SSC CGL 2024 Tier-I Official Paper (Held On: 11 Sept, 2024 Shift 1) (Previous Year Paper)

Given equation: 14014 × 14 − 10 ÷ 8 + 14 = ?

According to the question, after '+' and '−' are interchanged and '×' and '÷' are interchanged:

14014 × 14 − 10 ÷ 8 + 14 = ? ⇒ 14014 ÷ 14 + 10 × 8 - 14 = ?

⇒ 14014 ÷ 14 + 10 × 8 - 14 = ?

⇒ 1001 + 10 × 8 - 14 = ?

⇒ 1001 + 80 - 14 = ?

⇒ 1081 - 14 = ?

⇒ 1067 = ?

Hence, "Option 3" is the correct answer.

Given word: MEADOW

According to the question all the letters in the word ‘MEADOW’ are arranged in English alphabetical order:

Thus, according to the final arrangement, two letter's i.e. O and W positions remains unchanged.

Hence, "Option 2" is the correct answer.

The logic followed here is:

(280, 140)

280 ÷ 2 = 140

140 = 140 (LHS = RHS)

(186, 93)

186 ÷ 2 = 93

93 = 93 (LHS = RHS)

So, checking each option one by one:

Option 1) (118, 59)

118 ÷ 2 = 59

59 = 59 (LHS = RHS)

Option 2) (92, 51)

92 ÷ 2 = 51

46 ≠ 51 (LHS ≠ RHS)

Option 3) (86, 48)

86 ÷ 2 = 48

43 ≠ 48 (LHS ≠ RHS)

Option 4) (166, 84)

166 ÷ 2 = 84

83 ≠ 84 (LHS ≠ RHS)

Thus, out of all the options, '(118, 59)' follows the same logic as given.

Hence, "Option 1" is the correct answer.

The figure which will look like the paper when unfolded is shown below:

Thus, option Figure 1 will look like the paper when unfolded.

Hence, "Option 1" is the correct answer.

The correct mirror image of the given combination when mirror is placed at MN is as shown below:

Detailed Explanation:

The line MN is the mirror

Option 1) The word "yzvon" so, the mirror image should be "

"⇒ Correct 

Option 2) The word "yzvon", the first letter is "y". So, the mirror image should be "

" ⇒ Option 2 is eliminated.

Option 3) The word "yzvon", the fifth letter is "n". So, the mirror image should be "

" ⇒ Option 3 is eliminated.

Option 4) The word "yzvon", the first letter is "y". So, the mirror image should be "

" ⇒ Option 2 is eliminated.

Hence, the correct answer is "Option 1".

Given equation: 48 ÷ 3 + 12 × 4 – 6 × 7 + 21 = 27

According to the question, after interchanging the numbers:

Option 1) 3 and 4

48 ÷ 3 + 12 × 4 – 6 × 7 + 21 = 27 ⇒ 48 ÷ 4 + 12 × 3 – 6 × 7 + 21 = 27

⇒ 48 ÷ 4 + 12 × 3 – 6 × 7 + 21 = 27

⇒ 12 + 12 × 3 – 6 × 7 + 21 = 27

⇒ 12 + 36 + 21 – 42 = 27

⇒ 69 – 42 = 27

⇒ 27 = 27 (LHS = RHS)

Option  2) 3 and 6

48 ÷ 3 + 12 × 4 – 6 × 7 + 21 = 27 ⇒ 48 ÷ 6 + 12 × 4 – 3 × 7 + 21 = 27

⇒ 48 ÷ 6 + 12 × 4 – 3 × 7 + 21 = 27

⇒ 8 + 12 × 4 – 3 × 7 + 21 = 27

⇒ 8 + 48 + 21 – 21 = 27

⇒ 77 – 21 = 27

⇒ 56 ≠ 27 (LHS ≠ RHS)

Option  3) 4 and 7

48 ÷ 3 + 12 × 4 – 6 × 7 + 21 = 27 ⇒ 48 ÷ 3 + 12 × 7 – 6 × 4 + 21 = 27

⇒ 48 ÷ 3 + 12 × 7 – 6 × 4 + 21 = 27

⇒ 16 + 12 × 7 – 6 × 4 + 21 = 27

⇒ 16 + 84 + 24 – 21 = 27

⇒ 124 – 21 = 27

⇒ 103 ≠ 27 (LHS ≠ RHS)

Option  4) 12 and 21

48 ÷ 3 + 12 × 4 – 6 × 7 + 21 = 27 ⇒ 48 ÷ 3 + 21 × 4 – 6 × 7 + 12 = 27

⇒ 48 ÷ 3 + 21 × 4 – 6 × 7 + 12 = 27

⇒ 16 + 21 × 4 – 6 × 7 + 12 = 27

⇒ 16 + 84 + 42 – 12 = 27

⇒ 142 – 42 = 27

⇒ 100 ≠ 27 (LHS ≠ RHS)

Hence, "Option 1" is the correct answer.

The logic followed here is:

Option 1) Bone – orthopaedic ⇒ Correct

Orthopaedic specialist treat bone issues.

Option 2) Uterus – urologist ⇒ Incorrect

Urologist specialize in urinary tract and male reproductive system.

Gynecologist specialize in uterus. 

Option 3) Stomach – gastroenterologist ⇒ Correct

Gastroenterologist specialize in stomach and digestive system.

Option 4) Eye – ophthalmologist ⇒ Correct

Ophthalmologist specialize in the eye.

Hence, "Option 2" is the correct answer

The logic followed here is: 

Logic: Number of letters - 1

'CONFUSED' is coded as '7'

Number of letters in 'CONFUSED' → 8 - 1 = 7

And,

'CHAIN' is coded as '4'

Number of letters in 'CHAIN' → 5 - 1 = 4

Similarly,

'ADULTHOOD' is coded as

Number of letters in 'ADULTHOOD' → 9 - 1 = 8

Hence, "Option 3" is the correct answer.

The logic followed here is:

Option 1) 151 : 19

19 × 8  - 1 = 151

152 - 1 = 151

151 = 151 (LHS = RHS)

Option 2) 128 : 16

16 × 8  - 1 = 128

128 - 1 = 128

127 ≠ 128 (LHS ≠ RHS)

Option 3) 135 : 17

17 × 8  - 1 = 135

136 - 1 = 135

135 = 135 (LHS = RHS)

Option 4) 103 : 13

13 × 8  - 1 = 103

104 - 1 = 103

103 = 103 (LHS = RHS)

Thus, out of all the options, '128 : 16' is the odd one out.

Hence, "Option 2" is the correct answer.

The logic followed here is:

1. New elements are added clockwise subsequently.

Thus, the final series is:

Hence, "Option 1" is the correct answer.

Given series: q p _ r _ r q _ p _ r p _ q _ p r _ p _ q

Option 1: r p q r r p r q

Filling in the blanks:

q p r r p r q r p q r p r q p r r p r q

This does not follow a consistent pattern. ❌

Option 2: r p q r r q r r

Filling in the blanks:

q p r r p r q q p r r p r q q p r r p r q

This follows a consistent pattern and matches. ✅

Option 3: r p q q r q r p

Filling in the blanks:

q p r r p q q r p q r p r q r p r p r q

This does not create a clear pattern. ❌

Option 4: r p q r r q r p

Filling in the blanks:

q p r r p q r q r p q r p r q r p r p r q

This does not follow a consistent pattern. ❌

Hence, "Option 2" is the correct answer.

The logic followed here is:

16 is related to 112

16 × 7 = 112

112 = 112 (LHS = RHS)

And,

26 is related to 182

26 × 7 = 182

182 = 182 (LHS = RHS)

Similarly,

44 is related to ?

44 × 7 = ?

308 = ?

Hence, "Option 1" is the correct answer.

The logic followed here is:

'Summer' is related to 'Season'

Summer is a type of season.

Similarly,

 'Cotton' is related to '_______'

Cotton is a type of material used to make cloth.

Hence, "Option 1" is the correct answer.

Additional InformationGrain → Cotton is not a type of grain; grains are typically cereals or seeds used as food (like wheat or rice), whereas cotton is a fiber.

Dye → While cotton can be dyed, it is not a type of dye itself. Dye refers to a coloring substance, not the raw material used for cloth.

Tree → Cotton comes from a plant, but it’s not a tree; it grows on a shrub or small plant.

The least possible Venn diagram for the given statements is as shown below :

Conclusions:

I. Some bottles are bins → Follow (As some bottles are flasks and all flasks are bins. As bottles has some part common with flasks which whole comes in bins, therefore it is true.)

II. Some jugs are bins → Follow (As all bottles are jugs, some bottles are flasks and all flasks are bins. As whole bottles comes in jugs and has some part common with flasks which whole comes in bins, therefore it is true.)

III. Some flasks are jugs → Follow (As all bottles are jugs and some bottles are flasks. As whole bottles comes in jugs and has some part common with flasks, therefore it is true.)

∴ Here, All conclusions I, II and III follow.

Hence, "Option 1" is the correct answer.

Decoding symbols:

Given: P + Q ÷ R − T × M

P + Q → P is the son of Q.

Q ÷ R → Q is the mother of R.

R − T → R is the wife of T.

T × M → T is the brother of M.

Thus, according to the family tree:

Option 1) M is the sister of T. → Incorrect as M can be either sister or brother of T.

Option 2) P is the brother of R. → Correct 

Option 3) Q is the mother of M. → Incorrect as Q is the mother-in-law of M's brother

Option 4) T is the brother of P. → Incorrect as T is the brother-in-law of P.

Hence, the correct answer is "Option 2"

The image embedded in the given figure is as shown below :

∴ Here, the given figure is embedded in Figure - 2.

Hence, the correct answer is "Option 1".

The logic followed here is:

1. First box series:

Right corner diagonal elements interchange positions.

The rest of the elements shift anticlockwise.

2. Second box series:

Third column element shift clockwise.

The rest of the elements shift clockwise.

Thus, the final series is:

Hence, "Option 4" is the correct answer.

The figure which will look like the paper when unfolded is shown below:

Thus, option Figure 3 will look like the paper when unfolded.

Hence, "Option 3" is the correct answer.

The number of triangles in the given figure is shown below:

Thus, as marked there are a total of 11 triangles.

Hence, "Option 1" is the correct answer.

The logic followed here is:

RATE : SCWI

And,

HIGH : IKJL

Similarly,

OPEN : ?

Hence, "Option 4" is the correct answer.

The logic followed here is:

Hence, "Option 1" is the correct answer.

The logic followed here is:

8 is related to 512

8³ = 512

512 = 512 (LHS = RHS)

And,

12 is related to 1728

123 = 1728

1728 = 1728 (LHS = RHS)

Similarly,

15 is related to ?

153 = ?

3375 = ?

Hence, "Option 3" is the correct answer.

The logic followed here is:

Hence, "Option 3" is the correct answer.

The logic followed here is:

Acrimony : Humanity

Acrimony is antonym of humanity.

Similarly,

Wield : ?

Wield is antonym of forgo.

Hence, "Option 2" is the correct answer.

Additional Information Acrimony → Means anger and bitterness

Humanity → Means kindness and compassion

Wield → Means to handle or use something, often with control or influence

Forgo → Means to decide not to have or do something that you want

Exert → Means to put forth effort or to put something to use. Synonym of wield.

Use → Means to avail oneself of something as a means or instrument to an end. Synonym of wield.

Apply → Means to put something to practical use. Synonym of wield.

The logic followed here is:

Logic: Positional value of consonants and double of the positional value of vowels.

​'DEMAND' is written as ‘410132144'

And,

'SUPPLY' is written as '194216161225'

 

Similarly,

'PRODUCT' is written as

Hence, "Option 1" is the correct answer.

The correct answer is Ultraviolet radiation.

Key Points

• The ozone layer is a region of Earth's stratosphere that absorbs most of the Sun's ultraviolet (UV) radiation.
• It contains a high concentration of ozone (O₃) molecules.
• The absorption of UV radiation by the ozone layer protects living organisms on Earth from potential damage such as skin cancer and cataracts.
• The ozone layer is mainly located in the lower portion of the stratosphere, from approximately 15 to 35 kilometers above Earth.

Additional Information

• Ozone (O₃)
• Ozone is a molecule composed of three oxygen atoms, formed naturally in the stratosphere.
• It is produced when oxygen molecules (O₂) are split by ultraviolet light and then recombine with other oxygen molecules.
• Ozone is crucial for absorbing the majority of the Sun's harmful ultraviolet radiation.
• Though beneficial in the stratosphere, ozone can be a pollutant at ground level, contributing to smog.
• Ultraviolet (UV) Radiation
• Ultraviolet radiation is a type of electromagnetic radiation with wavelengths shorter than visible light but longer than X-rays.
• UV radiation is divided into three types based on wavelength: UVA, UVB, and UVC.
• UVC is the most harmful but is completely absorbed by the ozone layer and oxygen in the atmosphere.
• UVB is partially absorbed by the ozone layer and can cause skin burns and cancer.
• UVA has the least energy and is not absorbed by the ozone layer, but it can still cause skin aging and contribute to skin cancer.
• Stratosphere
• The stratosphere is the second major layer of Earth's atmosphere, just above the troposphere and below the mesosphere.
• It extends from about 10 to 50 kilometers above the Earth's surface.
• The stratosphere is characterized by a temperature inversion, meaning temperatures increase with altitude.
• This temperature increase is due to the absorption of ultraviolet radiation by the ozone layer.

The correct answer is Home Rule League.

Key Points

• The Home Rule League was a national political organization in India that aimed to achieve self-government within the British Empire.
• It was established by Lokmanya Bal Gangadhar Tilak and Annie Besant in 1916.
• The organization was divided into two branches: Tilak's Home Rule League (based in Maharashtra) and Besant's Home Rule League (based in Madras).
• The leagues were influential in mobilizing Indian public opinion and educating the masses on self-rule and nationalistic ideas.

Additional Information

• Indian Association
• The Indian Association was founded by Surendranath Banerjee and Ananda Mohan Bose in 1876.
• It aimed to promote political education and rights among Indians and was a precursor to the Indian National Congress.
• Theosophical Society
• The Theosophical Society was founded by Helena Petrovna Blavatsky, Henry Steel Olcott, and others in 1875 in New York City.
• Annie Besant was a prominent member who later became its president and played a significant role in India's independence movement.
• East Indian Association
• The East Indian Association was founded by Dadabhai Naoroji in 1866 in London.
• It aimed to promote Indian interests and create a platform for Indian grievances in the UK.
• Home Rule League
• The Home Rule League was a movement that sought self-government for India within the British Empire.
• It drew inspiration from the Irish Home Rule Movement and was a significant milestone in India's struggle for independence.
• Bal Gangadhar Tilak's league operated primarily in western India, while Annie Besant's league covered the rest of the country.

The correct answer is 1983.

Key Points

• India did not host the ICC Cricket World Cup in 1983.
• The 1983 Cricket World Cup was hosted by England.
• India won the 1983 Cricket World Cup by defeating the West Indies in the final.
• India has hosted the ICC Cricket World Cup in 1987, 1996, and 2011, 2023.

Additional Information

• ICC Cricket World Cup
• The ICC Cricket World Cup is the international championship of One Day International (ODI) cricket.
• The event is organized by the sport's governing body, the International Cricket Council (ICC), every four years.
• The tournament is one of the world's most viewed sporting events and is considered the "flagship event of the international cricket calendar" by the ICC.
• England hosted the first three editions of the World Cup (1975, 1979, and 1983).
• India's World Cup Wins
• India has won the ICC Cricket World Cup twice, in 1983 and 2011.
• In 1983, India defeated the West Indies by 43 runs at Lord's, London.
• In 2011, India defeated Sri Lanka by 6 wickets at Wankhede Stadium, Mumbai.
• Hosting Countries
• India has co-hosted the ICC Cricket World Cup with other countries on three occasions:
• 1987 - Co-hosted with Pakistan
• 1996 - Co-hosted with Pakistan and Sri Lanka
• 2011 - Co-hosted with Sri Lanka and Bangladesh
• 2023 - hosted by India
• The 1983 World Cup was held in England, where India emerged as the champions for the first time.

The correct answer is Option 2.

Key Points

• Tajul Ma'asir was authored by Hasan Nizami.
• Khazain-ul Futuh was written by Amir Khusrav.
• Tarikh-i-Firuzshahi was penned by Ziauddin Barani.
• Tarikh-i-Mubarakshahi was authored by Yahya bin Ahmad Sirhindi.

Additional Information

• Tajul Ma'asir
• This is a historical text written by Hasan Nizami.
• It records the early years of the Delhi Sultanate, particularly the reign of Qutb-ud-din Aibak.
• Khazain-ul Futuh
• Also known as "The Treasures of Victory," it was authored by Amir Khusrav.
• This book chronicles the military campaigns of Alauddin Khilji and is a significant source for the history of his reign.
• Tarikh-i-Firuzshahi
• Written by Ziauddin Barani, it is a historical account of the Delhi Sultanate.
• It details the reigns of several sultans from Balban to Firuz Shah Tughlaq.
• Tarikh-i-Mubarakshahi
• Authored by Yahya bin Ahmad Sirhindi, this book provides a historical account of the Delhi Sultanate.
• It covers the period from the foundation of the Delhi Sultanate up to the 15^th century, with a particular focus on the reigns of different rulers.

The correct answer is Land and other renewable resources are under pressure.

Key Points

• Overpopulation leads to excessive demand for land, causing urban sprawl and deforestation as more land is needed for housing, agriculture, and infrastructure.
• Renewable resources such as water, forests, and soil face immense pressure due to overpopulation, leading to their degradation and depletion.
• High population density results in increased consumption and waste production, putting additional stress on land and renewable resources.
• Overpopulation exacerbates environmental pollution and reduces the availability of clean air and water, impacting overall ecosystem health.

Additional Information

• Overpopulation
• Overpopulation occurs when the number of people exceeds the carrying capacity of the environment, leading to environmental degradation and resource depletion.
• It is driven by factors such as high birth rates, lower mortality rates, and migration.
• Overpopulation can result in severe economic, social, and environmental challenges, including unemployment, poverty, and loss of biodiversity.
• Urban Sprawl
• Urban sprawl refers to the uncontrolled expansion of urban areas into rural land.
• It leads to habitat destruction, increased air and water pollution, and greater reliance on automobiles, contributing to higher greenhouse gas emissions.
• Managing urban sprawl requires effective urban planning and policies promoting sustainable development.
• Deforestation
• Deforestation is the large-scale removal of forests, often to clear land for agriculture, urban development, or logging.
• It results in the loss of biodiversity, disruption of water cycles, and contribution to climate change through increased carbon emissions.
• Efforts to combat deforestation include reforestation, sustainable land management practices, and enforcement of environmental regulations.

The correct answer is Personal income tax.

Key Points

• Personal income tax is a type of direct tax levied by the government on the income of individuals and entities.
• The collection of personal income tax saw an increase as per the 10 February 2023 budget.
• This increase can be attributed to various economic factors such as higher earnings, improved compliance, and broader tax base.
• Personal income tax forms a significant portion of the revenue collected by the government, which is used for public welfare and development projects.

Additional Information

• Personal Income Tax
• It is a direct tax that individuals or entities pay on their income to the government.
• Income tax rates and slabs are determined by the government and can vary based on the amount of income earned.
• In most countries, including India, individuals are required to file an annual income tax return detailing their earnings and taxes due.
• Personal income tax is used by the government to fund various public services and infrastructure projects.
• Octroi Duties
• Octroi is a local tax collected on various goods entering a municipality or any specific area.
• It was a common form of taxation in India but has largely been abolished and replaced by other forms of indirect taxation.
• Corporate Tax
• Corporate tax is a direct tax imposed on the net income or profit of corporations and other business entities.
• The tax rate for corporations is usually different from that for individuals.
• Corporate tax is a significant source of revenue for the government.
• Commercial Tax
• Commercial tax is a broad term that can include various types of taxes levied on commercial activities.
• This can include sales tax, value-added tax (VAT), and goods and services tax (GST).
• Commercial taxes are typically indirect taxes collected by the government.

The correct answer is the Rosenmund catalyst.

Key Points

• Rosenmund catalyst is a catalyst specifically used in the hydrogenation of acyl chlorides to aldehydes.
• The catalyst consists of palladium (Pd) deposited on barium sulfate (BaSO₄).
• It is named after the German chemist Karl Wilhelm Rosenmund, who developed this catalytic process.
• The presence of barium sulfate helps to poison the palladium, preventing it from over-reducing the aldehyde to the corresponding alcohol.

Additional Information

• Hillman Reaction Catalyst
• The Hillman reaction is a carbon-carbon bond-forming reaction involving the addition of an activated alkene to an aldehyde or ketone in the presence of a catalyst.
• It generally requires a base catalyst, not Pd/BaSO₄.
• Cannizzaro Reaction Catalyst
• The Cannizzaro reaction involves the base-induced disproportionation of non-enolizable aldehydes to yield a primary alcohol and a carboxylic acid.
• This reaction typically uses a strong base like NaOH or KOH as the catalyst.
• Aldol Reaction Catalyst
• The aldol reaction involves the formation of a β-hydroxy ketone or aldehyde through the reaction of an enolate with another carbonyl compound.
• It usually requires a base or acid catalyst, not Pd/BaSO₄.

The correct answer is Tropical evergreen forests.

Key Points

• Tropical evergreen forests are dense forests found near the equator and close to the tropics. They have a warm and wet climate throughout the year.
• Ebony and Mahogany trees are typically found in tropical evergreen forests due to the high rainfall and humidity that support their growth.
• These forests have a multi-layered structure with an abundance of different species of trees, shrubs, climbers, and epiphytes.
• The biodiversity in tropical evergreen forests is extremely rich, making them some of the most productive and valuable ecosystems on Earth.

Additional Information

• Mangrove Forests
• Mangrove forests are coastal ecosystems found in tropical and subtropical regions. They are characterized by salt-tolerant trees and shrubs that grow in intertidal zones.
• These forests are crucial for protecting coastlines from erosion and providing habitats for a wide variety of marine life.
• Tropical Deciduous Forests
• Tropical deciduous forests, also known as monsoon forests, are found in regions with seasonal rainfall. Trees in these forests shed their leaves during the dry season to conserve water.
• These forests are less dense than tropical evergreen forests and are home to a variety of animal species.
• Montane Forests
• Montane forests are found in mountainous regions where the altitude affects the climate and vegetation. These forests can be divided into lower montane and upper montane forests.
• They are characterized by cooler temperatures and different flora compared to tropical forests, including coniferous trees at higher elevations.

The correct answer is Labour Party.

Key Points

• In the 1945 general election, the Labour Party won a landslide victory, securing 393 seats out of 640.
• This election marked a significant turning point in British political history, with the Labour Party forming its first majority government.
• The Labour Party, led by Clement Attlee, implemented numerous social reforms, including the establishment of the National Health Service (NHS).
• The 1945 election is often seen as a mandate for post-war reconstruction and the creation of a welfare state.

Additional Information

• Labour Party
• The Labour Party is a centre-left political party in the United Kingdom.
• It was founded in 1900, growing out of the trade union movement and socialist parties of the 19^th century.
• The party's platform has historically included policies aimed at reducing inequality and promoting social welfare.
• The Labour Party's 1945 victory is often credited to its promises of widespread social reform and economic recovery following World War II.
• Clement Attlee
• He was the leader of the Labour Party from 1935 to 1955 and served as Prime Minister from 1945 to 1951.
• Attlee's government is known for nationalizing major industries and public utilities and establishing the NHS.
• Under his leadership, the Labour government implemented extensive social reforms, laying the foundations for the modern British welfare state.
• National Health Service (NHS)
• The NHS was established in 1948, providing healthcare to all UK residents based on need rather than the ability to pay.
• It was one of the major social reforms introduced by the post-1945 Labour government.
• The creation of the NHS is considered one of the Labour Party's most significant achievements.
• 1945 General Election
• The election was held on 5 July 1945, with the results declared on 26 July after votes from servicemen overseas were counted.
• It was the first general election to be held in Britain since 1935, as elections had been suspended during World War II.
• The Labour Party's victory ended nearly a decade of Conservative government under Winston Churchill.

The correct answer is 2008.

Key Points

• The Duty-Free Tariff Preference (DFTP) Scheme for Least Developed Countries (LDCs) was announced by India in 2008.
• This scheme aims to provide preferential market access for exports from LDCs to the Indian market.
• Under this scheme, India offers duty-free access to a wide range of products originating from LDCs.
• The initiative is part of India's commitment to support the economic development of LDCs and integrate them into the global trading system.

Additional Information

• Least Developed Countries (LDCs)
• LDCs are a group of countries recognized by the United Nations as the poorest and most vulnerable in the world.
• These countries face severe structural impediments to sustainable development.
• They are characterized by low income, weak human assets, and economic vulnerability.
• As of 2023, there are 46 countries classified as LDCs by the United Nations.
• Duty-Free Tariff Preference (DFTP) Scheme
• The DFTP Scheme was announced by India in 2008 to promote trade with LDCs.
• It provides duty-free access to 98% of India's tariff lines for products originating from LDCs.
• The scheme covers a wide range of products including agricultural goods, textiles, and industrial products.
• This initiative aims to enhance the export capabilities of LDCs and foster economic growth through trade.
• India's Trade Policy for LDCs
• India's trade policy for LDCs is guided by the principles of South-South cooperation.
• It emphasizes the importance of providing market access to LDCs to support their economic development.
• India has been actively involved in providing technical assistance and capacity-building support to LDCs.
• India's trade policy aligns with its broader foreign policy objectives of promoting inclusive growth and development.
• Global Trading System
• The global trading system refers to the international framework that governs trade between countries.
• It includes agreements, institutions, and practices that facilitate the exchange of goods and services across borders.
• The World Trade Organization (WTO) plays a central role in regulating the global trading system.
• Efforts to integrate LDCs into the global trading system aim to ensure that these countries benefit from globalization and trade liberalization.

The correct answer is Pankaj Udhas.

Key Points

• Pankaj Udhas is a renowned Indian ghazal singer who has been active in the music industry for decades.
• He is known for his soulful voice and has contributed significantly to popularizing ghazal music in India and abroad.
• Pankaj Udhas has received numerous awards and accolades throughout his career, highlighting his impact on Indian music.
• Receiving the prestigious Deenanath Mangeshkar Award in April 2023 is a testament to his enduring talent and contribution to the art form.

Additional Information

• Deenanath Mangeshkar Award
• Named after the renowned Marathi theater actor and Hindustani classical vocalist, Deenanath Mangeshkar, this award is one of the most prestigious in the Indian music and arts community.
• It is presented annually by the Mangeshkar family in memory of their father, to recognize outstanding contributions in the fields of music, drama, art, and social work.
• The award ceremony often sees the presence of notable personalities from various fields, making it a significant cultural event.
• Past recipients of the Deenanath Mangeshkar Award include legends like Lata Mangeshkar, Asha Bhosle, and Pandit Jasraj, among others.
• Ghazal Music
• Ghazal is a form of poetry that expresses the pain of loss and the beauty of love in spite of that pain. It is traditionally composed of rhyming couplets and a refrain, with each line sharing the same meter.
• The roots of the ghazal can be traced back to 7^th-century Arabic poetry. It later spread to South Asia, where it developed a unique form of its own.
• Ghazal singing is a complex art that requires mastery over both classical music and the subtleties of language and poetry.
• Famous ghazal singers include Mehdi Hassan, Jagjit Singh, and Ghulam Ali, who have brought this genre to the mainstream audience.

The correct answer is 2021.

Key Points

• The Pradhan Mantri Ayushman Bharat Health Infrastructure Mission was launched in 2021.
• It is one of the largest pan-India schemes for strengthening healthcare infrastructure across the country.
• The mission aims to fill critical gaps in public health infrastructure, especially in critical care facilities and primary care in both urban and rural areas.
• It seeks to establish a network of diagnostic labs, integrated public health labs, and other healthcare facilities to improve the health infrastructure in India.

Additional Information

• Ayushman Bharat - Pradhan Mantri Jan Arogya Yojana (AB-PMJAY)
• It is a national health insurance scheme spearheaded by the Ministry of Health and Family Welfare.
• It is considered to be the world's largest government-financed health assurance initiative.
• It aims to provide free access to health insurance coverage for India's low-income earners.
• AB-PMJAY provides a cover of Rs. 5 lakhs per family per year, catering specifically to secondary and tertiary care hospitalization across public and private empanelled hospitals throughout the country.
• This significant scheme is fully financed by the Indian government, serving as an important stepping stone towards achieving universal healthcare in India.
• Pradhan Mantri Suraksha Bima Yojana (PMSBY)
• It is a government-backed accident insurance scheme in India launched on May 9, 2015, by PM Narendra Modi.
• PMSBY aims to provide a highly affordable insurance scheme for the poor and underprivileged people.
• It is available to individuals in the age group of 18 to 70 years who own a bank account.
• At a nominal annual premium of Rs.20, beneficiaries receive a risk coverage of Rs.2 lakh for accidental death and full disability, and Rs.1 lakh for partial disability.
• This prime ministerial scheme plays a pivotal role in uplifting the vulnerable strata of society and is a step towards protection against unforeseen risks.
• Pradhan Mantri Jeevan Jyoti Bima Yojana (PMJJBY)
• It was launched on 9^th May 2015 by PM Narendra Modi.
• It is a government-backed life insurance scheme in India aimed at increasing the penetration of life insurance coverage among Indians.
• It is available to individuals aged 18 to 50 years with a bank account.
• This scheme offers a life cover of Rs. 2 lakhs for a one-year period, which extends from June 1^st to May 31^st of the next year.
• The annual premium for this policy is ₹ 436 (US$5.50).
• The amount will be automatically debited from the subscriber's account annually.
• The PMJJBY scheme is an important initiative taken by the Indian government to provide affordable life insurance to its citizens$.

The correct answer is Dinoflagellates.

Key Points

• Gonyaulax is a genus of dinoflagellates, which are a type of plankton found in marine and freshwater environments.
• Dinoflagellates are characterized by their two flagella that allow them to move through the water.
• Many dinoflagellates, including Gonyaulax, are bioluminescent and can produce light through chemical reactions within their cells.
• Gonyaulax species are often associated with harmful algal blooms, sometimes referred to as "red tides," which can produce toxins harmful to marine life and humans.

Additional Information

• Euglenoids
• Euglenoids are a group of single-celled organisms that have characteristics of both plants and animals.
• They are primarily found in freshwater environments and are known for their ability to photosynthesize using chloroplasts.
• Euglena is a well-known example of euglenoids.
• Chrysophytes
• Chrysophytes, also known as golden algae, are a group of algae found in both freshwater and marine environments.
• They have a distinctive golden-brown color due to the presence of pigments like carotenoids and xanthophylls.
• Chrysophytes can be unicellular or form colonies.
• Protozoans
• Protozoans are a diverse group of single-celled eukaryotic organisms that are primarily heterotrophic.
• They can be free-living or parasitic and are found in a variety of environments, including soil, water, and inside other organisms.
• Examples of protozoans include amoebas, paramecia, and plasmodia.
• Dinoflagellates
• Dinoflagellates are a group of single-celled organisms that are part of the plankton community.
• They possess two flagella which help in their locomotion.
• Some dinoflagellates are photosynthetic, while others are heterotrophic.
• They play a crucial role in marine ecosystems and can cause harmful algal blooms.

The correct answer is Maitraka.

Key Points

• The Maitraka dynasty ruled in the western part of India, primarily the region of present-day Gujarat.
• Valabhi, the capital city of the Maitraka dynasty, was an important cultural and educational center during their reign.
• The dynasty was founded by Senapati Bhatarka, a former Gupta Empire military commander, around the middle of the 5^th century CE.
• The Maitrakas were patrons of Buddhism and Jainism, and Valabhi was known for its Buddhist monasteries and Jain temples.

Additional Information

• Valabhi
• Valabhi was an ancient city located in the present-day Bhavnagar district of Gujarat, India.
• It served as the capital of the Maitraka dynasty from the 5^th to the 8^th century CE.
• Valabhi was renowned as a center of learning and attracted scholars from various parts of India.
• The city was known for its educational institutions, particularly Buddhist monasteries, which were comparable to those at Nalanda.
• Maitraka Dynasty
• The Maitraka dynasty was founded by Senapati Bhatarka, a former military governor of the Gupta Empire.
• They ruled primarily over the Saurashtra region of Gujarat from the 5^th to the 8^th century CE.
• The Maitrakas played a significant role in the cultural and religious development of western India.
• The dynasty came to an end in the mid-8^th century CE, likely due to Arab invasions and internal strife.
• Gupta Empire
• The Gupta Empire was an ancient Indian empire that existed from approximately 320 to 550 CE.
• Founded by Maharaja Sri Gupta, the empire is known for its achievements in the arts, architecture, sciences, religion, and philosophy.
• The period of the Gupta Empire is often referred to as the Golden Age of India due to the extensive cultural developments and prosperity.
• The Gupta rulers supported Hinduism, Buddhism, and Jainism, fostering a diverse cultural and religious landscape.
• Buddhism and Jainism
• Buddhism is a major world religion founded by Siddhartha Gautama, known as the Buddha, in the 5^th century BCE in India.
• Buddhism emphasizes the Four Noble Truths and the Eightfold Path as a way to achieve enlightenment and end suffering.
• Jainism is an ancient Indian religion that teaches non-violence, truth, and asceticism.
• Founded by Mahavira in the 6^th century BCE, Jainism emphasizes the principles of non-attachment and self-discipline.

The correct answer is Tamil Nadu.

Key Points

• Bharatanatyam is a classical dance form that originated in Tamil Nadu, India.
• It is known for its fixed upper torso, bent legs, and intricate footwork.
• The dance is usually accompanied by classical music and is known for its elaborate costumes and expressive hand gestures.
• Bharatanatyam is believed to be one of the oldest classical dance traditions in India, with roots going back over 2000 years.

Additional Information

• Classical Dance Forms in India:
• India is home to several classical dance forms, each associated with different states and cultural traditions.
• Some of the prominent classical dance forms include:
• Kathak: Originated in North India, particularly in Uttar Pradesh. It is known for its intricate footwork and spins.
• Kathakali: From Kerala, known for its elaborate costumes and dramatic expressions.
• Kuchipudi: Originated in Andhra Pradesh, it involves storytelling through dance and drama.
• Odissi: From Odisha, characterized by its fluid movements and sculptural poses.
• Manipuri: From Manipur, known for its graceful and gentle movements.
• Mohiniyattam: Also from Kerala, it is known for its feminine grace and lyrical movements.
• Significance of Bharatanatyam:
• Bharatanatyam is often considered the embodiment of the South Indian cultural and spiritual ethos.
• It is traditionally performed by women and is known for its storytelling through dance, with themes usually revolving around Hindu mythology and spiritual ideas.
• The performance includes a combination of pure dance (Nritta), expressive dance (Nritya), and dramatic dance (Natya).
• The intricate hand gestures (mudras), facial expressions (rasas), and body movements (adavus) are integral parts of Bharatanatyam.

The correct answer is Gamma.

Key Points

• Gamma rays are a type of electromagnetic radiation with the shortest wavelength and the highest energy.
• They are produced by nuclear reactions, such as those occurring in nuclear explosions and radioactive decay.
• Gamma rays are also generated by cosmic events, such as supernovae and the decay of certain subatomic particles in space.
• Due to their high energy, gamma rays can penetrate most materials and require dense substances like lead for shielding.

Additional Information

• Electromagnetic Spectrum
• The electromagnetic spectrum encompasses all types of electromagnetic radiation, ranging from radio waves to gamma rays.
• It is categorized by wavelength or frequency, with radio waves having the longest wavelengths and gamma rays having the shortest.
• Other types of electromagnetic radiation include microwaves, infrared, visible light, ultraviolet, and X-rays.
• Nuclear Reactions
• Nuclear reactions involve changes in an atom's nucleus and can release significant amounts of energy.
• Examples include fission, where a nucleus splits into smaller parts, and fusion, where nuclei combine to form a larger nucleus.
• These reactions can produce high-energy particles and gamma rays.
• Radioactive Decay
• Radioactive decay is the process by which unstable atomic nuclei lose energy by emitting radiation.
• Common types of radioactive decay include alpha decay, beta decay, and gamma decay.
• Gamma decay involves the emission of gamma rays, which often accompanies alpha or beta decay to rid the nucleus of excess energy.
• Cosmic Events
• Cosmic events, such as supernovae, are powerful explosions that occur when stars exhaust their nuclear fuel and collapse under their gravity.
• These events produce a wide range of electromagnetic radiation, including gamma rays.
• Gamma-ray bursts, which are brief but intense emissions of gamma rays, are among the most energetic events in the universe.

The correct answer is Bhutan and Meghalaya.

Key Points

• Bhutan shares its borders with four Indian states: Arunachal Pradesh, Assam, West Bengal, and Sikkim.
• Meghalaya is a state in northeastern India that shares its borders with Assam and Bangladesh but does not share a border with Bhutan.
• Bhutan is a landlocked country located in the Eastern Himalayas and is bordered by India to the south and China to the north.
• Meghalaya, known as the "Abode of Clouds," is one of the seven northeastern states of India and is famous for its rich biodiversity and unique cultural heritage.

Additional Information

• Bhutan:
• Bhutan is a small, landlocked country in South Asia located in the Eastern Himalayas.
• It is bordered by India to the south, east, and west, and China to the north.
• Bhutan's capital and largest city is Thimphu.
• The country is known for its monasteries, fortresses (or dzongs), and dramatic landscapes that range from subtropical plains to steep mountains and valleys.
• Meghalaya:
• Meghalaya is a state in northeastern India.
• The name means "the abode of clouds" in Sanskrit.
• Meghalaya covers an area of approximately 22,430 square kilometers.
• The state is known for its high rainfall, subtropical forests, and biodiversity.
• Arunachal Pradesh:
• Arunachal Pradesh is a state in northeastern India.
• It borders the states of Assam and Nagaland to the south, and shares international borders with Bhutan to the west, Myanmar to the east, and China to the north.
• It is known as the "Land of the Rising Sun" in India due to its easternmost location.
• Assam:
• Assam is a state in northeastern India, south of the eastern Himalayas along the Brahmaputra and Barak River valleys.
• It is bordered by Bhutan and Arunachal Pradesh to the north, Nagaland and Manipur to the east, Meghalaya, Tripura, Mizoram, and Bangladesh to the south, and West Bengal to the west.
• Dispur, a suburb of Guwahati, is the state capital of Assam.
• West Bengal:
• West Bengal is a state in the eastern region of India along the Bay of Bengal.
• It shares international borders with Bangladesh in the east, Nepal, and Bhutan in the north, and borders the Indian states of Odisha, Jharkhand, Bihar, Sikkim, and Assam.
• Kolkata (formerly Calcutta) is the capital of West Bengal.

The correct answer is 26^th November.

Key Points

• Constitution Day is also known as Samvidhan Divas in India.
• It is observed on 26^th November every year to commemorate the adoption of the Constitution of India.
• The Constitution of India was adopted by the Constituent Assembly on 26^th November 1949, and it came into effect on 26^th January 1950.
• On 19^th November 2015, the Government of India declared 26^th November as Constitution Day.

Additional Information

• Constitution of India
• The Constitution of India is the supreme law of India.
• It lays down the framework defining fundamental political principles, establishes the structure, procedures, powers, and duties of government institutions, and sets out fundamental rights, directive principles, and the duties of citizens.
• It is the longest written constitution of any country on earth.
• Dr. B.R. Ambedkar is regarded as the chief architect of the Indian Constitution.
• Key Features of the Constitution
• Federal Structure: The Constitution provides for a federal system of government with a division of powers between the central and state governments.
• Parliamentary System: It adopts a parliamentary system of government where the executive is responsible to the legislature.
• Fundamental Rights: It guarantees fundamental rights to all citizens, which include the right to equality, freedom, and protection against discrimination.
• Directive Principles of State Policy: These are guidelines for the framing of laws by the government, aimed at creating social and economic conditions under which citizens can lead a good life.
• Secular State: The Constitution declares India to be a secular state, meaning that it does not favor any religion and allows individuals to practice any religion of their choice.
• Significance of Constitution Day
• Constitution Day is celebrated to honor and remember the importance of the Constitution and its framers.
• It serves as a reminder of the values and principles enshrined in the Constitution, such as justice, liberty, equality, and fraternity.
• The day is observed with various activities like reading the Preamble to the Constitution, organizing debates, and discussions on constitutional values and principles.

The correct answer is Indian Audit and Accounts Department.

Key Points

• The Indian Audit and Accounts Department (IAAD) is responsible for auditing the accounts of the Union and State governments and public sector organizations.
• The Comptroller and Auditor General (CAG) of India is the head of the IAAD and is responsible for ensuring that public funds are used efficiently and for the intended purposes.
• The IAAD is a constitutional authority under Article 148 of the Constitution of India, which ensures its independence from the executive branch of the government.
• The CAG of India is appointed by the President of India and has a tenure of six years or up to the age of 65 years, whichever is earlier.

Additional Information

• Indian Civil Accounts Organisation (ICAO)
• ICAO is headed by the Controller General of Accounts (CGA), who is the principal advisor on accounting matters to the Government of India.
• It is responsible for establishing and maintaining a technically sound management accounting system.
• The CGA also prepares a critical analysis of expenditures, revenues, borrowings, and the deficit for the Finance Minister.
• Controller General of Accounts (CGA)
• The CGA is the apex accounting authority of the Government of India under the Department of Expenditure, Ministry of Finance.
• It oversees the management of government accounts and preparation of the Union Government's financial statements.
• The CGA's responsibilities include maintaining the accounts of the central government and ensuring a robust financial management system.
• Institute of Chartered Accountants of India (ICAI)
• ICAI is a statutory body established by an Act of Parliament, the Chartered Accountants Act, 1949.
• It regulates the profession of Chartered Accountants in India.
• ICAI provides education, examination, and certification of Chartered Accountants, and also sets professional standards and code of ethics.

The correct answer is Only statements 3.

Key Points

• Statement 1 is incorrect: The UDAN scheme, also known as Ude Desh ka Aam Nagrik, was launched in 2017, and it has completed seven years of its implementation in 2024.
• Statement 2 is incorrect: The UDAN scheme is not the flagship scheme of the Ministry of Science and Technology. It is the flagship scheme of the Ministry of Civil Aviation.
• Statement 3 is correct: The Airports Authority of India (AAI) is the implementing agency of the UDAN scheme.
• The UDAN scheme aims to make air travel affordable and widespread, thereby boosting inclusive national economic growth, job growth, and air transport infrastructure development in all regions and states of India.

Additional Information

• UDAN Scheme (Ude Desh ka Aam Nagrik)
• UDAN is a regional airport development and "Regional Connectivity Scheme" (RCS) of Government of India, aimed at making air travel affordable and widespread.
• The scheme is jointly funded by the central government and state governments.
• Under the scheme, financial incentives in terms of concessions from the central and state governments and airport operators are extended to selected airlines to encourage operations from unserved and underserved airports, and keep airfares affordable.
• The UDAN scheme envisions the enhancement of aviation infrastructure and air connectivity in tier II and tier III cities.
• Ministry of Civil Aviation
• The Ministry of Civil Aviation of Government of India is responsible for formulating national policies and programmes for the development and regulation of the Civil Aviation sector in the country.
• It oversees airport facilities, air traffic services, and maintenance of the air transportation system.
• The Ministry also ensures the implementation of various schemes, including the UDAN scheme, to promote regional connectivity and affordable air travel.
• Airports Authority of India (AAI)
• The Airports Authority of India (AAI) is a statutory body, working under the Ministry of Civil Aviation, Government of India.
• AAI is responsible for creating, upgrading, maintaining, and managing civil aviation infrastructure in India.
• It manages a total of 137 airports, which include 24 International Airports, 10 Customs Airports, 80 Domestic Airports, and 23 Civil Enclaves at Defence airfields.
• AAI also provides air traffic management (ATM) services over the entire Indian airspace and adjoining oceanic areas.

The correct answer is Mumbai Marathon.

Key Points

• The Mumbai Marathon, officially known as the Tata Mumbai Marathon, is recognized as the largest marathon in Asia.
• This marathon was first held in the year 2004 and has since grown to become one of the most prestigious marathons in the world.
• It attracts participants from various parts of the globe, including elite athletes as well as amateur runners.
• In addition to promoting fitness and sportsmanship, the Mumbai Marathon also raises significant funds for numerous charities and social causes each year.

Additional Information

• Marathon:
• A marathon is a long-distance running race with an official distance of 42.195 kilometers (26.219 miles), usually run as a road race.
• The marathon has an ancient origin, inspired by the run of the Greek soldier Pheidippides from the battlefield of Marathon to Athens to announce the Greek victory over the Persians.
• Today, marathons are held all over the world, with the most famous ones being the Boston Marathon, London Marathon, New York City Marathon, Berlin Marathon, Chicago Marathon, and Tokyo Marathon.
• Delhi Half Marathon:
• The Delhi Half Marathon is another prominent long-distance running event held annually in New Delhi, India.
• The race covers a distance of 21.0975 kilometers (13.1094 miles) and is known for attracting both national and international runners.
• It is part of the "Great Delhi Run" and is organized by Procam International.
• Pinkathon:
• Pinkathon is India’s biggest women's run, created with the objective of promoting fitness and health among women and to spread awareness about breast cancer.
• Founded by fitness enthusiast and actor Milind Soman, Pinkathon includes events such as 3k, 5k, 10k, and half-marathon races.
• The event is held in various cities across India and encourages women of all ages and backgrounds to participate.
• Kaveri Trail Marathon:
• The Kaveri Trail Marathon is a unique marathon event held along the banks of the river Kaveri in the state of Karnataka, India.
• This marathon is known for its scenic route that includes trails through the countryside, making it a favorite among nature-loving runners.
• The event includes a full marathon, half marathon, and shorter distance races like 10k and 5k.

The correct answer is Muslim.

Key Points

• Shab-e-Barat is a significant Islamic observance that is celebrated by Muslims around the world.
• It is observed on the night between the 14^th and 15^th day of the Islamic month of Sha'ban.
• Muslims believe that on this night, God writes the destinies of all individuals for the coming year and forgives the sins of those who seek forgiveness.
• It is a night of prayer, reflection, and seeking forgiveness, often involving staying awake all night in devotion and worship.

Additional Information

• Sha'ban
• Sha'ban is the eighth month of the Islamic lunar calendar.
• It is considered a significant month for Muslims as it precedes the holy month of Ramadan.
• Many Muslims fast during this month and increase their worship in preparation for Ramadan.
• Islamic Calendar
• The Islamic calendar, also known as the Hijri calendar, is a lunar calendar consisting of 12 months in a year of 354 or 355 days.
• The calendar is used to determine the proper days of Islamic holidays and rituals, such as the annual period of fasting and the proper time for the pilgrimage to Mecca.
• Importance of Prayer in Islam
• Prayer, or Salah, is one of the Five Pillars of Islam, which are the foundation of a Muslim's faith and practice.
• It is a physical, mental, and spiritual act of worship that is observed five times every day at prescribed times.
• Prayers are performed facing the Kaaba in Mecca, and include specific recitations and movements.
• Seeking Forgiveness in Islam
• Seeking forgiveness, or Istighfar, is an important concept in Islam.
• Muslims believe that God is Merciful and Forgiving, and they regularly seek forgiveness for their sins and shortcomings.
• This practice is especially emphasized during significant nights such as Shab-e-Barat.

The correct answer is Option 2.

Key Points

• IIPDF was set up in 2007 to support the development of quality infrastructure projects.
• The fund provides financial support for project development activities of the Central Government and State Governments.
• The scheme is notified under the Department of Economic Affairs, which plays a crucial role in the economic development of the country.
• The funds for IIPDF are provided by the Central Government to assist in creating a pipeline of viable infrastructure projects.

Additional Information

• India Infrastructure Project Development Fund (IIPDF)
• The IIPDF was established to provide financial support for the development of public-private partnership (PPP) projects.
• The fund is intended to assist project authorities by providing the necessary resources for project preparation, including feasibility studies, detailed project reports, and other preparatory activities.
• The IIPDF aims to enhance the quality and bankability of infrastructure projects, making them more attractive to private sector investments.
• This initiative is part of the government's broader strategy to improve infrastructure and promote economic growth through increased private sector participation.
• Department of Economic Affairs (DEA)
• The DEA is a department under the Ministry of Finance, Government of India.
• It is responsible for formulating and monitoring the country's economic policies and programs, including fiscal policy, monetary policy, and financial regulations.
• The DEA plays a pivotal role in managing the country's economic infrastructure, ensuring sustainable growth and development.
• The department also oversees international economic relations, including India's participation in multilateral financial institutions.
• Public-Private Partnership (PPP)
• PPP is a collaborative arrangement between the government and private sector entities for the provision of public infrastructure and services.
• It leverages the expertise, efficiency, and capital of the private sector to deliver public projects, while the government provides regulatory and policy support.
• PPP models are used in various sectors, including transportation, healthcare, education, and utilities, to enhance service delivery and infrastructure development.
• The success of PPP projects depends on effective project planning, risk-sharing mechanisms, and transparent contractual agreements.

The correct answer is Tansen.

Key Points

• Tansen was one of the nine jewels (Navratnas) in the court of Emperor Akbar.
• He was a prominent figure in North Indian classical music and is known for his contributions to Hindustani music.
• Tansen's real name was Ramtanu Pandey, and he was born in a Hindu Gaur Brahmin family in Gwalior.
• He is credited with creating several ragas, including raga Darbari Kanada, raga Miyan ki Todi, and raga Miyan ki Malhar.

Additional Information

• Navratnas
• The term "Navratnas" refers to the nine extraordinary people in the court of Emperor Akbar who were known for their exceptional abilities and expertise in various fields.
• The Navratnas included scholars, poets, musicians, and advisors who played significant roles in Akbar's administration and cultural life.
• Besides Tansen, the other Navratnas were Abul Fazl, Faizi, Raja Todar Mal, Raja Man Singh, Abdul Rahim Khan-i-Khana, Fakir Aziao-Din, Mullah Do Piaza, and Raja Birbal.
• Each of these individuals was recognized for their unique contributions to the Mughal court and the broader Indian cultural landscape.
• Hindustani Classical Music
• Hindustani classical music is one of the two main subgenres of Indian classical music, the other being Carnatic music.
• It originated in the northern regions of the Indian subcontinent and has a rich tradition of ragas and talas.
• It emphasizes improvisation and the exploration of the raga, a framework for melodic improvisation.
• Tansen is considered one of the greatest musicians in Hindustani classical music and has left a lasting impact on its development.

The correct answer is Kiran Bedi.

Key Points

• Kiran Bedi is a retired Indian Police Service (IPS) officer, social activist, and former tennis player.
• She was the first woman to join the Indian Police Service (IPS) in 1972.
• Kiran Bedi has been an active advocate for several social causes including prison reform, crime prevention, and women’s empowerment.
• She served as the Lieutenant Governor of Puducherry from 2016 to 2021, during which her book 'Fearless Governance' was published.

Additional Information

• Indian Police Service (IPS)
• The IPS is one of the three All India Services of the Government of India.
• It was constituted in 1948 and provides leaders and commanders to staff the state police and all-India Central Armed Police Forces.
• IPS officers are recruited through the Union Public Service Commission (UPSC) Civil Services Examination.
• They play a crucial role in maintaining public order, counter-terrorism, border policing, and disaster management among other responsibilities.
• Lieutenant Governor of Puducherry
• The Lieutenant Governor of Puducherry is the constitutional head of the Union Territory of Puducherry.
• The Lieutenant Governor is appointed by the President of India for a term of five years.
• They have similar powers and functions as a Governor of a state in India.
• The role includes overseeing the administration and ensuring that governance in the territory is carried out in accordance with the law.
• Social Activism
• Social activism involves advocating for changes in society to address social issues and improve the quality of life for individuals and communities.
• It includes activities like campaigning, protests, community organizing, and policy advocacy.
• Notable areas of social activism include human rights, environmental protection, gender equality, and social justice.
• Activists use various methods to raise awareness, influence public opinion, and bring about legislative or social change.

Shortcut Trick

Divide the given number 999 by the divisor 99 to find the remainder.

999 ÷ 99 = 10 with a remainder of 9.

The smallest number to add = Divisor − Remainder.

Required number = 99 − 9 = 90.

∴ The correct answer is 90.

Alternate Method

Given:

Number = 999

Divisor = 99

Formula Used:

Dividend = (Divisor × Quotient) + Remainder

Number to be added = Divisor − Remainder

Calculations:

⇒ First, divide 999 by 99 to identify the quotient and the remainder.

⇒ 999 = (99 × 10) + 9

⇒ Thus, the remainder is 9.

⇒ To make the given number perfectly divisible, we must add the difference between the divisor and the remainder.

⇒ Number to be added = Divisor − Remainder

⇒ Number to be added = 99 − 9 = 90

⇒ Alternatively, the next multiple of 99 greater than 999 is 99 × 11 = 1089.

⇒ Required addition = 1089 − 999 = 90

∴ The correct answer is 90.

Additional Information

Rule for Addition

When a number N is divided by a divisor D giving a remainder R, the smallest number to be added to N to make it completely divisible by D is (D − R).

Rule for Subtraction

When a number N is divided by a divisor D giving a remainder R, the smallest number to be subtracted from N to make it completely divisible by D is exactly the remainder R itself.

Divisibility Rule of 99

A number is exactly divisible by 99 if it is completely divisible by both 9 (the sum of its digits is a multiple of 9) and 11 (the difference of alternating sums of its digits is 0 or a multiple of 11).

Shortcut Trick If x + 1/x = p, then x − 1/x = √(p2 − 4). Given p = 2√10, so x − 1/x = √(40 − 4) = √36 = 6. If x − 1/x = k, then x3 − 1/x3 = k3 + 3k. Substituting k = 6: x3 − 1/x3 = 63 + 3 × 6 = 216 + 18 = 234. ∴ The correct answer is 234.

Alternate Method Given: x + 1/x = 2√10, where x > 1 Formula Used: (x − 1/x)2 = (x + 1/x)2 − 4 x3 − 1/x3 = (x − 1/x)3 + 3(x − 1/x) Calculations: ⇒ (x − 1/x)2 = (2√10)2 − 4 ⇒ (x − 1/x)2 = 4 × 10 − 4 ⇒ (x − 1/x)2 = 40 − 4 = 36 ⇒ Since x > 1, x − 1/x will be positive. So, x − 1/x = √36 = 6 ⇒ Now, substitute this into the cube formula: ⇒ x3 − 1/x3 = (6)3 + 3 × 6 ⇒ x3 − 1/x3 = 216 + 18 ⇒ x3 − 1/x3 = 234 ∴ The correct answer is 234.

Additional Information Square Rule If x + 1/x = a, then x2 + 1/x2 = a2 − 2. Cube Rule (Plus) If x + 1/x = a, then x3 + 1/x3 = a3 − 3a. Sign Conversion Rule If x + 1/x = a, then x − 1/x = √(a2 − 4). Similarly, if x − 1/x = a, then x + 1/x = √(a2 + 4).

Shortcut Trick

Valid votes received by Q can be directly found using successive percentage multipliers.

Q's Valid Votes = Total Electorate × Polled % × Valid % × Q's Share %

⇒ Q's Valid Votes = 75,60,000 × 90% × 85% × (100% − 78%)

⇒ Q's Valid Votes = 75,60,000 × (9 ÷ 10) × (17 ÷ 20) × (11 ÷ 50)

⇒ Q's Valid Votes = 7560 × 9 × 17 × 11 = 12,72,348

∴ The correct answer is 12,72,348.

Alternate Method

Given:

Total votes of the electorate = 75,60,000

Percentage of voters who did not vote = 10%

Percentage of invalid votes = 15%

Percentage of valid votes secured by P = 78%

Calculations:

⇒ Number of votes polled = (100% − 10%) of 75,60,000

⇒ Number of votes polled = 90% of 75,60,000 = (90 ÷ 100) × 75,60,000 = 68,04,000

⇒ Number of valid votes = (100% − 15%) of 68,04,000

⇒ Number of valid votes = 85% of 68,04,000 = (85 ÷ 100) × 68,04,000 = 57,83,400

⇒ Since P got 78% of the valid votes, Q must have received the remaining valid votes.

⇒ Percentage of valid votes Q received = 100% − 78% = 22%

⇒ Number of valid votes Q got = 22% of 57,83,400

⇒ Number of valid votes Q got = (22 ÷ 100) × 57,83,400 = 12,72,348

∴ The correct answer is 12,72,348.

Additional Information

Successive Percentage Method

When a base value continuously undergoes percentage reductions or increments sequentially, the final value can be obtained via a single chain product: Base × (1 ± R₁/100) × (1 ± R₂/100).

Election Base Shifting

It is crucial to remember that the percentage of invalid votes is calculated strictly on the 'Polled Votes', not on the 'Total Electorate'. The base automatically changes after every reduction in real-time election distribution problems.

Shortcut Trick

By the Intersecting Chords Theorem, the product of the segments of each intersecting chord is equal.

MO × ON = OP × OQ

9 × 5 = OP × 6

OP = 45 ÷ 6 = 7.5 cm

∴ The correct answer is 7.5 cm.

Alternate Method

M N P Q O 9 cm 5 cm 6 cm OP = ?

Given:

Two chords MN and PQ intersect at point O inside the circle.

Length of segment MO = 9 cm

Length of segment ON = 5 cm

Length of segment OQ = 6 cm

Formula Used:

Intersecting Chords Theorem: When two chords intersect inside a circle, the product of their respective segments is equal.

⇒ MO × ON = OP × OQ

Calculations:

⇒ 9 × 5 = OP × 6

⇒ 45 = 6 × OP

⇒ OP = 45 ÷ 6

⇒ OP = 15 ÷ 2

⇒ OP = 7.5 cm

∴ The correct answer is 7.5 cm.

Additional Information

Intersecting Secants Theorem

If two secants are drawn to a circle from one exterior point P, the product of the external segment and the total secant length is equal for both secants (PA × PB = PC × PD).

Tangent-Secant Theorem

If a tangent and a secant meet at an exterior point P, the square of the tangent length is equal to the product of the secant's external segment and its total length (PT² = PA × PB).

Perpendicular from Center

A perpendicular drawn from the center of a circle to any chord bisects the chord into two equal halves.

Shortcut Trick

In a right-angled △ABC right-angled at C, the total sum of angles is 180°.

Since ∠C = 90°, the sum of the remaining two angles must be A + B = 90°.

We are required to find the value of the expression sin A × cos B × cot(A + B).

By substituting A + B = 90° into the expression, we get cot(90°), which equals 0.

Because any finite value multiplied by 0 results in 0, the entire expression evaluates to 0 without needing to find tan A.

∴ The correct answer is 0.

Alternate Method

Given:

In a right-angled △ABC, ∠C = 90°

tan A = √3

Formula Used:

tan θ = Perpendicular ÷ Base

Sum of all internal angles in a triangle = 180°

Calculations:

⇒ We are given tan A = √3.

⇒ In a standard right-angled triangle, we know that tan 60° = √3, which means ∠A = 60°.

⇒ The sum of the three internal angles is 180°, so ∠A + ∠B + ∠C = 180°.

⇒ 60° + ∠B + 90° = 180°

⇒ ∠B = 180° − 150° = 30°

⇒ Now, we must calculate the specific parts of the expression:

⇒ sin A = sin 60° = √3 ÷ 2

⇒ cos B = cos 30° = √3 ÷ 2

⇒ A + B = 60° + 30° = 90°

⇒ cot(A + B) = cot 90° = 0

⇒ We substitute these values directly into the given expression:

⇒ sin A × cos B × cot(A + B) = (√3 ÷ 2) × (√3 ÷ 2) × 0

⇒ sin A × cos B × cot(A + B) = 0

∴ The correct answer is 0.

Additional Information

Trigonometric Ratios of Complementary Angles

In any right-angled triangle, the two acute angles A and B are complementary, meaning their sum equates to exactly 90° (A + B = 90°). This establishes specific complementary identities like sin A = cos B, tan A = cot B, and sec A = cosec B.

Zero Property of Multiplication

When taking the product of several numbers or trigonometric terms together, if any single term evaluates to 0, the entire expression will invariably evaluate to 0 regardless of how large or complex the other individual values might be.

Trigonometric Standard Angles

It is beneficial to memorize the standard output limits for primary angles (0°, 30°, 45°, 60°, 90°). For instance, tan 60° corresponds to √3, while properties like cot 90° seamlessly evaluate to 0 since cos 90° is 0 and sin 90° is 1.

Shortcut Trick

Convert dimensions into the same unit: Length = 495 cm, Breadth = 1665 cm.

For the least number of tiles, the size of the square tile must be maximum.

Maximum side of the square tile = HCF(495, 1665) = 45 cm.

Least number of tiles = (Area of Courtyard) ÷ (Area of One Tile).

Least number of tiles = (495 × 1665) ÷ (45 × 45) = 11 × 37 = 407.

∴ The correct answer is 407 tiles.

Alternate Method

Given:

Length of courtyard (L) = 4 m 95 cm = 495 cm

Breadth of courtyard (B) = 16 m 65 cm = 1665 cm

Formula Used:

Area of rectangle = Length × Breadth

Area of square tile = Side²

Total number of tiles = Area of the rectangle ÷ Area of the square tile

Calculations:

⇒ To minimize the number of square tiles, we need the largest possible tile size.

⇒ The size of the largest square tile is the highest common factor (HCF) of the length and breadth.

⇒ Prime factorization of 495 = 3 × 3 × 5 × 11

⇒ Prime factorization of 1665 = 3 × 3 × 5 × 37

⇒ HCF(495, 1665) = 3 × 3 × 5 = 45 cm

⇒ So, the side of each identical square tile = 45 cm

⇒ Number of tiles required = (L × B) ÷ (Side × Side)

⇒ Number of tiles required = (495 × 1665) ÷ (45 × 45)

⇒ Number of tiles required = (495 ÷ 45) × (1665 ÷ 45)

⇒ Number of tiles required = 11 × 37 = 407

∴ The correct answer is 407 tiles.

Additional Information

Application of HCF in Mensuration

When asked to find the largest identical square shape that perfectly fits inside a rectangle without leaving gaps, always calculate the Highest Common Factor (HCF) of the dimensions.

Least Number of Tiles Rule

To minimize the number of tiles required to completely fill an area, the size of each tile must be maximized. Number of tiles = (Total Area) ÷ (HCF × HCF).

Conversion of Units

Remember that 1 meter (m) = 100 centimeters (cm). Always ensure all measurements are brought into a common single unit prior to finding the HCF or computing the area.

Shortcut Trick

Total Cost = Area of Track × Rate per m²

Total Cost = π(R² − r²) × Rate

Total Cost = (22/7) × (28² − 25²) × 28

Total Cost = 22 × (28 − 25) × (28 + 25) × 4

Total Cost = 22 × 3 × 53 × 4 = 13992

∴ The correct answer is ₹13,992.

Alternate Method

Given:

Outer radius (R) = 28 m

Inner radius (r) = 25 m

Rate of levelling = ₹28 per m²

Formula Used:

Area of circular track = π(R² − r²)

Calculations:

⇒ Area = (22/7) × (28² − 25²)

⇒ Area = (22/7) × (28 − 25) × (28 + 25)

⇒ Area = (22/7) × 3 × 53

⇒ Area = 3498/7 m²

⇒ Total Cost = Area × Rate

⇒ Total Cost = (3498/7) × 28

⇒ Total Cost = 3498 × 4

⇒ Total Cost = 13992

∴ The correct answer is ₹13,992.

Additional Information

Area of a Circular Ring

The region bounded by two concentric circles is called a circular ring or track. Area = π(R² − r²) = π(R − r)(R + r).

Difference Between Fencing and Levelling

Fencing relates to the boundary, so Cost of Fencing = Perimeter × Rate per unit length. Levelling refers to making the surface flat, so Cost of Levelling = Area × Rate per unit area.

Perimeter of a Semicircle

The total perimeter includes the curved arc and the straight diameter. Perimeter = πr + 2r = r(π + 2).

Shortcut Trick

Ratio of efficiency of faster pipe to slower pipe = 1.5 : 1 = 3 : 2.

Total combined efficiency = 3 + 2 = 5 units/min.

Total capacity of tank = Combined efficiency × Time = 5 × 15 = 75 units.

Time required by faster pipe alone = Total capacity ÷ Faster pipe efficiency = 75 ÷ 3 = 25 minutes.

∴ The correct answer is 25 minutes.

Alternate Method

Given:

Time taken by both pipes together = 15 minutes.

Faster pipe fills 1.5 times as fast as the slower pipe.

Method Used:

Total Work = Combined Efficiency × Time Taken

Calculations:

⇒ Let the efficiency of the slower pipe be 2 units/min.

⇒ Efficiency of the faster pipe = 1.5 × 2 = 3 units/min.

⇒ Combined efficiency of both pipes = 3 + 2 = 5 units/min.

⇒ Total Work = Combined Efficiency × Combined Time

⇒ Total Work = 5 × 15 = 75 units.

⇒ Time required by faster pipe = Total Work ÷ Efficiency of faster pipe

⇒ Time = 75 ÷ 3 = 25 minutes.

∴ The correct answer is 25 minutes.

Additional Information

Pipes & Cisterns

If a pipe can fill a tank in x hours, its efficiency (part filled in 1 hour) is 1/x. For an outlet pipe emptying the tank in y hours, its efficiency is −1/y.

Efficiency & Time Relationship

Time taken to complete a work is inversely proportional to the efficiency. Ratio of Time = 1 ÷ Ratio of Efficiency.

Combined Work Formula

When two pipes working together take times A and B respectively, their combined time T is given by T = (A × B) ÷ (A + B).

Shortcut Trick

Using the complementary angle properties: sec(90° − θ) = cosec θ and cos(90° − θ) = sin θ.

Therefore, sec 35° = cosec 55° and cos 25° = sin 65°.

The expression becomes: (cosec 55° / cosec 55°) − (sin 65° / sin 65°)

⇒ 1 − 1 = 0

∴ The correct answer is 0.

Alternate Method

Given:

(sec 35° / cosec 55°) − (cos 25° / sin 65°)

Formula Used:

sec(90° − θ) = cosec θ

cos(90° − θ) = sin θ

Calculations:

⇒ sec 35° = sec(90° − 55°) = cosec 55°

⇒ cos 25° = cos(90° − 65°) = sin 65°

Substituting these values into the given expression:

⇒ (cosec 55° / cosec 55°) − (sin 65° / sin 65°)

⇒ 1 − 1

⇒ 0

∴ The correct answer is 0.

Additional Information

Complementary Angles in Trigonometry

sin(90° − θ) = cos θ, tan(90° − θ) = cot θ, and sec(90° − θ) = cosec θ.

Basic Trigonometric Identities

sin²θ + cos²θ = 1, sec²θ − tan²θ = 1, and cosec²θ − cot²θ = 1.

Reciprocal Relations

sin θ = 1 / cosec θ, cos θ = 1 / sec θ, and tan θ = 1 / cot θ.

Shortcut Trick

Side of the equilateral triangle = Perimeter ÷ 3 = 36 ÷ 3 = 12 units.

Area = (√3 ÷ 4) × (side)²

Area = (√3 ÷ 4) × 144 = 36√3 square units.

∴ The correct answer is 36√3 square units.

Alternate Method

Given:

Perimeter of the equilateral triangle = 36 units

Formula Used:

Perimeter of an equilateral triangle = 3 × a (where 'a' is the side length)

Area of an equilateral triangle = (√3 ÷ 4) × a²

Calculations:

⇒ 3 × a = 36

⇒ a = 36 ÷ 3 = 12 units

⇒ Area = (√3 ÷ 4) × 12²

⇒ Area = (√3 ÷ 4) × 144

⇒ Area = 36√3 square units

∴ The correct answer is 36√3 square units.

Additional Information

Altitude of an Equilateral Triangle

The height (or altitude) of an equilateral triangle is given by h = (√3 ÷ 2) × a, where 'a' is the length of the side.

Inradius and Circumradius

For an equilateral triangle, Inradius (r) = a ÷ (2√3) and Circumradius (R) = a ÷ √3. The ratio of the circumradius to the inradius is always 2:1.

Area of an Isosceles Triangle

Area = (b ÷ 4) × √(4a² − b²), where 'a' is the length of the two equal sides and 'b' is the base.

Shortcut Trick

Put X = 45° (valid as X is not 0° or 90°). From a sinX = b cosX ⇒ a(1/√2) = b(1/√2) ⇒ a = b.

Substitute in first equation: a(1/√2)³ + a(1/√2)³ = (1/√2) × (1/√2).

⇒ 2a / (2√2) = 1/2 ⇒ a/√2 = 1/2 ⇒ a = 1/√2. Thus, b = 1/√2.

Required value = a² + b² = (1/√2)² + (1/√2)² = 1/2 + 1/2 = 1.

∴ The correct answer is 1.

Alternate Method

Given:

a sin³X + b cos³X = sinX cosX

a sinX = b cosX

Formula Used:

sin²X + cos²X = 1

Calculations:

⇒ In the first expression, rewrite b cos³X as (b cosX) × cos²X

⇒ a sin³X + (b cosX) × cos²X = sinX cosX

⇒ Substitute b cosX = a sinX into the above equation:

⇒ a sin³X + (a sinX) × cos²X = sinX cosX

⇒ Take out the common term a sinX:

⇒ a sinX × (sin²X + cos²X) = sinX cosX

⇒ Using the formula sin²X + cos²X = 1:

⇒ a sinX × 1 = sinX cosX

⇒ Since X ≠ 0°, sinX ≠ 0, so dividing both sides by sinX gives:

⇒ a = cosX

⇒ Now substitute a = cosX into the second given equation a sinX = b cosX:

⇒ cosX × sinX = b cosX

⇒ Since X ≠ 90°, cosX ≠ 0, so dividing both sides by cosX gives:

⇒ b = sinX

⇒ Now calculate the required value a² + b²:

⇒ a² + b² = cos²X + sin²X

⇒ a² + b² = 1

∴ The correct answer is 1.

Additional Information

Fundamental Trigonometric Identities

There are three primary Pythagorean identities: sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, and 1 + cot²θ = cosec²θ.

Value Putting Strategy

When options are absolute constants (independent of variables), replacing variables with valid standard angles (like 30°, 45°, or 60°) quickly yields the answer without complex algebra. Always avoid angles causing division by zero or infinity.

Domain Constraints in Simplification

The question explicitly states X is neither 0° nor 90° because sin(0°) = 0 and cos(90°) = 0, which would lead to an invalid elimination of variables when simplifying equations by cancellation.

Shortcut Trick

Direct formula for dishonest dealer total gain %: [ (Profit % + Less Weight %) ÷ (100 − Less Weight %) ] × 100

Given, Profit % = 10% and Less Weight % = 12%.

⇒ Total Gain % = [ (10 + 12) ÷ (100 − 12) ] × 100

⇒ Total Gain % = (22 ÷ 88) × 100 = (1 ÷ 4) × 100 = 25%

∴ The correct answer is 25%.

Alternate Method

Given:

Weight used is 12% less than the true weight.

Profit claimed on selling price = 10%.

Formula Used:

Profit = Selling Price (SP) − Actual Cost Price (CP)

Gain % = (Profit ÷ Actual CP) × 100

Calculations:

⇒ Let the true weight be 1000 gm and its cost price be ₹1000.

⇒ The merchant claims a profit of 10% on the cost price of the true weight.

⇒ Selling Price (SP) = ₹1000 + (10% of ₹1000) = ₹1100.

⇒ He uses 12% less weight, so the actual weight given = 1000 gm − (12% of 1000 gm).

⇒ Actual weight = 1000 − 120 = 880 gm.

⇒ Since 1000 gm costs ₹1000, the Actual Cost Price (CP) for 880 gm = ₹880.

⇒ Profit earned = SP − Actual CP = 1100 − 880 = ₹220.

⇒ Gain % = (220 ÷ 880) × 100

⇒ Gain % = (1 ÷ 4) × 100 = 25%.

∴ The correct answer is 25%.

Additional Information

Dishonest Dealer Concept

A dishonest dealer cheats either by altering the weight (giving less than promised) or by manipulating the price. The actual Cost Price is always based on the actual quantity delivered.

Successive Percentage Change

If an item is marked up by X% and then a discount of Y% is given, the net change is: Net % = X − Y − (X × Y) ÷ 100.

Markup and Discount

Markup Percentage = [ (Marked Price − Cost Price) ÷ Cost Price ] × 100

Selling Price (SP) Formula

When Profit is P%, SP = CP × (100 + P) ÷ 100. When Loss is L%, SP = CP × (100 − L) ÷ 100.

Shortcut Trick

Let Atul finish the race in T seconds. Vishu covers (900 − 135) = 765 m in (T + 20) seconds.

In the second case, Vishu covers (900 − 189) = 711 m in (T + 8) seconds.

Difference in distance for Vishu = 765 − 711 = 54 m, and difference in time = 20 − 8 = 12 seconds.

Vishu's speed = 54 ÷ 12 = 4.5 m/s.

Time taken by Vishu to cover 900 m = 900 ÷ 4.5 = 200 seconds = 3 minutes 20 seconds.

∴ The correct answer is 3 minutes 20 seconds.

Alternate Method

Given:

Total distance of the race = 900 m

In Case 1, Atul gives Vishu a head-start of 20 seconds and beats him by 135 m.

In Case 2, Atul gives Vishu a start of 189 m and beats him by 8 seconds.

Formula Used:

Distance = Speed × Time

Time = Distance ÷ Speed

Calculations:

Let Atul's speed be v_a and the time taken by Atul to cover 900 m be T seconds.

Let Vishu's speed be v_v.

Case 1: Vishu runs for (T + 20) seconds but falls short by 135 m.

⇒ Distance covered by Vishu = 900 − 135 = 765 m

⇒ Time taken to cover 765 m = T + 20

⇒ 765 ÷ v_v = T + 20 --- (Equation 1)

Case 2: Vishu gets a 189 m distance start, so he only needs to run 900 − 189 = 711 m.

Atul finishes in T seconds, but beats Vishu by 8 seconds.

⇒ Time taken by Vishu to cover 711 m = T + 8

⇒ 711 ÷ v_v = T + 8 --- (Equation 2)

Subtracting Equation 2 from Equation 1:

⇒ (765 ÷ v_v) − (711 ÷ v_v) = (T + 20) − (T + 8)

⇒ (765 − 711) ÷ v_v = 12

⇒ 54 ÷ v_v = 12

⇒ v_v = 54 ÷ 12 = 4.5 m/s

Time taken by Vishu to complete the full 900 m race:

⇒ Time = Distance ÷ Speed

⇒ Time = 900 ÷ 4.5

⇒ Time = 200 seconds

⇒ 200 seconds = 3 minutes 20 seconds

∴ The correct answer is 3 minutes 20 seconds.

Additional Information

Head-start in Distance

When runner A gives B a start of x meters in a race of L meters, A covers the full L meters while B covers (L − x) meters.

Head-start in Time

When runner A gives B a head-start of t seconds, B begins running t seconds before A starts the race.

Beating by Distance or Time

If A beats B by x meters, B is x meters behind when A finishes. If A beats B by t seconds, B reaches the finish line t seconds after A.

Given:

Total number of students in the university = 7000.

In the B.Com course, there are 60% girls.

In the B.Sc. C.Sci course, there are 40% boys, which means 60% girls.

 

Calculation:

From the above pie chart,

20% of the total students are in B.Com.

25% of the total students are in B.Sc. C.Sci.

B. Com:

Number of students in B.Com = (20% of 7000) = (20/100) ×7000 = 1400

Number of girls in B.Com = 60% of the 1400 students in B.Com:

= 60 ×(1400/100) = 840

B.Sc. C.Sci:

​Number of students in B.Sc. C.Sci = (25% of 7000) = (25/100) × 7000 =1750

Number of girls in B.Sc. C.Sci = 60% of the 1750 students in B.Sc. C.Sci:

60 × (1750/100) = 1050

The total number of girls in B.Com and B.Sc. C.Sci are:

840 + 1050 = 1890

Finally, we need to calculate what percentage the total number of girls represents of the total students in the university (7000 students).

Percentage of girls = (Total number of girls / 7000) × 100

= (1890 / 7000) ×100 = 27 %

The correct answer is option 4.

Shortcut Trick

Remainder = 32

Divisor = 2 × 32 = 64

Quotient = 64 ÷ 4 = 16

Dividend = (64 × 16) + 32 = 1024 + 32 = 1056

∴ The correct answer is 1056.

Alternate Method

Given:

Remainder = 32

Divisor = 4 × Quotient = 2 × Remainder

Formula Used:

Dividend = (Divisor × Quotient) + Remainder

Calculation:

⇒ Divisor = 2 × 32 = 64

⇒ 4 × Quotient = 64

⇒ Quotient = 64 ÷ 4 = 16

⇒ Dividend = (64 × 16) + 32

⇒ Dividend = 1024 + 32

⇒ Dividend = 1056

∴ The correct answer is 1056.

Additional Information

Division Algorithm

The core theorem states that Dividend = (Divisor × Quotient) + Remainder, where the remainder must always be greater than or equal to 0 and strictly less than the divisor.

Number of Divisors

For any integer represented in its prime factorization form as N = p^a × q^b × r^c, the total number of divisors is given by (a + 1) × (b + 1) × (c + 1).

Divisibility Rules

A number is divisible by 4 if its last two digits form a number divisible by 4, and it is divisible by 8 if its last three digits form a number divisible by 8.

Shortcut Trick

Time (T) = (SI fraction × 100) ÷ Rate

T = (3/5 × 100) ÷ 10 = 6 years.

Simple Interest = (Principal × Rate × Time) ÷ 100

SI = (16000 × 14 × 6) ÷ 100 = 13440

∴ The correct answer is ₹13,440.

Alternate Method

Given:

Simple Interest (SI₁) = 3/5 of Sum (P₁)

Rate (R₁) = 10% p.a.

New Principal (P₂) = ₹16,000

New Rate (R₂) = 14% p.a.

Formula Used:

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

Step 1: Find Time (T) SI = 3/5 × Sum Rate = 10% p.a. T = (3 × 100) ÷ (5 × 10) = 6 yrs

Step 2: Find Interest P = ₹16,000 R = 14% p.a., T = 6 yrs SI = P × R × T ÷ 100

Final Interest = ₹13,440

Calculations:

Let the required time be T years.

⇒ SI₁ = (P₁ × R₁ × T) ÷ 100

⇒ 3/5 × P₁ = (P₁ × 10 × T) ÷ 100

⇒ 3/5 = T ÷ 10

⇒ T = (3 × 10) ÷ 5 = 6 years

Now, calculate the simple interest (SI₂) on ₹16,000 for 6 years at 14% p.a.

⇒ SI₂ = (16000 × 14 × 6) ÷ 100

⇒ SI₂ = 160 × 84

⇒ SI₂ = 13440

∴ The correct answer is ₹13,440.

Additional Information

Simple Interest (SI)

Simple interest is calculated uniformly on the original principal amount. The formula is SI = (P × R × T) ÷ 100, where P is the principal, R is the rate of interest, and T is the time period.

Amount in Simple Interest

The total amount A at the end of the given time period is the sum of the initial principal and the generated simple interest. Formula: A = P + SI = P × (1 + (R × T) ÷ 100).

Finding Principal from Interest

When the simple interest generated over a period is known, the principal can be calculated by rearranging the standard formula as: P = (SI × 100) ÷ (R × T).

Shortcut Trick

If a group is divided into multiple sub-groups and the average of each sub-group is identically the same, then the combined overall average remains unchanged.

The average score of the first 12 students is 62.

The average score of the remaining 18 students is also 62.

Since both parts of the group share the exact same average, the overall average of all 30 students will directly be 62.

∴ The correct answer is 62.

Alternate Method

Given:

⇒ Total number of students in the group = 30

⇒ Average score of the first 12 students = 62

⇒ Average score of the remaining students (30 − 12 = 18) = 62

Formula Used:

⇒ Combined Average = (n₁ × A₁ + n₂ × A₂) ÷ (n₁ + n₂)

12 Students Avg: 62

18 Students Avg: 62

Total Group: 30 Students Overall Average = 62

Calculations:

⇒ Total sum of scores for the first 12 students = 12 × 62 = 744

⇒ Total sum of scores for the remaining 18 students = 18 × 62 = 1116

⇒ Total sum of scores for all 30 students = 744 + 1116 = 1860

⇒ Overall Average of the group = Total sum of scores ÷ Total number of students

⇒ Overall Average = 1860 ÷ 30

⇒ Overall Average = 62

∴ The correct answer is 62.

Additional Information

Combined Average Method

When two individual groups of sizes n₁ and n₂ have calculated averages A₁ and A₂ respectively, their overall combined average is represented algebraically as (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Constant Property of Averages

If a constant mathematical operation (addition, subtraction, multiplication, or division) is applied uniformly to all data points within a set, the calculated average of the new set reflects the exact same identical mathematical operation applied to the original average.

Weighted Average Application

The weighted average technique is specifically utilized when different individual values contribute uniquely to the total pool based on their frequency or respective weights, computed using the standard expression (Σw_ix_i) ÷ Σw_i.

Shortcut Trick

In a rhombus, diagonals act as perpendicular bisectors for each other.

Any point equidistant from vertices A and C (OA = OC) must lie on the perpendicular bisector of AC.

Hence, the interior point O must exclusively lie on the diagonal segment BD.

This makes D, O, and B collinear, forming a straight angle ∠DOB = 180º.

Required value = ⁵/₉ × 180º = 100º.

∴ The correct answer is 100º.

Alternate Method

Given:

ABCD is a rhombus.

O is an interior point such that OA = OC.

Formula Used:

The locus of all points equidistant from two points A and C is the perpendicular bisector of the line segment AC.

            A C B D O

Calculations:

⇒ In rhombus ABCD, the diagonal BD functions strictly as the perpendicular bisector of the diagonal AC.

⇒ Because OA = OC, the interior point O is geometrically bounded to lie on this specific perpendicular bisector.

⇒ Consequently, O must lie on the interior line segment connecting points B and D.

⇒ With O positioned directly between B and D, the points D, O, and B become entirely collinear.

⇒ A collinear line visually forms a completely straight angle, meaning ∠DOB = 180º.

⇒ Required measure = ⁵/₉ × ∠DOB

⇒ Required measure = ⁵/₉ × 180º = 100º

∴ The correct answer is 100º.

Additional Information

Properties of a Rhombus

A rhombus is a type of quadrilateral where all four sides possess an equal length. Its unique diagonal property dictates that diagonals perpendicularly bisect each other at a 90º intersection while also actively bisecting opposite interior angles.

Locus of Equidistant Points

Any generic point mapping an identical and equal distance dynamically relative to two fixed stationary points A and B will fundamentally form an invisible tracing line representing their shared perpendicular bisector.

Straight Angle

Whenever three sequential points are geometrically aligned collinear on a straight plane path, the resulting primary inner vertex translates dynamically into a strict unbent straight angle measuring precisely 180º.

Given:

The bar graph below shows the production of coffee (in lakh tons) by four companies A, B, C and D over a period of four years from 2010 to 2013. 

Formula used:

Combined average = (Sum of all values in Group 1 + Sum of all values in Group 2) / (Total number of values in both groups)

Percentage = (quantity1/quantity2) × 100 

Calculation:

The total production of coffee (in lakh tons) by company A over the period of four years = 60 + 90 + 140 + 220 = 510

The total production of coffee (in lakh tons) by company B over the period of four years = 70 + 100 + 150 + 210 = 530

The total production of coffee (in lakh tons) by company C over the period of four years = 50 + 190 + 180 + 250 = 670

The total production of coffee (in lakh tons) by company D over the period of four years = 120 + 170 + 200 + 260 = 750

Now,

The combined average production for four years of companies A and C is:

= (510 + 670)/8 = 147.5

The combined average production for four years of companies B and D is:

= (530 + 750)/8 = 160

Required percentage:

= [(160 - 147.5)/160] × 100

= 12.5/160 × 100

= 7.81% less

Hence, The combined average production for four years of companies A and C is 7.81% percentage less than the combined average production for four years of companies B and D.

The correct answer is option 1.

Shortcut Trick

Solve equations (1) and (3) directly since they contain only variables x and z.

Multiply equation (1) by 3 to get: 3x + 6z = 9.

Subtract equation (3) from this: (3x + 6z) − (3x − 5z) = 9 − (−13) ⇒ 11z = 22 ⇒ z = 2.

Substitute z = 2 into equation (1): x + 4 = 3 ⇒ x = −1.

Substitute x = −1 and z = 2 into equation (2): −1 + 2y + 6 = 5 ⇒ 2y = 0 ⇒ y = 0.

∴ The correct answer is x = −1, y = 0, z = 2.

Alternate Method

Given:

x + 2z = 3   ... (i)

x + 2y + 3z = 5   ... (ii)

3x − 5z = −13   ... (iii)

Calculation:

⇒ From equation (i), we can express x in terms of z:

⇒ x = 3 − 2z   ... (iv)

⇒ Substitute equation (iv) into equation (iii):

⇒ 3(3 − 2z) − 5z = −13

⇒ 9 − 6z − 5z = −13

⇒ 9 − 11z = −13

⇒ −11z = −13 − 9

⇒ −11z = −22

⇒ z = 2

⇒ Now, substitute z = 2 back into equation (iv):

⇒ x = 3 − 2(2)

⇒ x = 3 − 4 = −1

⇒ Finally, substitute x = −1 and z = 2 into equation (ii) to find y:

⇒ (−1) + 2y + 3(2) = 5

⇒ −1 + 2y + 6 = 5

⇒ 2y + 5 = 5

⇒ 2y = 0

⇒ y = 0

∴ The correct answer is x = −1, y = 0, z = 2.

Additional Information

Linear Equations in Three Variables

A system of three linear equations can have a unique solution, infinite solutions, or no solution depending on the determinants formed by their coefficients.

Substitution Method

This method involves expressing one variable in terms of the others from one equation and substituting it into the remaining equations to reduce the number of variables.

Elimination Method

By multiplying equations with suitable constants and adding or subtracting them, we can eliminate variables step-by-step to efficiently solve the system of equations.

Shortcut Trick

Total increase in salary over 9 years (15 − 6) = ₹52,997 − ₹28,400 = ₹24,597

Since the increment is fixed every year, divide the total increase by the number of years.

⇒ Annual increment = 24597 ÷ 9 = ₹2,733

∴ The correct answer is ₹2,733.

Alternate Method

Given:

Salary after 6 years = ₹28,400

Salary after 15 years = ₹52,997

Year 6 ₹28,400

Year 15 ₹52,997

Gap = 9 Years 9 Increments = ₹24,597

1 Increment = ₹24,597 ÷ 9 = ₹2,733

Calculations:

Let the initial salary be S and the fixed annual increment be I.

⇒ S + 6I = 28400     --- (Equation 1)

⇒ S + 15I = 52997     --- (Equation 2)

Subtracting Equation 1 from Equation 2:

⇒ (S + 15I) − (S + 6I) = 52997 − 28400

⇒ 9I = 24597

⇒ I = 24597 ÷ 9

⇒ I = 2733

∴ The correct answer is ₹2,733.

Additional Information

Arithmetic Progression (AP)

A sequence where the difference between consecutive terms is constant. A salary growing by a fixed increment follows an AP where the nth term is given by T_n = a + (n − 1)d.

Simple Interest Analogy

A fixed annual increment behaves mathematically the same way as Simple Interest, where the principal remains constant and a uniform amount (interest) is consistently added year over year.

Shortcut Trick

Difference in ratio parts of Q and R = 9 − 2 = 7 parts.

Given 7 parts = ₹560 ⇒ 1 part = ₹80.

Share of S = 3 parts.

Share of S = 3 × 80 = ₹240.

∴ The correct answer is ₹240.

Alternate Method

Given:

Ratio of shares of P, Q, R, and S = 4 : 9 : 2 : 3

Difference between the shares of Q and R = ₹560

Calculation:

Let the shares of P, Q, R, and S be 4x, 9x, 2x, and 3x respectively.

⇒ Share of Q − Share of R = 560

⇒ 9x − 2x = 560

⇒ 7x = 560

⇒ x = 560 ÷ 7

⇒ x = 80

⇒ Share of S = 3x

⇒ Share of S = 3 × 80 = 240

∴ The correct answer is ₹240.

Additional Information

Ratio & Proportion

A ratio establishes a quantitative relation between two amounts, reflecting the number of times one contains the other. If quantities are in the ratio a : b, their actual values can be considered as ax and bx for calculation purposes.

Unitary Method

A foundational mathematical technique where the value of a single unit is determined first (e.g., 1 part = Total Difference ÷ Ratio Difference), and then multiplied by the required number of units to find the target answer.

Given:

Marks obtained by Suresh in Mathematics = 70

Marks obtained by Ramesh in Mathematics = 85

Marks obtained by Ankith in Mathematics = 90

Marks obtained by Ranjith in Mathematics = 95

Marks obtained by Aryan in Mathematics = 75

Formula used:

Average marks = $\dfrac{\text{Sum of all marks}}{\text{Number of students}}$

Calculations:

Sum of all marks in Mathematics = 70 + 85 + 90 + 95 + 75

Sum = 415

Number of students = 5

Average marks = $\dfrac{415}{5}$

⇒ Average marks = 83

∴ The average marks obtained by all five students in Mathematics is 83.

Given:

Number of female qualified candidates from State X in 2010 = 168

Ratio of male to female qualified candidates in 2010 = 5 : 7

Percentage of qualified candidates from State X in 2010 = 60%

Formula used:

Let the total number of qualified candidates from State X in 2010 be Q.

Since the ratio of male to female candidates is 5 : 7, the number of female qualified candidates = $\dfrac{7}{12} \times Q$ and the number of male qualified candidates = $\dfrac{5}{12} \times Q$.

Given that the number of female qualified candidates is 168, we can write: $\dfrac{7}{12} \times Q = 168$.

Calculations:

$\dfrac{7}{12} \times Q = 168$

⇒ $Q = 168 × 12 /7$

⇒ $Q = 288$

Now, the total number of qualified candidates from State X in 2010 is 288. Since 60% of the appeared candidates qualify, we can write:

$\dfrac{60}{100} \times \text{Total appeared candidates} = 288$

⇒ $\text{Total appeared candidates} = \frac{288× 100}{60}$

⇒ $\text{Total appeared candidates} = 480$

∴ The number of appeared candidates from State X in 2010 is 480.

Shortcut Trick

Selling Price (SP) can be calculated directly by multiplying the Marked Price with successive discount factors.

SP = MP × (100 − D₁)/100 × (100 − D₂)/100

SP = 1200 × (85/100) × (90/100)

SP = 1200 × 0.85 × 0.9 = 918

∴ The correct answer is ₹918.

Alternate Method

Given:

Marked Price (MP) = ₹1200

Successive discounts = 15% and 10%

Formula Used:

Selling Price = MP × (1 − D₁/100) × (1 − D₂/100)

Calculations:

⇒ Price after 1^st discount = 1200 − (15/100 × 1200)

⇒ Price = 1200 − 180 = ₹1020

⇒ SP after 2^nd discount = 1020 − (10/100 × 1020)

⇒ SP = 1020 − 102 = ₹918

∴ The correct answer is ₹918.

Additional Information

Effective Discount Formula

When two successive discounts of A% and B% are given, the equivalent single discount can be directly determined using: D = (A + B − A×B/100)%.

Relation between MP, CP, Profit%, and Discount%

The exact ratio of Marked Price (MP) to Cost Price (CP) when a certain profit is made after giving a discount is: MP/CP = (100 + Profit%) / (100 − Discount%).

Buy X Get Y Free Discount

In scenarios involving free items, the net percentage discount is computed as: Discount % = [Y ÷ (X + Y)] × 100.

The correct answer is: Option 3.

Key Points

• "clique" is a small, exclusive group of people with shared interests or other features in common, who spend time together and do not readily allow others to join them. (गुट)
• Example: The high school students formed a clique that was difficult for outsiders to penetrate.

Therefore, the correct answer is: Option 3 i.e. clique.

Additional Information

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

• Oblique (तिरछा): Neither parallel nor at a right angle to a specified or implied line; slanting.
• Example: The artist drew oblique lines to create an abstract pattern.
• Pique (आक्रोश): A feeling of irritation or resentment resulting from a slight, especially to one's pride.
• Example: She left the meeting in a fit of pique after her ideas were dismissed.
• Antique (पुराना): A collectible object such as a piece of furniture or work of art that has a high value because of its considerable age.
• Example: She collects antique jewelry from the Victorian era.

The correct answer is: Option 3.

Key Points

• The word "telescope" means an instrument designed for viewing distant objects, especially in space. (दूरबीन)
• Example: Galileo used a telescope to observe the moons of Jupiter.
• "Telescope" allows astronomers to see far-away celestial bodies like stars, planets, and galaxies. (दूरबीन)
• Example: The Hubble Space Telescope has provided some of the most detailed images of the universe.

Therefore, the correct answer is: Option 3.

Additional Information

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

• Microscope (सूक्ष्मदर्शी): An instrument used for viewing very small objects, such as cells, that are not visible to the naked eye.
• Example: The scientist used a microscope to examine the bacteria.
• Spectrograph (स्पेक्ट्रोग्राफ): An instrument that separates light into a frequency spectrum and records the signal using a camera.
• Example: The spectrograph was used to analyze the light from the distant star.
• Binoculars (दूरबीन): An optical instrument with a lens for each eye, used for viewing distant objects.
• Example: We used binoculars to watch the birds from afar.

The correct answer is: Option 4.

Key Points

• "Upstairs" refers to the upper floor of a building. (ऊपरी मंजिल)
• Example: I was upstairs when somebody rang the doorbell.
• Hence, the correct spelling of the word is "Upstairs".

Therefore, the correct answer is: Option 4.

Additional Information

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

• Upstares (गलत वर्तनी): Incorrect spelling of "Upstairs".
• Example: Incorrect usage in the sentence.
• Upstaire (गलत वर्तनी): Incorrect spelling of "Upstairs".
• Example: Incorrect usage in the sentence.
• upsatires (गलत वर्तनी): Incorrect spelling of "Upstairs".
• Example: Incorrect usage in the sentence.

The correct answer is: Option 2.

Key Points

• The word "Adversity" means a difficult or unpleasant situation. (कठिनाई)
• Example: She showed great courage in the face of adversity.
• "Misfortune" refers to bad luck or an unlucky event. (दुर्भाग्य)
• Example: He had the misfortune of losing his wallet on the trip.
• Hence, we can infer that the synonym of 'Adversity' is 'Misfortune'.

Therefore, the correct answer is: Option 2.

Additional Information

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

• Success (सफलता): The accomplishment of an aim or purpose.
• Example: His hard work led to great success in his career.
• Pleasure (सुख): A feeling of happy satisfaction and enjoyment.
• Example: She finds great pleasure in reading books.
• Advantage (लाभ): A condition or circumstance that puts one in a favorable or superior position.
• Example: Having a car gives you an advantage when traveling long distances.

The correct answer is: Option 2.

Key Points

• The word "Forbid" means to refuse to allow (something); to order (someone) not to do something. (मना करना)
• Example: The school forbids students from using mobile phones during classes.
• "Allow" refers to letting (someone) do something; giving permission for something. (अनुमति देना)
• Example: Parents should allow their children to express their opinions freely.
• Hence, we can infer that the opposite of 'Forbid' is 'Allow'.

Therefore, the correct answer is: Option 2.

Additional Information

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

• Prohibit (प्रतिबंधित करना): Formally forbid (something) by law, rule, or other authority.
• Example: The new policy will prohibit smoking in all public places.
• Call (बुलाना): To cry out in a loud voice; to summon.
• Example: She called out for help when she saw the fire.
• Forsake (त्यागना): To abandon or leave (someone or something).
• Example: He decided to forsake his job to pursue his passion for painting.

The correct answer is Option (1) i.e. DCBAE

Key Points

• The sentence logically starts with the phrase that sets the context of the situation, which is part (D) "despite the heavy traffic."
• Next follows part (C) "the boss arrived at the," which continues the main clause.
• Then part (B) "meeting on time," completes the main clause describing the boss's punctuality.
• Part (A) "while the employees," adds a subordinate clause introducing a comparison group affected by the situation.
• Finally, part (E) "were late," completes the sentence by specifying the state of the employees.

Therefore, the correct answer is DCBAE.

Additional Information

• Option 2 (DACEB): This option places part A too early, disrupting the flow of the contextual information.
• Option 3 (BACED): This option starts with part B, which leads to a confusing sentence structure and disrupts logical sequencing.
• Option 4 (ACEDB): This option starts with part A, which disrupts the flow and logical order of the sentence.

The correct answer is 'D' i.e. this part of the sentence has an error.

Key Points

• The phrase 'laid down a treasure of substantiation' is incorrect. The correct phrasal verb to use in this context is 'laid out a treasure of substantiation'.
• The word 'laid out' means to explain or present something clearly.
• This phrasal verb is appropriate because Darwin's book presents a well-explained and clear body of evidence for the theory of evolution.

Hence, the correct answer is option 4.

Correct sentence: Charles Darwin is renowned for his book on evolution, 'On the Origin of Species', which laid out a treasure of substantiation that evolution occurs, and projected a mechanism, that is, natural selection, for how it does so.

Additional Information

• When using phrasal verbs such as 'laid out', ensure they fit the context of the sentence for proper meaning.
• Each phrasal verb has a specific usage, and using them correctly enhances sentence clarity and coherence.