = 100 − (40% of 100) = 100 − 40 = 60

⇒ Price after 2^nd discount (Selling Price) = 60 − (20% of 60) = 60 − 12 = 48

⇒ Total Discount = MP − SP = 100 − 48 = 52

⇒ Single Equivalent Discount % = (Total Discount ÷ MP) × 100

⇒ Equivalent Discount % = (52 ÷ 100) × 100 = 52%

∴ The correct answer is 52%.

Additional Information

Successive Discount for Three Percentages

If three successive discounts d₁%, d₂%, and d₃% are given, the equivalent Single Discount is: 100 − [100 × (100−d₁)÷100 × (100−d₂)÷100 × (100−d₃)÷100].

Relation between CP and MP

When the profit percentage (P%) and discount percentage (D%) are known, the ratio of Marked Price (MP) to Cost Price (CP) is computed directly using the formula: MP/CP = (100 + P%) ÷ (100 − D%).

Buy X Get Y Free

If a shopkeeper offers 'Buy X, Get Y Free', the total items given to the customer are X + Y. The discount percentage is calculated as: Discount % = [Y ÷ (X + Y)] × 100.

Calculations:

Step 1: Determine what 40% of 50 marks is:

40% of 50 = (40/100) × 50 = 20 marks.

Step 2: Identify the students who scored 20 or more in Chemistry:

From the table, the number of students who scored:

20 and above = 66 students

The number of students eligible to pursue higher studies in Chemistry is 66.

Shortcut Trick

Standard Identity: If x³ + y³ + z³ = 3xyz, then x + y + z = 0.

Given equation: 8a³ + b³ + 27c³ = 18abc

Rewrite as: (2a)³ + (b)³ + (3c)³ = 3 × (2a) × (b) × (3c)

Here x = 2a, y = b, and z = 3c.

⇒ 2a + b + 3c = 0 ⇒ b + 3c = −2a

∴ The correct answer is b + 3c = −2a.

Alternate Method

Given:

8a³ + b³ + 27c³ = 18abc

Formula Used:

x³ + y³ + z³ − 3xyz = (x + y + z)(x² + y² + z² − xy − yz − zx)

If x³ + y³ + z³ = 3xyz, then either x + y + z = 0 or x = y = z.

Calculations:

⇒ The given expression can be arranged as follows by bringing all terms to one side:

⇒ 8a³ + b³ + 27c³ − 18abc = 0

⇒ Now, represent each term as a perfect cube:

⇒ (2a)³ + (b)³ + (3c)³ − 3 × (2a) × (b) × (3c) = 0

⇒ Comparing this directly with the algebraic identity, we can substitute x = 2a, y = b, and z = 3c.

⇒ According to the identity rule, for the expression to be zero, the sum of the base variables must be zero.

⇒ x + y + z = 0

⇒ 2a + b + 3c = 0

⇒ Moving 2a to the right side of the equation:

⇒ b + 3c = −2a

This strictly matches the relation given in the options.

∴ The correct answer is b + 3c = −2a.

Additional Information

Core Algebraic Identity

a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca).

Conditional Cubes Identity

If a + b + c = 0, then substituting this into the main identity simplifies to a³ + b³ + c³ = 3abc.

Sum of Squares Form

a² + b² + c² − ab − bc − ca = ½[(a − b)² + (b − c)² + (c − a)²].

Equality Condition

If a³ + b³ + c³ = 3abc and a + b + c ≠ 0, it strictly means a = b = c.

Shortcut Trick

Let the original Cost Price = 100 units.

First dealer makes 30% profit ⇒ SP₁ = Cost Price for second dealer = 130 units.

Total profit is 40% on original Cost Price ⇒ Final SP = 140 units.

Profit for the second dealer = Final SP − CP₂ = 140 − 130 = 10 units.

Profit % for second dealer = (10 ÷ 130) × 100 = 100 ÷ 13 = 7 ⁹/₁₃ %.

∴ The correct answer is 7 ⁹/₁₃ %.

Alternate Method

Given:

Total profit on the article = 40%

Profit made by the first dealer = 30%

Formula Used:

Successive Percentage Formula: Net Profit % = a + b + (a × b) ÷ 100

Calculations:

⇒ Let the profit percentage made by the second dealer be b.

⇒ By applying the successive percentage formula we equate it to the total profit of 40%.

⇒ 40 = 30 + b + (30 × b) ÷ 100

⇒ 40 − 30 = b + 0.3b

⇒ 10 = 1.3b

⇒ b = 10 ÷ 1.3 = 100 ÷ 13

⇒ b = 7 ⁹/₁₃ %

∴ The correct answer is 7 ⁹/₁₃ %.

Additional Information

Successive Profits

When an item is sold multiple times sequentially, the net profit percentage is calculated using the successive percentage formula: Net % = a + b + (a × b) ÷ 100.

Marked Price & Discount

Discount is always given on the Marked Price (MP). The resulting selling price is: SP = MP × (100 − Discount%) ÷ 100.

Dishonest Dealer

If a dealer sells goods at Cost Price but uses false weight, the actual profit percentage is calculated as: Profit % = (True Weight − False Weight) ÷ False Weight × 100.

Shortcut Trick

Initial ratio of Men to Women = 5 : 3

Final ratio of Men to Women = 5 : 4

Men's ratio part (5) remains constant as only women are added.

Increase in women's ratio = 4 − 3 = 1 part.

1 part = 150 women ⇒ Men = 5 parts = 150 × 5 = 750.

∴ The correct answer is 750 men.

Alternate Method

Given:

Initial ratio of Men to Women = 5 : 3

Number of additional women employed = 150

Final ratio of Men to Women = 5 : 4

Calculation:

⇒ Let the initial number of men and women be 5x and 3x respectively.

⇒ After adding 150 women, the number of women becomes (3x + 150).

⇒ The new ratio of men to women is 5 : 4.

⇒ 5x / (3x + 150) = 5 / 4

⇒ 20x = 5 × (3x + 150)

⇒ 20x = 15x + 750

⇒ 20x − 15x = 750

⇒ 5x = 750

⇒ The number of men is 5x, which is exactly 750.

∴ The correct answer is 750 men.

Additional Information

Compound Ratio

When two or more ratios are multiplied together, it is called a compound ratio. For individual ratios a : b and c : d, the compound ratio is ac : bd.

Duplicate & Triplicate Ratio

The duplicate ratio of a : b is a² : b². The triplicate ratio is a³ : b³.

Componendo and Dividendo

If a / b = c / d, then (a + b) / (a − b) = (c + d) / (c − d). This rule is very helpful in quickly solving proportional equations.

Shortcut Trick

If sin A + cos A = k, then we directly find sin A cos A = (k² − 1) ÷ 2.

Here, k = 1 / 2√2, so k² = 1 / 8.

sin A cos A = (1/8 − 1) ÷ 2 = −7 / 16.

We know the identity, sin⁴A + cos⁴A = 1 − 2(sin A cos A)².

Result = 1 − 2(−7 / 16)² = 1 − 2(49 / 256) = 1 − 49 / 128 = 79 / 128.

∴ The correct answer is 79/128.

Alternate Method

Given:

sin A + cos A = 1 / 2√2

Formula Used:

(a + b)² = a² + b² + 2ab

sin²A + cos²A = 1

a⁴ + b⁴ = (a² + b²)² − 2a²b²

Calculations:

Squaring both sides of the given equation:

⇒ (sin A + cos A)² = (1 / 2√2)²

⇒ sin²A + cos²A + 2 sin A cos A = 1 / 8

⇒ 1 + 2 sin A cos A = 1 / 8

⇒ 2 sin A cos A = 1/8 − 1

⇒ 2 sin A cos A = −7 / 8

⇒ sin A cos A = −7 / 16

Now, finding the value of sin⁴A + cos⁴A:

⇒ sin⁴A + cos⁴A = (sin²A + cos²A)² − 2 sin²A cos²A

⇒ sin⁴A + cos⁴A = 1² − 2(sin A cos A)²

⇒ sin⁴A + cos⁴A = 1 − 2(−7 / 16)²

⇒ sin⁴A + cos⁴A = 1 − 2(49 / 256)

⇒ sin⁴A + cos⁴A = 1 − 49 / 128

⇒ sin⁴A + cos⁴A = (128 − 49) / 128 = 79 / 128

∴ The correct answer is 79/128.

Additional Information

Sum of 4^th Powers

sin⁴θ + cos⁴θ = 1 − 2 sin²θ cos²θ

Sum of 6^th Powers

sin⁶θ + cos⁶θ = 1 − 3 sin²θ cos²θ

Difference to Sum Relation

If sin θ + cos θ = x, then sin θ − cos θ = ±√(2 − x²).

Shortcut Trick

Using basic reductions: cos(90° − θ) = sinθ and sin(90° + θ) = cosθ.

Numerator = 4sinθcos³θ − 4cosθsin³θ = 4sinθcosθ(cos²θ − sin²θ).

Using double angle formulas: Numerator = 2 × (2sinθcosθ) × cos2θ = 2sin2θcos2θ = sin4θ.

Denominator = cos(90° + 4θ) = −sin4θ.

Result = sin4θ ÷ (−sin4θ) = −1.

∴ The correct answer is -1.

Alternate Method

Given:

[4cos(90° − θ)sin³(90° + θ) − 4sin(90° + θ)cos³(90° − θ)] ÷ cos((180° + 8θ) ÷ 2)

Formula Used:

cos(90° − θ) = sinθ

sin(90° + θ) = cosθ

cos(90° + x) = −sinx

sin2x = 2sinxcosx

cos2x = cos²x − sin²x

Calculations:

⇒ Simplifying the numerator:

⇒ 4sinθcos³θ − 4cosθsin³θ

⇒ 4sinθcosθ(cos²θ − sin²θ)

⇒ 2 × (2sinθcosθ) × (cos²θ − sin²θ)

⇒ 2 × sin2θ × cos2θ

⇒ sin4θ

⇒ Simplifying the denominator:

⇒ cos(180° ÷ 2 + 8θ ÷ 2)

⇒ cos(90° + 4θ)

⇒ −sin4θ

⇒ Now, substituting both values into the given expression:

⇒ Expression = sin4θ ÷ (−sin4θ)

⇒ Expression = −1

∴ The correct answer is -1.

Additional Information

Trigonometric Signs in Quadrants (ASTC Rule)

Quadrant I (0° to 90°): All functions are positive.

Quadrant II (90° to 180°): Only sin and cosec are positive.

Quadrant III (180° to 270°): Only tan and cot are positive.

Quadrant IV (270° to 360°): Only cos and sec are positive.

Double Angle Formulas

sin2x = 2sinxcosx = (2tanx) ÷ (1 + tan²x)

cos2x = cos²x − sin²x = 2cos²x − 1 = 1 − 2sin²x

Complementary and Supplementary Angles

sin(90° − x) = cosx and cos(90° − x) = sinx

sin(180° − x) = sinx and cos(180° − x) = −cosx

Shortcut Trick

By adding 1 to both sides, the given expression becomes a perfect cube.

a³ + 3a² + 3a + 1 = 7 + 1

⇒ (a + 1)³ = 8

⇒ a + 1 = 2 ⇒ a = 1

Substitute a = 1 into a² + 2a ⇒ 1² + 2(1) = 3

∴ The correct answer is 3.

Alternate Method

Given:

a³ + 3a² + 3a = 7

Formula Used:

(x + y)³ = x³ + y³ + 3x²y + 3xy²

Calculations:

We know that the given expression is very close to the expansion of (a + 1)³.

Add 1 to both sides of the equation to complete the perfect cube on the left side:

⇒ a³ + 3a² + 3a + 1 = 7 + 1

⇒ a³ + 3(a²)(1) + 3(a)(1)² + 1³ = 8

⇒ (a + 1)³ = 2³

Taking the cube root on both sides:

⇒ a + 1 = 2

⇒ a = 2 − 1 = 1

Now, substitute the value of a = 1 in the required expression a² + 2a:

⇒ (1)² + 2(1)

⇒ 1 + 2 = 3

∴ The correct answer is 3.

Additional Information

Perfect Cube Expansion

(a + b)³ = a³ + b³ + 3ab(a + b) = a³ + b³ + 3a²b + 3ab²

Negative Perfect Cube

(a − b)³ = a³ − b³ − 3ab(a − b) = a³ − b³ − 3a²b + 3ab²

Sum and Difference of Cubes

a³ + b³ = (a + b)(a² − ab + b²) and a³ − b³ = (a − b)(a² + ab + b²)

Shortcut Trick

Total Interest (SI) = Amount − Principal = 1230 − 1040 = ₹190.

Interest for 1 year = Total Interest ÷ Time = 190 ÷ 1.5 = 190 × (2/3) = ₹380/3.

Rate % = (Interest for 1 year ÷ Principal) × 100.

Rate % = (380/3 ÷ 1040) × 100 = 38000 ÷ 3120 = 475 ÷ 39 = 12 ⁷/₃₉ %.

∴ The correct answer is 12 ⁷/₃₉ %.

Alternate Method

Given:

Principal (P) = ₹1040

Amount (A) = ₹1230

Time (T) = 1.5 years = 3/2 years

Formula Used:

Simple Interest (SI) = A − P

SI = (P × R × T) ÷ 100

Calculations:

⇒ SI = 1230 − 1040 = ₹190

⇒ 190 = [1040 × R × (3/2)] ÷ 100

⇒ 190 = (520 × R × 3) ÷ 100

⇒ 190 × 100 = 1560 × R

⇒ 19000 = 1560 × R

⇒ R = 19000 ÷ 1560

⇒ R = 1900 ÷ 156

⇒ R = 475 ÷ 39 = 12 ⁷/₃₉ %

∴ The correct answer is 12 ⁷/₃₉ %.

Additional Information

Simple Interest Amount Formula

The total amount after simple interest is accumulated over T years is calculated as A = P × [1 + (R × T) ÷ 100].

Compound Interest (CI)

In Compound Interest, interest is earned on both the principal and previously accumulated interest. Formula: A = P × (1 + R ÷ 100)^T.

SI vs CI Difference

For a time period of 2 years, the difference between Compound Interest and Simple Interest on the same principal and rate is given by D = P × (R ÷ 100)².

Calculations:

Step 1: Calculate the average production of type A bikes over the years:

Total production of type A = 157 + 194 + 271 + 290 = 912.

Average production = Total production / Number of years = 912 / 4 = 228.

Step 2: Compare the production of type C bikes with 228 for each year:

2015: Production of type C = 255 (greater than 228).

2016: Production of type C = 227 (less than 228).

2017: Production of type C = 213 (less than 228).

2018: Production of type C = 239 (greater than 228).

Step 3: Count the number of years where production of type C is less than 228:

Years: 2016 and 2017 (2 years).

The number of years is 2.

Shortcut Trick

For a given cylinder, the ratio of Total Surface Area (TSA) to Curved Surface Area (CSA) is derived directly as (h + r) / h.

Given, height (h) = 12 cm and diameter = 28 cm ⇒ radius (r) = 14 cm.

Required Ratio = (12 + 14) / 12

Required Ratio = 26 / 12 = 13 / 6

∴ The correct answer is 13 : 6.

Alternate Method

Given:

⇒ Height of the cylinder (h) = 12 cm

⇒ Diameter of the cylinder (d) = 28 cm

⇒ Radius (r) = d ÷ 2 = 28 ÷ 2 = 14 cm

Formulas Used:

⇒ Total Surface Area (TSA) = 2πr(h + r)

⇒ Curved Surface Area (CSA) = 2πrh

Calculation:

⇒ Ratio = TSA ÷ CSA

⇒ Ratio = [2 × π × r × (h + r)] ÷ [2 × π × r × h]

⇒ Ratio = (h + r) ÷ h

⇒ Ratio = (12 + 14) ÷ 12

⇒ Ratio = 26 ÷ 12

⇒ Ratio = 13 ÷ 6

⇒ Ratio = 13 : 6

∴ The correct answer is 13 : 6.

Additional Information

Volume of a Cylinder

The capacity of a cylinder is calculated using the formula: Volume = πr²h.

Surface Area of a Cone

Curved Surface Area = πrl and Total Surface Area = πr(l + r), where slant height l = √(r² + h²).

Surface Area of a Sphere

The total curved surface of a sphere is given by Surface Area = 4πr².

The correct answer is: Option 4 i.e. 'To disclose'.

Key Points

• The word "To bring to light" means to reveal or disclose something that was previously unknown or hidden. (प्रकाश में लाना)
• Example: The investigation brought to light several facts that were previously unknown.
• "To disclose" refers to making something known or public; it is the act of revealing information. (प्रकट करना)
• Example: The company disclosed its financial results for the year.
• Hence, we can infer that the meaning of 'To bring to light' is 'To disclose'.

Therefore, the correct answer is: Option 4 i.e. 'To disclose'.

Additional Information

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

• To engage in conversation (बातचीत में शामिल होना): To start or participate in a dialogue.
• Example: She loves to engage in conversation with people from different cultures.
• To lighten (हल्का करना): To make something less heavy or intense.
• Example: He tried to lighten the mood by telling a joke.
• To disengage (अलग करना): To separate or release from something to which it is attached or connected.
• Example: She managed to disengage herself from the conversation without being rude.

The correct answer is Option 2 (adcbe).

 

Key Points

• Arrange the parts so the sentence has a clear subject, verb and a coherent subordinate clause.
• Start with the subject phrase: (a) false news websites and add the coordinating noun phrase (d) and social networking sites to form the compound subject.
• Follow with the main verb phrase (c) thrive because the advertisements and politicians, which introduces the reason clause.
• Complete the reason clause with (b) spreading propaganda about politics (modifying “advertisements and politicians”) and end with (e) make a lot of money as the effect inside the clause.
• Therefore, the correct answer is Option 2.

Reconstructed sentence: False news websites and social networking sites thrive because the advertisements and politicians spreading propaganda about politics make a lot of money.

 

Additional Information

• Option 1 (aecbd): This sequence starts awkwardly and does not flow logically.
• Option 3 (adecb): It is not correct because it places "spreading propaganda about politics" before the reason for thriving
• Option 4 (aedcb): This arrangement makes the sentence difficult to follow, as it misplaces key information about how these websites thrive.

Note: This is a PYP question, and the official answer key has marked (correct option) as the correct answer, hence we cannot make any changes to it.