SSC CGL 2024 Tier-I Official Paper (Held On: 24 Sept, 2024 Shift 1) (Previous Year Paper)

The logic followed here is:

Given Sequence: _TUVTR_WU_UXVN_Y

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

Option 1) SUUP → STUV / TRUW / UUUX / VNPY

Option 2) SUPU → STUV / TRUW / UPUX / VNUY

Option 3) SVUP → STUV / TRVW / UUUX / VNPY

Option 4) PSVU → PTUV / TRSW / UVUX / VNUY

Hence, the correct answer is "SUPU".

Statements:

All spoons are forks.

All forks are knives.

No knife is a spatula.

The least possible Venn diagram is as follows:

Conclusions:

I. Some knives are spoons. - True (because All spoons are forks, and All forks are knives. So, Some knives are spoons too)

II. No fork is a spatula. - True (because All forks are knives and No knife is a spatula. So, No fork is a spatula it is true)

Hence, the correct answer is "Only conclusions I and II follow".

The logic followed here is:

Hence, the correct answer is "92".

BODMAS Table: 

After decoding signs:

 

Given equation: 125 ÷ 5 + 1809 × 9 – 14 = ?

After interchanging the signs then:

⇒ 125 × 5 - 1809 ÷ 9 + 14 = ?

⇒ 125 × 5 - 201 + 14

⇒ 625 - 201 + 14

⇒  639 - 201 = 438

Hence, the correct answer is "438".

The logic followed here is:

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

Now,

For (8, 9, 7):

⇒ (9 + 7) ÷ 2

⇒ 16 ÷ 2 = 8.

For (24, 13, 35):

⇒ (13 + 35) ÷ 2

⇒ 48 ÷ 2 = 24.

Similarly, for (17, 11, 23):

⇒ (11 + 23) ÷ 2

⇒ 34 ÷ 2 = 17.

Hence, the correct answer is "Option 1".

The logic followed here is:

'RX-21' is related to 'UU-11' 

'PM-39' is related to 'SJ-29'

Similarly, DP-17 is related to:

Hence, the correct answer is "GM-7".

The logic followed here is:

'PUPIL' is written as '162116912'

'PURGE’ is written as '16211875'

Similarly, 'PURSE' will be written as:

Hence, the correct answer is "162118195".

The logic followed here is:

From figure 1 to 2 and figure 3 to 4:

Symbols are shifting their position in zig-zag way.

From figure 2 to 3 and figure 4 to 5:

Top-right, middle, and bottom-left symbols are interchanging their position.

Top-left and bottom-right letters are interchanging their position.

Hence, the correct answer is "Option 2".

BODMAS Table: 

Given equation: 20 + 4 ÷ 2 × 3 − 6 = ?

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

⇒ 20 ÷ 4 + 2 − 3 × 6 = ?

⇒ 20 ÷ 4 + 2 − 3 × 6 = ?

⇒ 5 + 2 − 18 = ?

⇒ 7 − 18 = −11.

Hence, the correct answer is "Option 3".

The logic followed here is:

From figure 1 to 2 and figure 3 to 4:

Top and bottom letters are the same.

All 3 horizontal symbols are shifting their position in a circular way.

From figure 2 to 3 and figure 4 to 5:

Left and right letters are the same.

All 3 vertical symbols are shifting their position in a circular way.

Hence, the correct answer is "Option 2".

For find the opposite surface of 'Eat', we need to compare the common surface in the given dices,

So, From Dice 1 and Dice 2,

From both dices, Cry and Play are common. So, remaining surface will be opposite to each other.

So, Dance will be opposite to Eat.

Hence, the correct answer is "Dance ".

Given word: 'DELIGHT'

After arranged in alphabetical order:

 

Now,

there are Three alphabets "D", "E", and "T" that will remain unchanged if each of the letters in the word 'DELIGHT' is arranged in English alphabetical order.

Hence, the correct answer is "Option 4".

Given Statements:

Some Mirrors are Decoratives.

No Decorative is a Plant.

All Plants are Trees.

The least possible Venn diagram is as follows:

Conclusions:

(I) Some Mirrors are Plants. - False (because there is no direct relation between mirror and plants so it can be possible but not definite)

(II) Some Decoratives are Trees. - False (because there is no direct relation between Decoratives are Trees so it can be possible but not definite)

Hence, the correct answer is "Neither conclusion (I) nor (II) follows".

The correct mirror image of the given figure is:

Hence, the correct answer is "Option 3".

The correct mirror image of the given figure is:

Hence, the correct answer is "Option 3".

For find the opposite surface of 'O', we need to compare the common surface in the given dices,

So, From Dice 1 and Dice 2,

From both dices, O is common and on the same surface. So, all remaining surface will be opposite to each other.

M is opposite to P.

N is opposite to Q.

So, R will be opposite to O.

Hence, the correct answer is "R".

According to the given information:

Thus the code for 'S' = 6

Hence, the correct answer is "6".

The logic followed here is: 1st number × 2 + 3rd number = 2nd number.

1)  12 – 122 – 99 → 12 × 2 + 99 = 24 + 99 = 123 ≠ 122

2)   89 – 212 – 34 → 89 × 2 + 34 = 178 + 34 = 212

3)  23 – 84 – 38 → 23 × 2 + 38 = 46 + 38 = 84

4)  58 – 139 – 23 → 58 × 2 + 23 = 116 + 23 = 139

Hence, the correct answer is "12 – 122 – 99".

The logic followed here is:

Logic: (1st number × 10) + 10 = 2nd number.

Now,

For, 33 : 340

⇒ (33 × 10) + 10

⇒ 330 + 10 = 340.

For, 48 : 490

⇒ (48 × 10) + 10

⇒ 480 + 10 = 490.

Similarly, for 63 : 640

⇒ (63 × 10) + 10

⇒ 630 + 10 = 640.

Hence, the correct answer is "Option 3".

Counting the triangles in the figure:

Hence, the correct answer is "11".

The logic followed here is:

LOI : QTN

VES : AJX

Similarly, AND : ?

Hence, the correct answer is "FSI".

The logic followed here is:

Option 1) CBE

Option 2) NMP

Option 3) UTW

Option 4) LKM

Hence, the correct answer is "LKM".

The logic followed here is:

Hence, the correct answer is "BOK".

The logic follows here is:

Logic: n³ - 3 & n² + 2

Now,

61 is related to 18

→ 4³ - 3 = 64 - 3 = 61,

→ 4² + 2 = 16 + 2 = 18.

213 is related to 38

→ 63 - 3 = 216 - 3 = 213,

→ 62 + 2 = 36 + 2 = 38.

Similarly, for 509

→ 83 - 3 = 512 - 3 = 509,

→ 82 + 2 = 64 + 2 = 66.

Hence, the correct answer is "Option 1".

Family Chart:

Given: A is the sister of B, C is the daughter of A, D is the sister of A and E is the brother of C.

So, D is the "Mother's sister" of E.

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

The correct answer is Tanvi Shah.

Key Points

• Tanvi Shah is an Indian playback singer who contributed to the song 'Jai Ho' from the movie Slumdog Millionaire.
• She became the first Indian woman to win a Grammy Award for her vocals in the song 'Jai Ho'.
• The song 'Jai Ho' was composed by AR Rahman with lyrics by Gulzar.
• The song won the Grammy Award for Best Song Written for Visual Media at the 52nd Annual Grammy Awards in 2010.

Additional Information

• Grammy Awards
• The Grammy Awards are presented by the Recording Academy to recognize achievements in the music industry.
• They were first established in 1959 and are considered one of the most prestigious awards in the music industry.
• The awards are given in various categories including Best New Artist, Record of the Year, Album of the Year, and Song of the Year.
• 'Jai Ho'
• 'Jai Ho' is a song composed by AR Rahman for the 2008 film Slumdog Millionaire.
• The song features a mix of Hindi, Urdu, and Punjabi lyrics, and was a significant part of the film's soundtrack.
• It gained international acclaim and contributed to the film's success, both critically and commercially.
• Slumdog Millionaire
• Slumdog Millionaire is a 2008 British drama film directed by Danny Boyle.
• The film is based on the novel 'Q & A' by Vikas Swarup and tells the story of a young man from the slums of Mumbai who competes on the Indian version of Who Wants to Be a Millionaire?
• The film was a major critical and commercial success, winning eight Academy Awards, including Best Picture and Best Director.

The correct answer is 1236 AD.

Key Points

• Raziya Sultan ascended the throne in 1236 AD, making her the first and only female ruler of the Delhi Sultanate.
• She was the daughter of Shams-ud-din Iltutmish, the third ruler of the Mamluk dynasty of Delhi.
• Raziya Sultan was known for her administrative skills and efforts to promote justice and equality in her kingdom.
• Despite facing opposition from the nobility, she managed to rule effectively for a short period.

Additional Information

• Delhi Sultanate
• The Delhi Sultanate was a Muslim kingdom based mostly in Delhi that stretched over large parts of the Indian subcontinent for 320 years (1206–1526).
• Five dynasties ruled over the Delhi Sultanate sequentially: the Mamluk (Slave) dynasty, the Khilji dynasty, the Tughlaq dynasty, the Sayyid dynasty, and the Lodi dynasty.
• The Sultanate is known for its cultural and architectural contributions, including the construction of Qutub Minar and the establishment of Islamic architecture in India.
• Mamluk Dynasty
• The Mamluk Dynasty, also known as the Slave Dynasty, was the first dynasty to rule the Delhi Sultanate from 1206 to 1290.
• It was founded by Qutb-ud-din Aibak, a former slave who became a general and later the Sultan of Delhi.
• The dynasty is noted for its military prowess and the establishment of a centralized administrative system in Northern India.
• Raziya Sultan
• Raziya Sultan (1205–1240) was the first and only female ruler of the Delhi Sultanate.
• She was known for dressing like a man and leading her troops into battle, challenging the traditional gender roles of her time.
• Raziya was a competent and just ruler, but her reign was cut short due to internal conflicts and opposition from the Turkish nobles.
• Her legacy remains as a symbol of female empowerment and leadership in a male-dominated society.

The correct answer is NW 5.

Key Points

• NW 5 stands for National Waterway 5 in India.
• NW 5 connects the delta channels of Mahanadi and Brahmani rivers and the East Coast Canal.
• National Waterway 5 is a significant part of India's inland water transport system.
• It plays a crucial role in the transportation of goods and resources through the states of Odisha and West Bengal.

Additional Information

• National Waterways in India:
• India has a network of inland waterways in the form of rivers, canals, backwaters, and creeks.
• National Waterways are a key component of the inland water transport system in India.
• The Inland Waterways Authority of India (IWAI) is the statutory authority in charge of these waterways.
• NW 1: Ganga-Bhagirathi-Hooghly river system from Allahabad to Haldia (1,620 km).
• NW 2: Brahmaputra river from Dhubri to Sadiya (891 km).
• NW 3: West Coast Canal from Kottapuram to Kollam (205 km).
• NW 4: Godavari and Krishna rivers along with Kakinada-Puducherry canal (1,095 km).
• NW 5: East Coast Canal integrated with Brahmani and Mahanadi delta rivers (588 km).
• Inland Waterways Authority of India (IWAI):
• The IWAI was constituted in 1986 by an Act of Parliament.
• It is responsible for the development and regulation of inland waterways for shipping and navigation.
• The authority primarily undertakes projects for the development of infrastructure, including dredging, construction of terminals, and navigation aids.
• Importance of Inland Water Transport:
• Inland water transport is cost-effective and environment-friendly.
• It reduces congestion on road and rail networks.
• It supports the movement of bulk goods such as coal, iron ore, food grains, and cement.
• It promotes regional and rural development by improving connectivity.

The correct answer is Dr. YV Reddy; 1998.

Key Points

• The Working Group under the chairmanship of Dr. YV Reddy was constituted in 1998.
• The group proposed a new intermediate monetary aggregate to be referred to as NM2.
• Dr. YV Reddy was a prominent Indian economist and served as the 21st Governor of the Reserve Bank of India.
• The proposal for NM2 was part of an effort to refine and improve the country's monetary policy framework.

Additional Information

• Monetary Aggregates:
• Monetary aggregates are broad categories measuring the total value of the money supply within an economy. They include various forms of money such as cash, demand deposits, and near money.
• They are used by central banks to assess the amount of money circulating within an economy, helping in formulating monetary policy.
• Common monetary aggregates include M1, M2, M3, and M4, which represent different levels of liquidity.
• Intermediate Monetary Aggregate NM2:
• NM2 is an intermediate monetary aggregate proposed to provide a better understanding and control over the monetary supply.
• It typically includes cash, demand deposits, and other near money instruments which are less liquid than those in M1 but more liquid than those in M3.
• Dr. YV Reddy:
• Yaga Venugopal Reddy served as the 21st Governor of the Reserve Bank of India from 2003 to 2008.
• He played a crucial role in shaping India's monetary policy and was known for his efforts to maintain financial stability.
• He was also involved in various international financial institutions and contributed significantly to economic policy discussions.

The correct answer is Maharashtra.

Key Points

• Tadoba National Park is located in the Chandrapur district of Maharashtra.
• It is also known as Tadoba Andhari Tiger Reserve, which is the largest and oldest national park in Maharashtra.
• The park was established in 1955 and covers an area of approximately 1,727 square kilometers.
• Tadoba National Park is famous for its significant population of Bengal tigers and is a prominent destination for wildlife enthusiasts and photographers.

Additional Information

• National Parks in India
• National parks are protected areas established by the government for the conservation of wildlife and biodiversity.
• India is home to a diverse range of national parks, each offering unique habitats and species.
• Some other famous national parks in India include Jim Corbett National Park in Uttarakhand, Kaziranga National Park in Assam, and Ranthambore National Park in Rajasthan.
• These parks play a crucial role in the conservation of endangered species and serve as important research and education centers.
• Tiger Reserves in India
• India is home to more than 50 tiger reserves, which are established under the Project Tiger initiative launched in 1973.
• Tiger reserves aim to protect and increase the population of Bengal tigers in the country.
• These reserves provide a safe habitat for tigers and other wildlife, while also promoting eco-tourism and community involvement in conservation efforts.
• The Tadoba Andhari Tiger Reserve is one of the most popular and successful tiger reserves in India.
• Biodiversity in Maharashtra
• Maharashtra is a state with rich biodiversity, encompassing various ecosystems such as forests, grasslands, and coastal regions.
• The state is home to several national parks, wildlife sanctuaries, and conservation reserves.
• In addition to Tadoba National Park, other notable protected areas in Maharashtra include Sanjay Gandhi National Park, Navegaon National Park, and Melghat Tiger Reserve.
• The state's diverse flora and fauna contribute to its ecological significance and attract nature enthusiasts from around the world.

The correct answer is To promote harmony and spirit of brotherhood.

Key Points

• The fundamental duty to promote harmony and the spirit of common brotherhood amongst all the people of India transcending religious, linguistic, regional, or sectional diversities is crucial in maintaining unity in diversity.
• This duty highlights the importance of respecting and tolerating different beliefs and practices within the country.
• It encourages citizens to rise above narrow considerations of caste, creed, and religion and to work towards the welfare of society as a whole.
• Promoting harmony and brotherhood is essential for fostering an environment where different communities can coexist peacefully and contribute to national development.

Additional Information

• Fundamental Duties:
• Fundamental Duties are a set of moral obligations that all citizens are expected to follow and respect.
• These duties were added to the Indian Constitution by the 42nd Amendment Act, 1976, under Article 51A.
• Initially, there were ten fundamental duties, and later, an eleventh duty was added by the 86th Amendment Act, 2002.
• Although these duties are non-justiciable, meaning they are not legally enforceable, they serve as a constant reminder of the responsibilities that come with citizenship.
• Promoting Harmony and Brotherhood:
• This duty is essential in a multicultural and pluralistic society like India, where people from various backgrounds coexist.
• It emphasizes the need for mutual respect, tolerance, and understanding among different communities.
• By promoting harmony, citizens can help prevent conflicts and ensure a peaceful and cohesive society.
• This duty also underscores the importance of national integration and unity, which are vital for the country's progress and development.
• Respect for Diversity:
• India is known for its rich cultural, religious, and linguistic diversity.
• Respecting this diversity is crucial for maintaining social harmony and fostering a sense of belonging among all citizens.
• Encouraging dialogue and interaction between different communities can help bridge gaps and build stronger relationships.
• Diversity should be seen as a strength and a source of inspiration for collective growth and development.

The correct answer is 1920.

Key Points

• The All India Trade Union Congress (AITUC) was established on 31 October 1920.
• It is the first national trade union in India.
• AITUC played a significant role in the Indian labour movement and is affiliated with the Communist Party of India.
• The founding conference of AITUC was held in Bombay (now Mumbai) with Lala Lajpat Rai as its first president.

Additional Information

• Trade Union
• A trade union is an organization of workers formed to protect and advance their rights and interests.
• Trade unions negotiate with employers on behalf of their members on issues such as wages, working conditions, and benefits.
• They also provide legal representation and support to members in disputes with employers.
• Trade unions play a crucial role in advocating for labor laws and policies that benefit workers.
• AITUC's Role in Indian Independence
• AITUC was actively involved in the Indian independence movement.
• It organized strikes and protests to challenge British colonial rule and demand better working conditions for Indian workers.
• Many prominent leaders of the independence movement, including Mahatma Gandhi and Jawaharlal Nehru, supported the activities of AITUC.
• After independence, AITUC continued to advocate for workers' rights and social justice in independent India.
• Communist Party of India (CPI)
• The Communist Party of India is one of the oldest political parties in India, founded in 1925.
• The CPI has historically been aligned with the Soviet Union and promoted Marxist-Leninist ideologies.
• The party played a significant role in the labor and peasant movements in India.
• AITUC is closely associated with CPI, and many of its leaders have been prominent members of the party.

The correct answer is Swami Dayanand Saraswati.

Key Points

• Swami Dayanand Saraswati was a renowned Hindu religious scholar, reformer, and the founder of the Arya Samaj.
• He established the Arya Samaj in Mumbai in 1875, which aimed at reviving Vedic ideologies.
• Swami Dayanand emphasized the values of the Vedas and sought to eradicate superstitions and societal evils prevalent in the Hindu society.
• He was a strong advocate of women's education and the upliftment of the underprivileged in society.

Additional Information

• Arya Samaj
• The Arya Samaj is a socio-religious reform movement in India that promotes values and practices based on the belief in the infallibility of the Vedas.
• It was founded by Swami Dayanand Saraswati on April 10, 1875, in Mumbai.
• The movement's slogan is "Krinvanto Vishwam Aryam" which means "Make the world noble".
• Arya Samaj has been instrumental in promoting education, especially for women, and eradicating social evils like child marriage and caste discrimination.
• Swami Dayanand Saraswati
• Born as Mool Shankar Tiwari on February 12, 1824, in Tankara, Gujarat.
• He was a staunch critic of idolatry and ritualistic worship and advocated for a return to the teachings of the Vedas.
• His notable work, "Satyarth Prakash" (The Light of Truth), outlines his vision of a reformed society.
• He also established educational institutions like the Dayanand Anglo-Vedic (DAV) schools and colleges.
• Debendranath Tagore
• He was a Hindu philosopher and religious reformer, associated with the Brahmo Samaj.
• He was the father of Nobel laureate Rabindranath Tagore.
• Though not directly related to the Arya Samaj, he played a significant role in the religious and social reform movements in Bengal.
• Swami Vivekanand
• Born as Narendranath Datta on January 12, 1863, he was a chief disciple of the 19th-century Indian mystic Ramakrishna.
• He founded the Ramakrishna Mission and the Ramakrishna Math.
• He is best known for his speech at the Parliament of the World's Religions in Chicago in 1893, where he introduced Hinduism to the Western world.
• Raja Ram Mohan Roy
• He was a prominent social and educational reformer who is often called the "Father of the Indian Renaissance".
• He founded the Brahmo Samaj in 1828, which played a key role in reforming and modernizing Indian society.
• He was a proponent of women's rights, especially the abolition of Sati and child marriage, and promoted the education of women.

The correct answer is Fragmentation.

Key Points

• Fragmentation is a form of asexual reproduction where the parent organism breaks into fragments, and each fragment can grow into a new organism.
• Red algae, which are primarily aquatic organisms, commonly reproduce by fragmentation.
• This method of reproduction ensures that red algae can quickly colonize an area, especially when conditions are favorable.
• Fragmentation in red algae can occur naturally due to water currents, or it can be induced by external factors such as being grazed by herbivores.

Additional Information

• Grafting
• Grafting is a horticultural technique where tissues from one plant are inserted into those of another so that the two sets of vascular tissues may join together.
• It is commonly used in agriculture and horticulture to propagate clones of desired plants.
• Cutting
• Cutting is a method of plant propagation where a piece of the plant, typically a stem or leaf, is cut and placed in a suitable environment to grow into a new plant.
• It is widely used for the propagation of houseplants and garden plants.
• Micropropagation
• Micropropagation is a method used to multiply plants under sterile conditions, often from very small plant parts, such as cells or tissues.
• It is used for the rapid multiplication of plants and the production of disease-free plants.
• Fragmentation
• As mentioned, fragmentation is a form of asexual reproduction where an organism is split into fragments, each capable of growing independently into a new organism.
• It is a common method of reproduction in many algae, including red algae, as well as in some plants and fungi.

This source code provides a detailed explanation of the correct answer with key points and additional information about the terminologies associated with the question.

The correct answer is Lord Ripon.

Key Points

• Lord Ripon is known as the father of local self-government in India for his efforts to introduce local governance reforms.
• In 1882, he passed a resolution that laid the foundation for local self-governance in India.
• His resolution allowed for the formation of local bodies with elected representatives, marking a significant step towards decentralization.
• Lord Ripon's reforms aimed to improve administrative efficiency and encourage public participation in local governance.

Additional Information

• Lord Cornwallis
• Lord Cornwallis served as the Governor-General of India from 1786 to 1793.
• He is known for his role in the establishment of the Permanent Settlement of Bengal in 1793, which introduced a new land revenue system.
• This system had long-lasting effects on the agrarian structure of Bengal and other parts of India.
• Lord Wellesley
• Lord Wellesley served as the Governor-General of India from 1798 to 1805.
• He is known for his aggressive expansionist policies and the establishment of British supremacy in India through the policy of Subsidiary Alliances.
• His tenure saw the defeat of Tipu Sultan in the Fourth Anglo-Mysore War and the annexation of large territories.
• Lord William Bentinck
• Lord William Bentinck served as the Governor-General of India from 1828 to 1835.
• He is known for his social and administrative reforms, including the abolition of Sati and suppression of Thuggee.
• He also introduced English as the medium of instruction in Indian education.
• Local Self-Government
• Local self-government refers to the administration of local areas by elected representatives who are accountable to the local community.
• It aims to decentralize administrative functions and promote public participation in governance.
• Local self-governance in India includes institutions like Panchayats in rural areas and Municipalities in urban areas.
• These institutions play a crucial role in the delivery of basic services, local development, and civic engagement.

The correct answer is Curling of milk.

Key Points

• Curling of milk is a chemical change.
• In this process, the proteins in the milk coagulate, forming curds and whey.
• This change is irreversible, which is a characteristic of chemical changes.
• The chemical composition of the milk changes during this process.

Additional Information

• Physical Change
• A physical change is a change in the state or properties of matter without any accompanying change in its chemical composition.
• Examples include melting, boiling, freezing, and cutting.
• Physical changes are usually reversible.
• In the options provided, heating of iron rod to red hot, evaporation of diesel, and sublimation of NH4Cl are all physical changes.
• Chemical Change
• A chemical change results in the formation of one or more new substances with new chemical and physical properties.
• Examples include rusting of iron, burning of wood, and fermentation.
• Chemical changes are usually not reversible.
• In the options provided, curling of milk is a chemical change.
• Heating of Iron Rod to Red Hot
• This is a physical change as it involves a change in the temperature of the iron rod.
• The iron rod can return to its original state when it cools down.
• Evaporation of Diesel
• This is a physical change where diesel changes from liquid to vapor.
• The process is reversible through condensation.
• Sublimation of NH4Cl
• Sublimation is the transition of a substance from solid to gas without passing through the liquid state.
• This is a physical change as it involves a change in state.
• The process is reversible; NH4Cl gas can be condensed back to solid.

The correct answer is Rohit Sharma and Jasprit Bumrah.

Key Points

• Rohit Sharma and Jasprit Bumrah were named the Wisden's cricketers of the year in the 2022 edition of the Almanack.
• This prestigious recognition is awarded by Wisden, a cricket reference book published annually in the United Kingdom.
• Rohit Sharma, known for his exceptional batting skills, has been a significant contributor to Indian cricket with numerous records to his name.
• Jasprit Bumrah, acclaimed for his unique bowling action and ability to deliver in crunch situations, has been a vital part of India's bowling attack.

Additional Information

• Wisden Cricketers' Almanack
• Often referred to simply as "Wisden" or "the Bible of Cricket," it is a cricket reference book published annually in the UK.
• It is considered the world's most famous sports reference book.
• The Almanack features articles, essays, and match reports, along with statistics and records.
• Wisden Cricketers of the Year are considered one of the highest honors in the sport, recognizing excellence in cricket.
• Rohit Sharma
• Rohit Sharma is an Indian international cricketer and the current captain of the Indian national team.
• He is a right-handed batsman and an occasional right-arm off-break bowler.
• Rohit is known for his record of scoring three double centuries in One Day Internationals (ODIs).
• He has also achieved the highest individual score in ODIs with 264 runs.
• Jasprit Bumrah
• Jasprit Bumrah is an Indian international cricketer who plays for the Indian national team in all formats of the game.
• He is known for his unorthodox bowling action and deadly yorkers.
• Bumrah has been a key player for India in both Test and limited-overs cricket.
• He is recognized for his ability to bowl in the death overs and his skill in swinging the ball both ways.

The correct answer is Betanin.

Key Points

• Betanin is a red pigment found in beetroots and is responsible for their characteristic color.
• It belongs to the class of betalains, which are water-soluble pigments.
• Betanin is used as a natural food colorant and has the E number E162.
• In addition to its coloring properties, betanin also exhibits antioxidant properties, which can provide health benefits.

Additional Information

• Curcumin
• Curcumin is a bright yellow chemical produced by some plants, mainly turmeric.
• It is used as a dietary supplement, in cosmetics, as a food coloring, and as flavoring in food.
• It has anti-inflammatory and antioxidant properties and is being studied for its potential health benefits.
• Beta Carotene
• Beta carotene is a red-orange pigment found in plants and fruits, especially carrots and colorful vegetables.
• It is a precursor of vitamin A, which is essential for vision, immune function, and skin health.
• Beta carotene is also an antioxidant, which helps protect cells from damage.
• Lycopene
• Lycopene is a bright red carotenoid hydrocarbon found in tomatoes and other red fruits and vegetables.
• It has antioxidant properties and may help prevent certain diseases, including heart disease and cancer.
• Lycopene is used as a food coloring and is also available as a dietary supplement.

The correct answer is Delhi, Chandigarh and Puducherry.

Key Points

• According to the Census of India 2011, Delhi, Chandigarh, and Puducherry are the Union Territories with the highest density of population.
• Delhi has the highest population density among all Union Territories and states in India.
• Chandigarh, being a well-planned city and a union territory, also has a high population density.
• Puducherry, with its small area and high population, ranks among the top Union Territories in terms of population density.

Additional Information

• Population Density
• Population density is defined as the number of people living per unit area of land, usually expressed as persons per square kilometer or square mile.
• It is an important parameter to understand the distribution of population in a region and helps in planning and development.
• Delhi
• Delhi is the capital city of India and has the highest population density in the country.
• According to the 2011 Census, Delhi's population density is 11,320 persons per square kilometer.
• Delhi's high population density is due to its status as the capital, attracting people from all over the country for employment, education, and better living standards.
• Chandigarh
• Chandigarh is a Union Territory that serves as the capital of both Punjab and Haryana.
• It is known for its well-planned layout and high standard of living.
• The population density of Chandigarh is 9,252 persons per square kilometer as per the 2011 Census.
• Puducherry
• Puducherry is a Union Territory comprising four small unconnected districts.
• It has a population density of 2,547 persons per square kilometer as per the 2011 Census.
• Puducherry's higher population density is attributed to its small geographical area combined with a relatively high population.

The correct answer is Article 54.

Key Points

• Article 54 of the Indian Constitution deals with the election of the President of India.
• The President is elected by an electoral college consisting of the elected members of both Houses of Parliament and the elected members of the Legislative Assemblies of States and Union territories.
• The process of election is conducted by the Election Commission of India.
• The election is held in accordance with the system of proportional representation by means of the single transferable vote.

Additional Information

• Article 72:
• Article 72 of the Indian Constitution empowers the President to grant pardons, reprieves, respites or remissions of punishment or to suspend, remit or commute the sentence of any person convicted of any offense.
• This power can be exercised in all cases where the punishment or sentence is by a court-martial, in cases where the punishment or sentence is for an offense against any law relating to a matter to which the executive power of the Union extends, and in all cases where the sentence is a sentence of death.
• Article 54:
• Article 54 deals with the election of the President.
• The President is elected by an electoral college consisting of elected members of both Houses of Parliament and Legislative Assemblies of States and Union territories.
• The election is held in accordance with the system of proportional representation by means of the single transferable vote.
• Article 74:
• Article 74 of the Indian Constitution states that there shall be a Council of Ministers with the Prime Minister at the head to aid and advise the President.
• The President shall, in the exercise of his functions, act in accordance with such advice.
• Article 66:
• Article 66 deals with the election of the Vice-President of India.
• The Vice-President is elected by the members of an electoral college consisting of the members of both Houses of Parliament.
• The election is held in accordance with the system of proportional representation by means of the single transferable vote.

The correct answer is Neon sign bulbs.

Key Points

• Neon sign bulbs are an excellent example of plasma as a state of matter.
• Plasma is created in neon sign bulbs when an electric current passes through the gas, ionizing it and creating plasma.
• The plasma in neon sign bulbs emits light, which is characteristic of neon signs.
• Plasma is the fourth state of matter, distinct from solid, liquid, and gas, and is created under high-energy conditions.

Additional Information

• Plasma
• Plasma is known as the fourth state of matter, consisting of a collection of free-moving ions and electrons.
• It is formed at very high temperatures when gases are ionized.
• Examples of plasma include the Sun, stars, lightning, and neon signs.
• Plasma is distinct from the other states of matter due to its unique properties such as electrical conductivity, magnetic fields, and the ability to emit light.
• Neon
• Neon is a noble gas that is colorless, odorless, and inert under standard conditions.
• It is used in neon signs where it emits a bright orange-red light when electrified.
• Neon signs work by passing an electric current through the neon gas, which ionizes the atoms and creates plasma.
• Ionization
• Ionization is the process by which an atom or molecule gains or loses electrons, forming ions.
• This process is fundamental in the formation of plasma.
• Ionization can occur through various means such as heating, electric fields, or radiation.

The correct answer is Padma Vibhushan.

Key Points

• Amjad Ali Khan is a renowned Indian classical musician who plays the sarod.
• He was awarded the Padma Vibhushan in 2001 by the Government of India.
• The Padma Vibhushan is the second-highest civilian award in India, given for exceptional and distinguished service.
• Amjad Ali Khan has received numerous other accolades for his contributions to Indian classical music, including the Padma Shri and Padma Bhushan.

Additional Information

• Padma Awards
• The Padma Awards are one of the highest civilian honors of India announced annually on the eve of Republic Day.
• They are given in three categories: Padma Vibhushan (for exceptional and distinguished service), Padma Bhushan (for distinguished service of a high order), and Padma Shri (for distinguished service).
• Instituted in 1954, these awards recognize achievements in all fields of activities or disciplines where an element of public service is involved.
• The awards are conferred by the President of India at ceremonial functions which are held at Rashtrapati Bhawan usually around March/April every year.
• Sarod
• The sarod is a stringed musical instrument used mainly in Indian classical music.
• It is known for its deep, weighty, introspective sound, and is an important instrument in the Hindustani classical tradition.
• The sarod is believed to have descended from the Afghan rubab.
• The instrument has a fretless fingerboard, and it is played with a plectrum.
• Amjad Ali Khan
• Amjad Ali Khan is one of the foremost sarod players in the world.
• He was born on October 9, 1945, into a family of musicians. His father, Haafiz Ali Khan, was also a famous sarod player.
• Amjad Ali Khan has performed at various prestigious venues around the world and has been honored with numerous awards and titles.
• His contributions to Indian classical music have been instrumental in popularizing the sarod globally.

The correct answer is Rivers, creeks, lakes, ponds, and streams are all freshwater habitats..

Key Points

• Freshwater habitats include lakes, ponds, rivers, streams, and creeks. These are environments with water that contains minimal amounts of dissolved salts.
• Freshwater habitats are crucial for a wide variety of organisms, including fish, amphibians, plants, and invertebrates.
• These habitats provide essential resources such as drinking water, food, and shelter for many species.
• Freshwater ecosystems are vital for human needs as well, providing water for drinking, agriculture, sanitation, and industrial processes.

Additional Information

• Freshwater
• Freshwater is defined as water with low concentrations of dissolved salts, typically less than 1%.
• It is found in rivers, lakes, streams, ponds, and groundwater.
• Freshwater is essential for most terrestrial life forms and is a critical resource for human survival.
• Freshwater Habitats
• These habitats include a variety of environments such as rivers, lakes, streams, ponds, and wetlands.
• Freshwater habitats support a diverse range of organisms, including fish, amphibians, reptiles, mammals, birds, and invertebrates.
• These ecosystems are dynamic and can vary significantly in their physical, chemical, and biological characteristics.
• Importance of Freshwater Ecosystems
• Freshwater ecosystems are crucial for maintaining biodiversity and ecological balance.
• They provide essential services such as water purification, flood regulation, and habitat for numerous species.
• Freshwater resources are used for drinking, irrigation, industry, recreation, and transportation.
• Conservation of freshwater habitats is vital for ensuring a sustainable supply of clean water for future generations.
• Threats to Freshwater Ecosystems
• Pollution from agricultural runoff, industrial discharges, and urbanization can degrade water quality and harm aquatic life.
• Over-extraction of water for irrigation, industry, and domestic use can deplete freshwater resources.
• Climate change can alter precipitation patterns, leading to changes in water availability and the health of freshwater ecosystems.
• Invasive species can disrupt native ecosystems and reduce biodiversity.

This source code provides a detailed solution for the question about freshwater habitats. It includes key points about the correct option and additional information explaining the related terminologies and concepts.

The correct answer is Pallava.

Key Points

• Mahendravarman I was a ruler of the Pallava dynasty who ruled over the southern part of India during the early 7th century.
• He is known for his patronage of arts and architecture, particularly for initiating the rock-cut architecture in Mahabalipuram.
• Mahendravarman I was a versatile scholar and a playwright, and he composed the famous Sanskrit play Mattavilasa-prahasana (The Delight of the Drunkards).
• The Pallavas were instrumental in the promotion of Tamil literature and culture, and they contributed significantly to the growth of Dravidian architecture.

Additional Information

• Maitraka Dynasty
• The Maitrakas ruled parts of present-day Gujarat from the late 5th century to the 8th century.
• They were known for their patronage of learning and religion, particularly Buddhism and Jainism.
• Pushyabhuti Dynasty
• The Pushyabhuti dynasty, also known as the Vardhana dynasty, ruled parts of northern India in the 6th and 7th centuries.
• The most notable ruler of this dynasty was Harsha Vardhana, who extended his empire across much of North India.
• Chalukya Dynasty
• The Chalukyas were a major dynasty that ruled large parts of southern and central India between the 6th and the 12th centuries.
• They are known for their contributions to art, architecture, and literature, particularly in the Deccan region.

The correct answer is Advocate General.

Key Points

• The Advocate General of the state is the highest law officer in the state.
• He/she is appointed by the Governor of the state.
• The Advocate General's duty is to advise the state government on legal matters.
• The Advocate General has the right to speak and take part in the proceedings of both houses of the state legislature, but without the right to vote.

Additional Information

• Attorney General of India
• The Attorney General is the highest law officer in the country.
• He/she is appointed by the President of India.
• The Attorney General's duty is to give advice to the Government of India on legal matters and perform other legal duties assigned to him/her.
• The Attorney General has the right to participate in the proceedings of both houses of Parliament but without the right to vote.
• Chief Justice of High Court
• The Chief Justice is the head of the judiciary in a state.
• He/she is appointed by the President of India in consultation with the Chief Justice of India and the Governor of the state.
• The Chief Justice's duty is to preside over the high court and ensure the administration of justice in the state.
• Auditor General
• The Comptroller and Auditor General of India (CAG) is the authority responsible for auditing the accounts of the state and central governments and public sector organizations.
• The CAG is appointed by the President of India.
• The CAG's duty is to ensure that public funds are used efficiently and for the intended purposes.

The correct answer is The Constitution (Scheduled Castes) Order (Amendment) Bill, 2021.

Key Points

• The Constitution (Scheduled Castes) Order (Amendment) Bill, 2021, was introduced to modify the list of Scheduled Castes in Tamil Nadu.
• This amendment bill aims to include certain communities in the list of Scheduled Castes in Tamil Nadu, thereby enabling them to avail benefits and protections guaranteed under the Constitution.
• The bill was introduced in the Rajya Sabha on February 8, 2021, by the Minister of Social Justice and Empowerment.
• Such amendments are periodically made to address the demands and needs of various communities to ensure equitable development and social justice.

Additional Information

• Scheduled Castes
• Scheduled Castes (SCs) are specific groups of people who are historically disadvantaged and have been subjected to untouchability and social exclusion.
• The Constitution of India provides various safeguards to protect and promote the socio-economic interests of SCs, including reservation in education and employment.
• The President of India, in consultation with the Governor of a state, issues orders specifying the SCs in that state.
• From time to time, amendments are made to the list of SCs to include or exclude communities based on social, educational, and economic criteria.
• Constitution Amendment Bills
• Constitution Amendment Bills are proposed changes to the Constitution of India.
• Such bills can be introduced in either house of Parliament and require a two-thirds majority of the members present and voting for passage.
• Amendments to the Constitution address various issues, including the rights of marginalized communities, electoral reforms, and changes in the structure of government.
• The Constitution (Scheduled Castes) Order (Amendment) Bill is one such amendment aimed at updating the list of SCs.
• Rajya Sabha
• Rajya Sabha, or the Council of States, is the upper house of India's Parliament.
• Members of the Rajya Sabha are elected by the elected members of State Legislative Assemblies, and by the members of the Electoral college for Union Territories, using a single transferable vote system.
• The Rajya Sabha has a maximum membership of 250 members, of which 12 are nominated by the President of India.
• The Rajya Sabha plays a crucial role in the legislative process, including the passage of amendment bills.

The correct answer is Tax and duty concessions.

Key Points

• Special Economic Zones (SEZs) are designated areas in countries that possess special economic regulations that differ from other areas in the same country.
• One of the primary benefits offered to businesses in SEZs is tax and duty concessions, which include exemptions or reductions in various taxes and duties such as income tax, sales tax, and customs duties.
• These concessions are designed to attract both foreign and domestic investments, foster job creation, and enhance the economic development of the region.
• Businesses operating in SEZs often enjoy simplified customs procedures, which reduce the time and cost of importing and exporting goods.

Additional Information

• Special Economic Zones (SEZs)
• SEZs are geographically designated areas within a country that are subject to unique economic regulations that are more liberal than the country's typical economic laws.
• These zones are created to encourage rapid economic growth by leveraging tax incentives, reduced regulations, and other measures to attract foreign investment and boost exports.
• SEZs often focus on specific industries, such as technology, manufacturing, or finance, to develop expertise and competitiveness in those areas.
• The goal of SEZs is to generate employment, increase trade balance, and facilitate the transfer of technology and knowledge.
• Tax and Duty Concessions
• These are financial incentives provided to businesses in the form of reduced tax rates, tax holidays, or exemptions from certain duties or tariffs.
• Such concessions can significantly lower the operating costs for businesses, making it more financially viable to set up operations in SEZs.
• Tax concessions often include exemptions from income tax, sales tax, property tax, and customs duties on imported raw materials and machinery.
• Duty concessions can help businesses by reducing or eliminating import and export duties, making it cheaper to bring in necessary materials and export finished products.
• Foreign Investment
• SEZs are designed to attract foreign direct investment (FDI) by offering a more favorable business environment compared to the rest of the country.
• FDI brings in capital, technology, and management know-how, which can contribute to the economic development of the region.
• SEZs often have more relaxed regulations on foreign ownership, allowing foreign investors to own a larger percentage of local businesses.
• Encouraging foreign investment in SEZs can also lead to the creation of joint ventures and partnerships between local and foreign companies.

The correct answer is India, Bangladesh.

Key Points

• India and Bangladesh will co-host the ICC Men's Cricket World Cup in 2031.
• This will be the first time Bangladesh will co-host the ICC Men's Cricket World Cup.
• India has previously hosted the ICC Men's Cricket World Cup in 1987, 1996, and 2011.
• The tournament is expected to bring significant economic and cultural benefits to both countries.

Additional Information

• ICC Men's Cricket World Cup
• The ICC Men's 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 first tournament was held in England in 1975.
• The format involves a qualification phase, which determines the teams that will participate in the tournament phase.
• The World Cup is one of the world's most viewed sporting events and is considered the "flagship event of the international cricket calendar" by the ICC.
• Co-hosting a Major Sporting Event
• Co-hosting involves two or more countries sharing the responsibilities and benefits of hosting a major sporting event.
• This can help to reduce costs, increase participation and viewership, and promote cultural exchange between the host countries.
• Co-hosting can also enhance infrastructure and tourism in the host countries.
• Economic and Cultural Benefits
• Hosting major sporting events can boost the economy by attracting tourists, creating jobs, and increasing spending on infrastructure.
• It can also promote cultural exchange and national pride, and provide a global platform to showcase the host countries.
• Successful hosting can enhance the international reputation of the host countries.

The correct answer is Magh Bihu.

Key Points

• Magh Bihu is one of the major festivals celebrated in Assam, marking the end of the harvest season in the region.
• It is celebrated in the Assamese month of Magh (January-February), hence the name Magh Bihu.
• During Magh Bihu, people build traditional huts called Meji and Bhelaghar with bamboo, leaves, and thatch, which are later set on fire.
• The festival is also known for its feasts called Uruka, where families and communities come together to prepare and enjoy various traditional dishes.

Additional Information

• Pedda Padunga
• This festival is celebrated in Andhra Pradesh and Telangana, coinciding with the harvest festival of Makar Sankranti.
• It involves traditional rituals, feasting, and kite flying.
• Thai Pongal
• Thai Pongal is a harvest festival celebrated in Tamil Nadu, dedicated to the Sun God.
• The festival spans four days, with each day having its own significance and rituals.
• Pongal
• Pongal is another name for Thai Pongal, celebrated in Tamil Nadu.
• The festival is marked by boiling the first rice of the season, which is offered to the Sun God.
• Makar Sankranti
• Makar Sankranti is celebrated across India under different names such as Magh Bihu in Assam, Pedda Padunga in Andhra Pradesh, and Thai Pongal in Tamil Nadu.
• The festival marks the transition of the Sun into the zodiac sign of Capricorn (Makara) and is associated with harvest and new beginnings.

The correct answer is Bicycle Kick.

Key Points

• The bicycle kick, also known as an overhead kick, is a popular move in football where a player kicks the ball in mid-air while making a backward somersault motion.
• This move is often used to shoot on goal or clear the ball from the defensive area.
• It requires exceptional athleticism, timing, and coordination to execute successfully.
• The bicycle kick is a spectacular move that is often celebrated by fans and players alike due to its difficulty and potential for dramatic goals.

Additional Information

• Third Man
• The term "Third Man" is associated with cricket and refers to a fielding position located near the boundary, behind the wicket-keeper on the off-side.
• Overs
• "Overs" is another term related to cricket, which refers to a set of six consecutive legal deliveries bowled by a single bowler.
• LBW
• "LBW" stands for "Leg Before Wicket," a rule in cricket used to determine if a batsman is out when the ball strikes any part of the body before hitting the bat, and it would have hit the stumps.

Shortcut Trick

For standard trigonometric angles, we know that sec45° = √2.

Comparing this with the given secθ = √2, we get θ = 45°.

We need to find the value of cosecθ.

Substituting θ = 45° into cosecθ, we get cosec45° = √2.

∴ The correct answer is √2.

Alternate Method

Given:

secθ = √2

Formula Used:

secθ = Hypotenuse / Adjacent

cosecθ = Hypotenuse / Opposite

Opposite = √(Hypotenuse² − Adjacent²)

Calculations:

⇒ secθ = √2 / 1

⇒ Comparing with the formula, Hypotenuse = √2 and Adjacent = 1

⇒ By Pythagoras Theorem: Opposite = √((√2)² − 1²)

⇒ Opposite = √(2 − 1) = √1 = 1

⇒ cosecθ = Hypotenuse / Opposite

⇒ cosecθ = √2 / 1 = √2

∴ The correct answer is √2.

Additional Information

Reciprocal Identities

sinθ = 1 / cosecθ | cosθ = 1 / secθ | tanθ = 1 / cotθ

Trigonometric Values for 45°

sin45° = 1/√2 | cos45° = 1/√2 | tan45° = 1

Pythagorean Identities

sin²θ + cos²θ = 1 | 1 + tan²θ = sec²θ | 1 + cot²θ = cosec²θ

Given:

Total estimated expenditure = ₹2,50,000

Electricity share = 11%, Rent share = 18%

Actual expenditure on electricity = 10% more than estimated

Actual expenditure on rent = 20% less than estimated

Other expenses remain the same as estimated.

Formula used:

Estimated expense = (Percentage Share) × (Total Estimated Expenditure) ÷ 100

Actual expense = Estimated Expense ± Change

Calculation:

Estimated electricity expense = $\frac{11 × 250000}{100} = 27500$

Actual electricity expense = $27500 + 10\% \text{ of } 27500 = 27500 + 2750 = 30250$

Estimated rent expense = $\frac{18 × 250000}{100} = 45000$

Actual rent expense = $45000 - 20\% \text{ of } 45000 = 45000 - 9000 = 36000$

Other expenses = Total estimated expenditure - (Electricity + Rent) = $\frac{(20 + 16 + 17 + 18)}{100} × 250000 = 177500$

Total actual expenditure = Electricity + Rent + Other Expenses = $30250 + 36000 + 177500 = 243750$

∴ The total actual expenditure is ₹2,43,750.

Shortcut Trick

Efficiency ratio of faster pipe to slower pipe = 6 : 1

Total combined efficiency = 6 + 1 = 7 units/min

Total capacity of the tank = Combined efficiency × Time taken = 7 × 40 = 280 units

Time taken by slower pipe = Total capacity ÷ Efficiency of slower pipe = 280 ÷ 1 = 280 minutes

∴ The correct answer is 280 minutes.

Alternate Method

Given:

One pipe can fill the tank 6 times faster than the other pipe.

Time taken by both pipes together to fill the tank = 40 minutes.

Formula Used:

Total Work = Efficiency × Time

Time = Total Work ÷ Efficiency

Calculations:

⇒ Let the slower pipe be B and the faster pipe be A.

⇒ Let the efficiency of the slower pipe (B) be 1 unit/min.

⇒ The efficiency of the faster pipe (A) = 6 units/min.

⇒ Combined efficiency of both pipes (A + B) = 6 + 1 = 7 units/min.

⇒ Total work (capacity of the tank) = Combined efficiency × Combined time taken

⇒ Total work = 7 × 40 = 280 units.

⇒ Time taken by the slower pipe alone = Total work ÷ Efficiency of slower pipe

⇒ Time taken by the slower pipe alone = 280 ÷ 1 = 280 minutes.

∴ The correct answer is 280 minutes.

Additional Information

Pipes and Cisterns Basics

If a pipe can fill a tank in x hours, its efficiency (part of the tank filled in 1 hour) is 1/x.

Efficiency and Time Relationship

Efficiency is inversely proportional to time. If Pipe A is 'n' times as fast as Pipe B, the ratio of their times to complete the work is 1 : n.

Emptying Pipes (Leaks)

For a pipe that empties a tank, its efficiency is taken as negative. Net efficiency = (Sum of filling efficiencies) − (Sum of emptying efficiencies).

Shortcut Trick

Interest = Amount − Principal = ₹24,800 − ₹10,800 = ₹14,000

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

Time = (14000 × 100) ÷ (10800 × 15.5)

Time = 14000 ÷ 1674 ≈ 8.36 years

∴ The correct answer is 8.36 years.

Alternate Method

Given:

Principal (P) = ₹10,800

Amount (A) = ₹24,800

Rate (R) = 15.5% p.a.

Formula Used:

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

Amount (A) = P + I

Calculations:

⇒ I = A − P

⇒ I = 24800 − 10800

⇒ I = 14000

⇒ 14000 = (10800 × 15.5 × T) ÷ 100

⇒ 14000 = 108 × 15.5 × T

⇒ 14000 = 1674 × T

⇒ T = 14000 ÷ 1674

⇒ T = 8.363...

⇒ T ≈ 8.36 years

∴ The correct answer is 8.36 years.

Additional Information

Simple Interest (SI)

Interest calculated strictly on the original principal amount for the full duration. Given by: SI = (P × R × T) ÷ 100.

Compound Interest (CI)

Interest calculated on the initial principal and also on the accumulated interest of previous periods. Formula: Amount = P × (1 + R ÷ 100)^T.

SI vs CI Difference

For the first year, Simple Interest and Compound Interest are identical if compounding happens annually. Differences start to accumulate from the second year onwards due to "interest on interest."

Shortcut Trick

For divisibility by 3, the sum of digits must be a multiple of 3.

Sum of digits of 6745k2 = 6 + 7 + 4 + 5 + k + 2 = 24 + k.

Since 24 is perfectly divisible by 3, 'k' must also be a multiple of 3.

Possible single-digit values for k are 0, 3, 6, and 9.

The greatest possible value among these is 9.

∴ The correct answer is 9.

Alternate Method

Given:

The 6-digit number is 6745k2.

The number is perfectly divisible by 3.

Formula Used:

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

Calculations:

⇒ Sum of digits = 6 + 7 + 4 + 5 + k + 2

⇒ Sum of digits = 24 + k

⇒ For the whole number to be divisible by 3, (24 + k) must be a multiple of 3.

⇒ Since 'k' is a single digit, its maximum possible value can be 9.

⇒ Let's substitute the highest possible digits starting from 9:

⇒ If k = 9: Sum = 24 + 9 = 33 (33 is divisible by 3)

⇒ If k = 8: Sum = 24 + 8 = 32 (32 is not divisible by 3)

⇒ Since 9 is the highest single-digit number and it perfectly satisfies the divisibility condition, k = 9.

∴ The correct answer is 9.

Additional Information

Divisibility Rule for 3

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

Divisibility Rule for 9

Similar to 3, a number is divisible by 9 if the sum of its digits is a multiple of 9.

Divisibility Rule for 6

A number is divisible by 6 if it satisfies both the divisibility rules of 2 (ends in an even digit) and 3.

Shortcut Trick

Let the total number of voters be T.

Candidate's votes = T × 80% (cast) × 96% (valid) × 80% (secured) = 15,360

⇒ T × (4/5) × (24/25) × (4/5) = 15,360

⇒ T × (384/625) = 15,360

⇒ T = 15,360 × (625/384) = 25,000

∴ The correct answer is 25,000 votes.

Alternate Method

Given:

⇒ Voters who cast their votes = 80%

⇒ Invalid votes = 4%

⇒ Candidate's secured votes = 80% of valid votes = 15,360

Calculation:

Let the total number of enrolled voters be 100x.

⇒ Number of votes cast = 80% of 100x = 80x

⇒ Number of valid votes = 96% of 80x = 76.8x

⇒ Votes secured by the candidate = 80% of 76.8x = 61.44x

According to the given question,

⇒ 61.44x = 15,360

⇒ x = 15,360 ÷ 61.44 = 250

⇒ Total number of voters = 100x = 100 × 250 = 25,000

∴ The correct answer is 25,000 votes.

Additional Information

Successive Percentage Application

When multiple percentages are applied in sequence (like cast votes, then valid votes), multiply the fraction equivalents directly: Final = Base × (1 − a/100) × (1 − b/100).

Valid vs Invalid Votes

Invalid votes are typically deducted from the total cast votes, not the total registered voters. Valid Votes = Total Cast Votes − Invalid Votes.

Majority / Winning Margin

In a typical two-candidate election, the winning margin is the difference between the winner's and the loser's votes. Margin = Winner's Votes − Loser's Votes.

Shortcut Trick Put the given options directly in the equation 2 sin2 θ + 3 sin θ − 2 = 0. Check for θ = 30° where sin 30° = 1/2. ⇒ 2(1/2)2 + 3(1/2) − 2 = 0 ⇒ 2(1/4) + 3/2 − 2 = 1/2 + 3/2 − 2 = 2 − 2 = 0 The equation is satisfied, so this is the correct value. ∴ The correct answer is 30°.

Alternate Method Given: 2 sin2 θ + 3 sin θ − 2 = 0, where 0 < θ < 90° Calculation: Let sin θ = x. The equation becomes a quadratic equation: ⇒ 2x2 + 3x − 2 = 0 ⇒ 2x2 + 4x − x − 2 = 0 ⇒ 2x(x + 2) − 1(x + 2) = 0 ⇒ (2x − 1)(x + 2) = 0 So, x = 1/2 or x = −2 Substituting x = sin θ back into the roots: ⇒ sin θ = 1/2 or sin θ = −2 Since the value of sin θ always lies between −1 and 1, sin θ = −2 is not possible. ⇒ sin θ = 1/2 For 0 < θ < 90°, we know the standard trigonometric value: ⇒ sin 30° = 1/2 ⇒ θ = 30° ∴ The correct answer is 30°.

Additional Information Trigonometric Values in First Quadrant (0° to 90°) sin 0° = 0, sin 30° = 1/2, sin 45° = 1/√2, sin 60° = √3/2, sin 90° = 1. The sine function increases from 0 to 1 in the first quadrant. Range of Sine and Cosine Functions For any real angle θ, the value of sin θ and cos θ always lies between −1 and 1. i.e., −1 ≤ sin θ ≤ 1 and −1 ≤ cos θ ≤ 1. Nature of Quadratic Equations For a quadratic equation ax2 + bx + c = 0, the roots can be factored directly or found using the formula x = (−b ± √(b2 − 4ac)) ÷ 2a. In trigonometric quadratics, we reject roots falling outside the allowed range of the specific trigonometric function.

Shortcut Trick

If sin x = cos y, then the sum of the angles is 90º (x + y = 90º).

⇒ 3A + (A − 26º) = 90º

⇒ 4A = 116º

⇒ A = 29º

∴ The correct answer is 29º.

Alternate Method

Given:

sin 3A = cos (A − 26º)

Formula Used:

sin θ = cos (90º − θ)

Calculation:

⇒ cos (90º − 3A) = cos (A − 26º)

Equating the angles since both are acute:

⇒ 90º − 3A = A − 26º

⇒ 4A = 90º + 26º

⇒ 4A = 116º

⇒ A = 116º ÷ 4

⇒ A = 29º

∴ The correct answer is 29º.

Additional Information

Complementary Angles Rule

When the sum of two angles is 90º, their sine and cosine values are equal. Examples: sin(90º − θ) = cos θ and cos(90º − θ) = sin θ.

Other Co-function Identities

tan(90º − θ) = cot θ and sec(90º − θ) = cosec θ.

Basic Trigonometric Identities

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

Shortcut Trick

In an isosceles triangle, the angles opposite to the equal sides are equal.

Since side XY = XZ, the opposite angles are equal ⇒ ∠Z = ∠Y = 80º.

The sum of all interior angles in any triangle is 180º.

∠X = 180º − (80º + 80º) = 180º − 160º = 20º.

∴ The correct answer is 20º.

Alternate Method

Given:

Triangle XYZ is an isosceles triangle.

Side XY = Side XZ

Measure of ∠Y = 80º

Formula Used:

Sum of interior angles of a triangle = 180º

X Y Z 80º 80º ?

Calculations:

⇒ In ΔXYZ, the sides XY and XZ are given as equal.

⇒ By the Isosceles Triangle Theorem, the angles opposite to the equal sides are also equal in measure.

⇒ The angle opposite to side XY is ∠Z, and the angle opposite to side XZ is ∠Y.

⇒ Therefore, ∠Z = ∠Y

⇒ ∠Z = 80º

⇒ According to the angle sum property, the sum of all three interior angles of the triangle is 180º.

⇒ ∠X + ∠Y + ∠Z = 180º

⇒ ∠X + 80º + 80º = 180º

⇒ ∠X + 160º = 180º

⇒ ∠X = 180º − 160º

⇒ ∠X = 20º

∴ The correct answer is 20º.

Additional Information

Isosceles Triangle Properties

A triangle that has at least two sides of equal length is known as an isosceles triangle. The angles opposite to these equal sides are also strictly equal. The altitude drawn to the unequal base bisects both the base and the vertex angle.

Angle Sum Property

The sum of the three interior angles of any triangle on a Euclidean plane is always equal to 180º. This foundational rule holds true regardless of the triangle being scalene, isosceles, or equilateral.

Exterior Angle Theorem

If any side of a triangle is extended, the exterior angle so formed is equal to the sum of the two opposite (remote) interior angles. ∠Exterior = ∠Interior₁ + ∠Interior₂.

Shortcut Trick

For a system of linear equations, check the ratio of coefficients of x and y.

Ratio of x coefficients = 3/2

Ratio of y coefficients = 2/3

Since 3/2 ≠ 2/3, the lines intersect at exactly one point.

∴ The correct answer is Unique solution.

Alternate Method

Given:

Equation 1: 3x + 2y = 7

Equation 2: 2x + 3y = 7

Concept Used:

For a system of linear equations a₁x + b₁y = c₁ and a₂x + b₂y = c₂:

⇒ If a₁/a₂ ≠ b₁/b₂ → Intersecting lines (Unique solution)

⇒ If a₁/a₂ = b₁/b₂ = c₁/c₂ → Coincident lines (Infinite solutions)

⇒ If a₁/a₂ = b₁/b₂ ≠ c₁/c₂ → Parallel lines (No solution)

Calculations:

⇒ From the given equations, a₁ = 3, b₁ = 2, c₁ = 7

⇒ And a₂ = 2, b₂ = 3, c₂ = 7

⇒ a₁/a₂ = 3/2

⇒ b₁/b₂ = 2/3

⇒ c₁/c₂ = 7/7 = 1

⇒ Comparing the ratios: 3/2 ≠ 2/3

⇒ Since a₁/a₂ ≠ b₁/b₂, the system of equations has exactly one point of intersection.

∴ The correct answer is Unique solution.

Additional Information

Consistent System

A system of linear equations is called consistent if it has at least one valid solution (either a unique solution or infinite solutions).

Inconsistent System

A system is called inconsistent if there is no set of values that satisfies both equations simultaneously (this corresponds to parallel lines).

Graphical Meaning

A unique solution means the two lines intersect at exactly one coordinate point (x, y) on the graph.

Given:

Expenditure and profit percentage of Company A and Company B for the year 2005:

Company A: Expenditure = ₹40 crore, Profit% = 60%

Company B: Expenditure = ₹35 crore, Profit% = 48%

Formula for Profit:

$\text{Profit} = \text{Expenditure} \times \frac{\text{Profit \%}}{100}$

Calculation:

Profit of Company A:

$\text{Profit}_A = 40 \times \frac{60}{100} = 40 \times 0.6 = 24 , \text{crore ₹}$

Profit of Company B:

$\text{Profit}_B = 35 \times \frac{48}{100} = 35 \times 0.48 = 16.8 , \text{crore ₹}$

Difference between profits:

$\text{Difference} = \text{Profit}_A - \text{Profit}_B = 24 - 16.8 = 7.2 , \text{crore ₹}$

∴ The difference between the profits of Company A and Company B in 2005 is ₹7.2 crore.

Shortcut Trick

Present ratio (Father : Amit) = (1 + 5) : 1 = 6 : 1, and after 6 years = 3.5 : 1 = 7 : 2.

Both ratio parts increase by exactly 1 unit (7 − 6 = 1 and 2 − 1 = 1) over 6 years.

∴ 1 part = 6 years ⇒ Present ages are 36 (Father) and 6 (Amit).

After 15 years (6 + 9), ages will be 51 and 21 respectively.

Required ratio = 51 ÷ 21 = 17/7 = 2 ³/₇.

∴ The correct answer is 2 ³/₇ times.

Alternate Method

Given:

Father's present age is 5 times more than Amit's age.

After 6 years, Father's age = 3.5 × Amit's age.

Calculations:

Let Amit's present age be x years.

⇒ Father's present age = x + 5x = 6x

After 6 years:

⇒ Amit's age = x + 6

⇒ Father's age = 6x + 6

According to the given condition:

⇒ 6x + 6 = 3.5 × (x + 6)

⇒ 6x + 6 = 3.5x + 21

⇒ 6x − 3.5x = 21 − 6

⇒ 2.5x = 15

⇒ x = 15 ÷ 2.5 = 6

Present ages:

⇒ Amit = 6 years

⇒ Father = 6 × 6 = 36 years

After a further 9 years (Total 6 + 9 = 15 years from present):

⇒ Amit's age = 6 + 15 = 21 years

⇒ Father's age = 36 + 15 = 51 years

Required ratio of Father's age to Amit's age:

⇒ 51 ÷ 21 = 17/7 = 2 ³/₇ times

∴ The correct answer is 2 ³/₇ times.

Additional Information

"Times" vs "Times More Than"

If A is n times B, then A = n × B. However, if A is n times more than B, then A = B + (n × B) = (n + 1) × B.

Ratio Method for Age Problems

When the age ratio changes over a fixed number of years, making the difference in ratio parts equal for both individuals can directly yield the age multiplier without forming linear equations.

Constant Age Difference

The numerical difference in ages between any two individuals always remains constant at any point in time, whether in the past or in the future.

Shortcut Trick

Mean Cost Price = Selling Price × [100 ÷ (100 + Gain%)]

⇒ Mean CP = 75 × [100 ÷ 120] = ₹62.5 per kg

By Alligation Cross Method: Quantity Ratio = (Mean CP − CP₂) : (CP₁ − Mean CP)

⇒ Ratio = (62.5 − 46) : (78 − 62.5) = 16.5 : 15.5

⇒ Ratio = 165 : 155 = 33 : 31

∴ The correct answer is 33 : 31.

Alternate Method

Given:

Cost Price (CP) of Sugar 1 = ₹78 per kg

Cost Price (CP) of Sugar 2 = ₹46 per kg

Selling Price (SP) of mixture = ₹75 per kg

Gain percentage = 20%

Formula Used:

Cost Price (CP) = [Selling Price × 100] ÷ [100 + Profit%]

Calculation:

⇒ Mean CP of the mixture = (75 × 100) ÷ (100 + 20)

⇒ Mean CP of the mixture = 7500 ÷ 120 = ₹62.5 per kg

By applying the rule of alligation (as shown in the diagram above):

⇒ Quantity of Sugar 1 : Quantity of Sugar 2 = (Mean CP − CP of Sugar 2) : (CP of Sugar 1 − Mean CP)

⇒ Required Ratio = (62.5 − 46) : (78 − 62.5)

⇒ Required Ratio = 16.5 : 15.5

⇒ Multiplying both sides by 10 to clear decimals:

⇒ Required Ratio = 165 : 155

⇒ Dividing both values by their highest common factor (5):

⇒ Required Ratio = 33 : 31

∴ The correct answer is 33 : 31.

Additional Information

Rule of Alligation

It is a quick cross-multiplication method used to find the ratio in which two ingredients at given prices must be mixed to produce a mixture of a desired central price. The ratio of cheaper quantity to dearer quantity is calculated as (CP of Dearer − Mean Price) : (Mean Price − CP of Cheaper).

Mean Price (Cost Price of Mixture)

The cost price of a unit quantity of the final mixture is called the mean price. Selling price should never be used directly in the alligation cross diagram; it must always be converted back into the mean cost price first.

Replacement Method

If a container holds x units of a liquid, and y units are taken out and replaced by water repeatedly, after n such operations, the remaining quantity of pure liquid left = x × (1 − y ÷ x)ⁿ.

Shortcut Trick

Since the time of running is constant for both, the ratio of distances covered is equal to the ratio of their speeds.

Ratio of speeds (Police : Thief) = 23 : 21

Difference in distance ratio = 23 − 21 = 2 units, which is equal to the initial gap of 100 m.

⇒ 1 unit = 100 ÷ 2 = 50 m

⇒ Distance run by the thief = 21 units = 21 × 50 = 1050 m

∴ The correct answer is 1050 m.

Alternate Method

Given:

Distance between policeman and thief = 100 m

Speed of thief = 21 km/h

Speed of policeman = 23 km/h

Formula Used:

Relative Speed (same direction) = Speed₁ − Speed₂

Time = Distance ÷ Relative Speed

Distance = Speed × Time

Calculations:

⇒ Relative speed = 23 − 21 = 2 km/h

⇒ Relative speed in m/s = 2 × (5 ÷ 18) = 5/9 m/s

⇒ Time taken to catch the thief = 100 ÷ (5/9) = 180 seconds

⇒ Distance covered by the thief = Speed of thief × Time taken

⇒ Distance covered = [21 × (5 ÷ 18)] × 180

⇒ Distance covered = 21 × 50 = 1050 m

∴ The correct answer is 1050 m.

Additional Information

Relative Speed in Same Direction

When two bodies move in the same direction, their relative speed is the difference between their individual speeds: S_relative = |S₁ − S₂|.

Relative Speed in Opposite Direction

When two bodies move towards each other, their relative speed is the sum of their individual speeds: S_relative = S₁ + S₂.

Proportionality of Distance and Speed

When the time traveled is constant, the distance covered is directly proportional to the speed: D₁/D₂ = S₁/S₂.

Shortcut Trick

Rearrange the given expression to group similar terms together:

⇒ [(3x − 2y) + 17] × [(3x − 2y) − 17]

Apply the difference of squares formula (a + b)(a − b) = a² − b²:

⇒ (3x − 2y)² − 17²

⇒ 9x² − 12xy + 4y² − 289

∴ The correct answer is 9x² − 12xy + 4y² − 289.

Alternate Method

Given:

Expression: (3x + 17 − 2y)(3x − 17 − 2y)

Formula Used:

Distributive property: (a + b + c)(d + e + f) = ad + ae + af + bd + be + bf + cd + ce + cf

Calculations:

Multiply each term of the first polynomial by each term of the second polynomial:

⇒ 3x(3x − 17 − 2y) + 17(3x − 17 − 2y) − 2y(3x − 17 − 2y)

⇒ (9x² − 51x − 6xy) + (51x − 289 − 34y) + (−6xy + 34y + 4y²)

Combine the like terms:

⇒ 9x² + (−51x + 51x) + (−6xy − 6xy) + (−34y + 34y) + 4y² − 289

⇒ 9x² + 0 − 12xy + 0 + 4y² − 289

⇒ 9x² − 12xy + 4y² − 289

∴ The correct answer is 9x² − 12xy + 4y² − 289.

Additional Information

Standard Algebraic Identities

Some common and useful algebraic identities include (a + b)² = a² + 2ab + b², (a − b)² = a² − 2ab + b², and a² − b² = (a + b)(a − b).

Distributive Property in Polynomials

When multiplying two polynomials, you must multiply each term in the first polynomial by every term in the second polynomial. Grouping and combining like terms simplifies the final expression efficiently.

Given:

Expression to solve: 11 - {(3 ÷ 4) of 8 - (4 - 8)}

Formula Used:

Order of operations: BODMAS/BIDMAS (Brackets, Orders (i.e. powers and square roots, etc.), Division and Multiplication, Addition and Subtraction)

Calculation:

First, solve the innermost brackets:

4 - 8 = -4

Next, solve the division and multiplication part:

(3 ÷ 4) of 8 = (3/4) × 8 = 3 × 2 = 6

Now, substitute these values back into the expression:

11 - {6 - (-4)}

Simplify the expression inside the brackets:

6 - (-4) = 6 + 4 = 10

Finally, subtract from 11:

11 - 10 = 1

The correct answer is option 3

Given:

Percentage of students passing out of College M:

2021: 80%

2022: 92%

Formula used:

Percentage Increase = [(New Value - Old Value) ÷ Old Value] × 100

Calculation:

New Value = 92, Old Value = 80

Percentage Increase = [(92 - 80) ÷ 80] × 100

⇒ Percentage Increase = (12 ÷ 80) × 100

⇒ Percentage Increase = 15%

∴ The percentage increase in students passing out in 2022 compared to 2021 is 15%.

Shortcut Trick

Inverse ratio of 2A = 4B = 6C gives A : B : C = (1/2) : (1/4) : (1/6) = 6 : 3 : 2.

Total share parts = 6 + 3 + 2 = 11 parts.

11 parts → ₹44,000

1 part → ₹4,000

A's share = 6 parts × 4,000 = ₹24,000.

∴ The correct answer is ₹24,000.

Alternate Method

Given:

2 × A's share = 4 × B's share = 6 × C's share

Total profit earned = ₹44,000

Calculations:

⇒ Let 2A = 4B = 6C = LCM(2, 4, 6)

⇒ LCM of 2, 4, and 6 = 12

⇒ 2A = 12 → A = 6

⇒ 4B = 12 → B = 3

⇒ 6C = 12 → C = 2

⇒ The ratio of their investments A : B : C = 6 : 3 : 2

⇒ Sum of ratio parts = 6 + 3 + 2 = 11 parts

⇒ 11 parts = ₹44,000

⇒ 1 part = 44,000 ÷ 11 = ₹4,000

⇒ Share of A = 6 parts = 6 × 4,000 = ₹24,000

∴ The correct answer is ₹24,000.

Additional Information

Compound Partnership

When investments are made for different time periods, the profit is distributed in the ratio of the product of capital and time. Profit Ratio = (C₁ × T₁) : (C₂ × T₂).

Active vs Sleeping Partner

An active partner manages the business and typically receives a salary or commission before the remaining profit is divided. A sleeping partner only invests capital without managing the affairs.

Equality of Multiples Trick

If given aA = bB = cC, the quickest way to find the ratio A : B : C is by taking the LCM of a, b, and c and dividing the LCM by each corresponding coefficient.

Given:

The table shows daily consumption (in gm/day) of rice, wheat, pulses, and vegetables over five years. We need to find if any two years have equal daily consumption.

Formula used:

Total daily consumption = Rice + Wheat + Pulses + Vegetables

Calculation:

For each year:

2019: 450 + 55 + 160 + 280 = 945 gm/day

2020: 430 + 60 + 150 + 300 = 940 gm/day

2021: 380 + 65 + 140 + 320 = 905 gm/day

2022: 350 + 70 + 125 + 400 = 945 gm/day

2023: 350 + 80 + 120 + 350 = 900 gm/day

The total daily consumption for 2019 and 2022 is the same: 945 gm/day.

∴ The daily consumption in 2022 is equal to that of 2019.

Shortcut Trick

Total SP = ₹1260 + ₹1440 = ₹2700

Total CP = 1260 × (100 ÷ 125) + 1440 × (100 ÷ 90) = ₹1008 + ₹1600 = ₹2608

Overall Gain = Total SP − Total CP = 2700 − 2608 = ₹92

Gain % = (92 ÷ 2608) × 100 = 575 ÷ 163 = 3 ⁸⁶/₁₆₃%

∴ The correct answer is 3 ⁸⁶/₁₆₃% Gain.

Alternate Method

Given:

Selling Price (SP) of first keyboard = ₹1260, Profit = 25%

Selling Price (SP) of second keyboard = ₹1440, Loss = 10%

Formula Used:

Cost Price (CP) = [100 ÷ (100 + Profit%)] × SP

Cost Price (CP) = [100 ÷ (100 − Loss%)] × SP

Gain % = (Gain ÷ Total CP) × 100

Calculations:

⇒ CP of first keyboard = (100 ÷ 125) × 1260 = (4 ÷ 5) × 1260 = ₹1008

⇒ CP of second keyboard = (100 ÷ 90) × 1440 = (10 ÷ 9) × 1440 = ₹1600

⇒ Total CP = 1008 + 1600 = ₹2608

⇒ Total SP = 1260 + 1440 = ₹2700

⇒ Total Gain = Total SP − Total CP = 2700 − 2608 = ₹92

⇒ Gain Percentage = (92 ÷ 2608) × 100

⇒ Gain Percentage = 9200 ÷ 2608 = 2300 ÷ 652

⇒ Gain Percentage = 575 ÷ 163 = 3 ⁸⁶/₁₆₃%

∴ The correct answer is 3 ⁸⁶/₁₆₃% Gain.

Additional Information

Overall Profit or Loss on Same Selling Price

When two identical items are sold at the same selling price, one at a profit of x% and the other at a loss of x%, there is always an overall loss given by Loss% = (x ÷ 10)². In this problem, selling prices are different, so individual calculation was required.

Marked Price and Discount

Selling Price (SP) = Marked Price (MP) × (100 − Discount%) ÷ 100. This relationship is useful when the items are sold after offering a flat discount on the catalog or marked price.

Dishonest Dealer Concept

When a dealer claims to sell items at his cost price but uses a false weight, his profit percent is evaluated as: Profit % = [Error ÷ (True Value − Error)] × 100.

Shortcut Trick

Selling Price can be calculated directly by applying successive discount percentage multipliers to the Marked Price.

SP = MP × (100 − D₁)% × (100 − D₂)%

SP = 15000 × 80% × 88%

SP = 15000 × 0.80 × 0.88 = 12000 × 0.88 = 10560

∴ The correct answer is ₹10,560.

Alternate Method

Given:

Marked Price (MP) = ₹15,000

First discount (D₁) = 20%

Second discount (D₂) = 12%

Formula Used:

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

Calculations:

⇒ SP = 15000 × (100 − 20)/100 × (100 − 12)/100

⇒ SP = 15000 × (80/100) × (88/100)

⇒ SP = 15000 × 4/5 × 22/25

⇒ SP = 15000 × 88/125

⇒ SP = 120 × 88

⇒ SP = 10560

∴ The correct answer is ₹10,560.

Additional Information

Effective Successive Discount

When two successive discounts of d₁% and d₂% are given, the equivalent single discount percentage can be calculated directly using the formula: [d₁ + d₂ − (d₁ × d₂)/100]%.

Marked Price vs Selling Price

A discount is always offered on the Marked Price (MP) of an item. The price obtained after deducting the discount is the final Selling Price (SP). The fundamental formula connects them as SP = MP − Discount.

Relation between CP and MP

If a profit of P% is made by a shopkeeper even after allowing a discount of D%, then the direct ratio between the Cost Price (CP) and the Marked Price (MP) is given by CP/MP = (100 − D)/(100 + P).

Shortcut Trick

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

Half of the chord length = 11 ÷ 2 = 5.5 cm.

Using Pythagoras theorem to find the distance (d) from the centre directly:

d = √(12.5² − 5.5²) = √[(12.5 + 5.5) × (12.5 − 5.5)]

d = √(18 × 7) = √126 ≈ 11.22 cm

∴ The correct answer is 11.2 cm.

Alternate Method

Given:

Radius of the circle (OA) = 12.5 cm

Length of the chord (AB) = 11 cm

Formula Used:

Pythagoras Theorem: Hypotenuse² = Base² + Perpendicular²

O

12.5 cm

d 5.5 cm 5.5 cm A B M

Calculations:

⇒ A perpendicular drawn from the centre (O) to a chord (AB) bisects the chord at point M.

⇒ AM = MB = 11 ÷ 2 = 5.5 cm.

⇒ In right-angled triangle OMA, the radius OA acts as the hypotenuse.

⇒ OA² = OM² + AM²

⇒ 12.5² = d² + 5.5²

⇒ 156.25 = d² + 30.25

⇒ d² = 156.25 − 30.25

⇒ d² = 126

⇒ d = √126

⇒ d ≈ 11.22 cm

Rounding to one decimal place, the distance is 11.2 cm.

∴ The correct answer is 11.2 cm.

Additional Information

Properties of a Chord

A perpendicular dropped from the centre of a circle to any of its chords bisects the chord into two equal halves. Conversely, a line segment drawn from the centre that bisects a chord is always perpendicular to it.

Equal Chords Property

Chords of equal length in the same circle are equidistant from the centre. If two different chords are positioned at the exact same distance from the centre, they must be perfectly equal in length.

Pythagorean Triplet Shortcut

If the values given in a geometry question are multiples of standard triplets like (3, 4, 5) or (5, 12, 13), it can save calculation time. Always look for fractional multiples, like multiplying a standard triplet by factors such as 2.5.

Shortcut Trick

Volume of a cylinder = π × r² × h

h = V ÷ (π × r²)

h = 600 ÷ (3.14 × 30²)

h = 600 ÷ 2826

h ≈ 0.21 cm

∴ The correct answer is 0.21 cm.

Alternate Method

Given:

Radius of the cylinder (r) = 30 cm

Volume of the cylinder (V) = 600 cm³

Value of π = 3.14

Formula Used:

Volume of a right circular cylinder = π × r² × h

Calculations:

⇒ V = π × r² × h

⇒ 600 = 3.14 × (30)² × h

⇒ 600 = 3.14 × 900 × h

⇒ 600 = 2826 × h

⇒ h = 600 ÷ 2826

⇒ h ≈ 0.2123 cm

⇒ h ≈ 0.21 cm

∴ The correct answer is 0.21 cm.

Additional Information

Curved Surface Area of a Cylinder

The curved surface area (CSA) of a right circular cylinder is given by 2 × π × r × h.

Total Surface Area of a Cylinder

The total surface area (TSA) includes the CSA and the area of the two circular bases, given by 2 × π × r × (r + h).

Volume of a Cone

A cone with the same base radius and height as a cylinder has exactly one-third of the cylinder's volume, given by (1 ÷ 3) × π × r² × h.

Shortcut Trick

In congruent triangles, corresponding parts are equal. Since ΔABC ≅ ΔPQR, we know that ∠A = ∠P.

The sum of the internal angles in ΔABC is 180º, which gives us ∠A + ∠C = 180º − ∠B.

Substitute ∠A with ∠P directly: ∠P + ∠C = 180º − 35º = 145º.

∴ The correct answer is 145º.

Alternate Method

Given:

ΔABC ≅ ΔPQR

AB = PQ = 8 units, BC = QR = 10 units

∠B = 35º

Concept Used:

If two triangles are congruent, their corresponding parts are equal (CPCTC).

The sum of angles in a triangle is exactly 180º.

A B C

P Q R

35º

35º

8 10

8 10

Calculations:

⇒ Since ΔABC ≅ ΔPQR, the corresponding angles map to each other in exactly the same order.

⇒ ∠A = ∠P, ∠B = ∠Q, and ∠C = ∠R

⇒ In ΔABC, the sum of internal angles equals 180º.

⇒ ∠A + ∠B + ∠C = 180º

⇒ Substitute the given value of ∠B = 35º into the equation:

⇒ ∠A + 35º + ∠C = 180º

⇒ ∠A + ∠C = 180º − 35º

⇒ ∠A + ∠C = 145º

⇒ Since ∠A = ∠P, substitute ∠A with ∠P in the equation:

⇒ ∠P + ∠C = 145º

∴ The correct answer is 145º.

Additional Information

Congruent Triangles (CPCTC)

When two triangles are congruent, all of their corresponding sides and angles are equal. This property is known as Corresponding Parts of Congruent Triangles are Congruent (CPCTC).

Angle Sum Property of a Triangle

The sum of all three internal angles of any planar triangle is strictly equal to 180º. i.e., ∠A + ∠B + ∠C = 180º.

Conditions for Congruency

Two triangles can be proven congruent using five standard criteria: SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and RHS (Right angle-Hypotenuse-Side).

Shortcut Trick

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

Here, arc PM subtends ∠MAP at the centre A and ∠MQP at point Q on the circumference.

⇒ ∠MQP = ∠MAP ÷ 2

⇒ ∠MQA = 110º ÷ 2 = 55º

∴ The correct answer is 55º.

Alternate Method

Given:

PQ is the diameter of the circle with centre A.

m∠MAP = 110º

Concept Used:

Angles on a straight line add up to 180º.

Angles opposite to equal sides in an isosceles triangle are equal.

The sum of all internal angles in a triangle is exactly 180º.

Calculations:

Since PAQ is a straight line, ∠MAP and ∠MAQ form a linear pair.

⇒ ∠MAQ = 180º − ∠MAP

⇒ ∠MAQ = 180º − 110º = 70º

In ΔMAQ, the sides AM and AQ are radii of the same circle.

⇒ AM = AQ

Since opposite angles of equal sides are equal in a triangle:

⇒ ∠AMQ = ∠MQA

The sum of all angles in ΔMAQ is 180º:

⇒ ∠MAQ + ∠AMQ + ∠MQA = 180º

⇒ 70º + 2 × ∠MQA = 180º

⇒ 2 × ∠MQA = 110º

⇒ ∠MQA = 55º

∴ The correct answer is 55º.

Additional Information

Angle at the Centre Theorem

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

Angle in a Semicircle

The angle subtended by a diameter at any point on the circumference is always a right angle (90º).

Angles in the Same Segment

Angles subtended by the same arc at any two points on the circumference in the same segment of the circle are always equal.

The correct answer is: Option 1.

Key Points

• The word "avariciousness" means extreme greed for wealth or material gain. (लोभ)
• Example: The avariciousness of the businessman led him to exploit his employees.
• "Generosity" refers to the quality of being kind and generous, often involving giving freely. (उदारता)
• Example: Her generosity knew no bounds as she donated a large sum to charity.
• Hence, we can infer that the opposite of "avariciousness" is "generosity".

Therefore, the correct answer is: Option 1.

Additional Information

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

• Criticism (आलोचना): The expression of disapproval of someone or something based on perceived faults or mistakes.
• Example: Her criticism of the new policy was harsh but fair.
• Hatred (घृणा): Intense dislike or ill will.
• Example: His hatred for injustice was evident in his passionate speeches.
• Envy (ईर्ष्या): A feeling of discontented or resentful longing aroused by someone else's possessions, qualities, or luck.
• Example: She felt envy towards her friend's success.

The correct answer is Option 2.

 

Key Points

• The active sentence “He has written a best-selling novel” is in the present perfect tense (has written).
• When converting to the passive voice, the tense remains the same:
• has written → has been written

So, the correct passive construction is: A best-selling novel has been written by him.

Additional Information

Why others are incorrect:

• Option 1: was being written → past continuous (wrong tense)
• Option 3: was written → simple past (tense changes)
• Option 4: would have been written → conditional perfect (changes meaning)

Therefore, the correct answer is Option 2.

The correct answer is Option (4) i.e. QSPR

Key Points

• The sentence begins with the subject "I have," which is correctly indicated by part (Q).
• Following the subject, "not seen" (S) continues the logical sequence, making it clear what the subject has not done.
• The next part, "her face," (P) provides the object that the subject has not seen.
• Ending with, "for a year" (R) completes the sentence by stating the duration.

Therefore, the correct answer is QSPR.

Additional Information

• Option 1 (PQRS): This option starts with "her face I have not seen for a year," which disrupts the logical flow and structure of the sentence.
• Option 2 (PSQR): This option starts with "her face not seen I have for a year," which creates an incorrect and confusing structure.
• Option 3 (SPQR): This option starts with "not seen her face I have for a year," which is awkward and grammatically incorrect.

The correct answer is: Congested.

Key Points

• The word "Barren" means lacking in vegetation and life; unable to produce much or any vegetation. (बंजर)
• Example: The barren landscape stretched as far as the eye could see, with no signs of life.
• "Congested" refers to an area that is overcrowded or filled to excess, often causing delays or blockages. (भीड़-भाड़ वाला)
• Example: The congested streets made it difficult to drive through the city during rush hour.
• Hence, we can infer that the opposite of 'Barren' is 'Congested'.

Therefore, the correct answer is: Congested.

Additional Information

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

• Believe (विश्वास करना): Accept something as true; feel sure of the truth of.
• Example: He couldn't believe his eyes when he saw the surprise party.
• Grumbled (बड़बड़ाना ): Complain or protest about something in a bad-tempered but typically muted way.
• Example: She grumbled about the long wait at the doctor's office.
• Glancing (झांकना): Taking a brief or hurried look.
• Example: He kept glancing at his watch during the meeting.

The correct answer is Option 1.

 

Key Points

• A group of lions is correctly referred to as a "pride," not a "herd."
• The other options refer to groups of different animals and are not appropriate substitutions for "a herd of cattle."

Therefore, the correct answer is Option 1.

 

Correct Sentence: "A pride of lions consists of related females, cubs, and a small number of adult males."

 

Additional Information

• Option 2: "pack of wolves" – A group of wolves is called a pack, but this does not fit the context of the sentence.
• Option 3: "school of fish" – A group of fish is called a school, and is not relevant in this context.
• Option 4: "flock of birds" – A group of birds is called a flock, and is not appropriate for the context.

The correct answer is: Option 1.

Key Points

• The idiom "a rainy day" refers to a time when money might unexpectedly be needed. (मुश्किल समय के लिए बचत)
• Example: It's always wise to save some money for a rainy day.
• "A raw deal" means being treated unfairly. (अन्यायपूर्ण व्यवहार)
• Example: She felt she got a raw deal when she was passed over for the promotion.
• "A rash of something" refers to a large number of unpleasant events of the same type happening within a short period. (घटनाओं की बाढ़)
• Example: There has been a rash of burglaries in our neighborhood recently.
• "A rap over the knuckles" means a mild reprimand or scolding. (हल्की फटकार)
• Example: The teacher gave him a rap over the knuckles for being late.
• Hence, we can infer that the most appropriate idiom for a time when money might unexpectedly be needed is "a rainy day".

Therefore, the correct answer is: Option 1.

Additional Information

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

• A raw deal (अन्यायपूर्ण व्यवहार): Being treated unfairly.
• Example: She felt she got a raw deal when she was passed over for the promotion.
• A rash of something (घटनाओं की बाढ़): A large number of unpleasant events of the same type happening within a short period.
• Example: There has been a rash of burglaries in our neighborhood recently.
• A rap over the knuckles (हल्की फटकार): A mild reprimand or scolding.
• Example: The teacher gave him a rap over the knuckles for being late.

The correct answer is: Option 4.

Key Points

• The word "Atheist" means a person who does not believe in the existence of God. (नास्तिक)
• Example: John declared himself an atheist, stating that he doesn't believe in any deities.
• "Amateur" refers to a person who engages in a pursuit, especially a sport, on an unpaid basis. (शौक़ीन)
• Example: She is an amateur painter who enjoys creating art in her free time.
• "Anarchy" means a state of disorder due to the absence or non-recognition of authority or other controlling systems. (अराजकता)
• Example: The country fell into anarchy after the government collapsed.
• "Autocrat" refers to a ruler who has absolute power. (तानाशाह)
• Example: The autocrat imposed strict rules and regulations on the people.

Therefore, the correct answer is: Option 4

The correct answer is: Option 3.

Key Points

• The word "Confidental" is incorrectly spelt. The correct spelling is "Confidential" which means intended to be kept secret. (गोपनीय)
• Example: The document contains confidential information that must not be shared.
• "Confidential" refers to something that is meant to be kept secret or private. (गोपनीय)
• Example: The company's financial records are confidential and not available to the public.

Therefore, the correct answer is: Option 3.

Additional Information

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

• Measurement (मापन): The act or process of measuring something.
• Example: Accurate measurement is crucial in scientific experiments.
• Region (क्षेत्र): A specific area or part of the world, country, etc.
• Example: The Amazon rainforest is a vast and diverse region.
• Strengths (ताकतें): This is the incorrect spelling; the correct spelling is "Strengths" which means qualities or abilities that someone or something has that gives it an advantage. (ताकतें)
• Example: One of her strengths is her ability to stay calm under pressure.

The correct answer is: hole.

Key Points

• The word "cavity" means an empty space within a solid object, often referring to a hollow area. (गुहा)
• Example: The dentist found a cavity in one of my molars during the check-up.
• "hole" refers to an opening or hollow space in something, which is similar to the meaning of cavity. (छेद)
• Example: The rabbit disappeared into a hole in the ground.
• Hence, we can infer that the correct word to replace 'cavity' is 'hole'.

Therefore, the correct answer is: hole.

Additional Information

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

• Elevation (उन्नति): The height above a given level, especially sea level.
• Example: The elevation of the mountain peak is over 8,000 meters.
• Height (ऊंचाई): The measurement of someone or something from head to foot or from base to top.
• Example: The height of the tower is 100 meters.
• Mound (ढेर): A raised area of earth or stones.
• Example: They built a small mound of stones as a marker.