DSSSB PGT Chemistry (Female) Official Paper (Held On: 06 Jul, 2018 Shift 1) (Previous Year Paper)

Karan said to Navika, "Your father's mother's only daughter-in-law is my sister."

Thus, Karan is the brother of Navika's mother.

Hence, the correct answer is "Option 2".

The logic followed here is:

Bicycle : Ride :: Boat : ?

Logic: Action 

In Bicycle : Ride → A bicycle is ridden.

Similarly,

In Boat : ? → A boat is rowed.

Here, "Boat : Row" is the correct pair as per the logic.

Hence, the correct answer is "Row".

The logic followed here is:

Logic:  Second number = (First number)²

For 5 : 25

→ (5)² = 25

Similarly,

For 9 : ?

→ (9)² = 81

→ The missing number is 81.

Hence, the correct answer is "Option 3".

The logic followed here is:

Logic: The second number is the product of the individual digits of the first number.

 logic:

For 234 : 24

→ Digits are 2, 3, 4

→ Product of digits = 2 × 3 × 4 = 25

→ 6 × 4 =  24

Similarly, 

For 456 : ?

→ Digits are 4, 5, 6

→ Product of digits = 4 × 5 × 6 = ?

→ 20 × 6 =120

Hence, the correct answer is "Option 1".

Calculation:

The words given are: Knife, Axe, Scissors, and Hatchet.

- Knife, Axe, and Hatchet are all tools used for cutting or chopping. Knife and Axe are typically handheld tools used to cut or chop, while a Hatchet is a smaller version of an axe. These three items are primarily used for cutting tasks.

• Scissors, on the other hand, are used for cutting with two blades that work in a scissor-like motion. It is a distinct tool because it is designed for precision cutting, unlike the others which are designed for more forceful cutting or chopping.

Hence, the word that is different from the others is "Scissors".

Given:

 Arjun starts from his home and goes straight for 3 km.

Then he turns right and goes for 5 km.

Finally, he turns left and goes for 3 km to reach the temple. 

Thus, the temple is in the North-East  from Arjun’s home if he started his journey facing North.

Hence, the correct answer is "Option 1".

Given:

 Misha starts from her home and goes straight for 2 km.

Then she turns right and goes for 3 km.

Finally, she turns left and goes for 2 km to reach the mall.

Thus, shortest distance between Misha’s home and the mall is 5 km.

Hence, the correct answer is "Option 2".

The least possible venn diagram of the given statements is:

Hence, the correct answer is "Option 2".

Given: Six friends, Aman, Bipin, Chhagan, Jagan, Magan, and Tapan, are sitting around a circular table facing one another, such that each friend is seated exactly opposite another friend.

Chhagan is sitting opposite Magan. Magan sits to Tapan’s immediate right.

Aman does not sit next to Bipin or Tapan. Jagan is sitting to Aman’s immediate right. 

Thus, Bipin is sittin between Tapan and Chhagan .

Hence, the correct answer is "Option 1".

Given: Six friends, Aman, Bipin, Chhagan, Jagan, Magan, and Tapan, are sitting around a circular table facing one another, such that each friend is seated exactly opposite another friend.

Chhagan is sitting opposite Magan. Magan sits to Tapan’s immediate right.

Aman does not sit next to Bipin or Tapan. Jagan is sitting to Aman’s immediate right. 

Thus, Jagan is sitting exactly opposite Tapan.

Hence, the correct answer is "Option 2".

FEDERAL is coded as GDEDSZM

Similarly,

GENETIC be coded  ?

Hence, the correct answer is "Option 1".

Given e×pression:

217 $ 7 & 4 # 5 @ 6

Given Symbol Replacements:

• '$' is replaced by '÷
• '&' is replaced by ‘×’
• '@' is replaced by ‘—’ (subtraction)
• '#' is replaced by ‘+’ (addition)

Original: 217 $ 7 & 4 # 5 @ 6

New equation: 217 ÷ 7 × 4 + 5 – 6

= 217 ÷ 7 × 4 + 5 – 6

= 31 × 4 + 5 – 6

= 124 + 5 – 6

= 129 – 6 = 123

Hence, the correct answer is "Option 1"$.

Given: Six friends are riding horses.

Visajirao rides faster than Dipajirao.

→ Visajirao > Dipajirao.

Prataprao rides faster than Visajirao.

→Prataprao > Visajirao > Dipajirao.

Dipajirao rides faster than Hilal but slower than Vithalrao. Vithalrao does not ride as fast as Visajirao.

→Prataprao > Visajirao > Vithalrao > Dipajirao > Hilal.

Thus, Prataprao  rides the fastest.

Hence, the correct answer is "Option 1".

The logic followed here is:

Hence, the correct answer is "Option 4".

The logic followed here is:

Logic: Square of the sum of upper number = lower number.

→ 4² + 5²  = 41

= 16 + 25 = 41.

→ 32 + 62  = 45

= 9 + 36 = 45.

Similarly,

→ 22 + 72  = ?

= 4 + 49 = 53.

Hence, the correct answer is "Option 3".

Statements:

All songs are stories.

Some stories are novels.

The least possible venn diagram is given:

Conclusions:

1. All novels are stories -False(because, some stories are novel is given, so it can be possible only).
2. Some stories are songs - True(because, all songs are stories it implies that some stories are songs).

Thus, Only conclusion 2 follows. 

Hence, the correct answer is "Option 2".

The logic followed here is:

Statement: Children under the age of 12 years should not be allowed to use mobile phones.

Argument I: Mobile phones are expensive and all children cannot afford them.

Argument II: By using mobile phones, children under 12 years can get exposed to harmful radiation.

Analysis:

Argument I focuses on the financial aspect, stating that mobile phones are expensive and not all children can afford them. While this is a valid point, it is not directly related to the harm caused by mobile phones themselves, which is the primary concern in the statement.

Argument II discusses the potential exposure to harmful radiation, which is a valid health concern when it comes to children using mobile phones. This directly supports the statement, as the harm caused by radiation is a strong reason to restrict mobile phone use among young children.

Thus, the strong argument is Argument II because it directly addresses the negative effects of mobile phone usage on children, which aligns with the statement about restricting mobile phone use for children under 12 years.

Hence, the correct answer is "Option 2"

Statement: "Only hard-working students have scored more than 60 per cent marks in the annual exam. Rishabh scored 66 per cent marks."

Conclusion I:

Rishabh is very intelligent → Does not follow(because The statement only links scoring over 60% to being hard-working. It says nothing about intelligence. A student can be hard-working without necessarily being "very intelligent," or vice-versa. We cannot infer intelligence from the given information).

Conclusion II:

Rishabh is a hard-working student. →  Follows (because The statement says "Only hard-working students have scored more than 60 per cent marks." Rishabh scored 66%, which is more than 60%. Therefore, based on the statement, Rishabh must be a hard-working student.

Therefore, only conclusion II follows.

The correct answer is 2) Only conclusion II follows.

The logic followed here is:

Situation: You are playing cricket with your friends near your home. When you hit the ball with your bat, the ball hits and breaks the window pane of a neighbour.

Appropriate Action:

In this situation, the most appropriate action would be to take responsibility for the damage caused. You should apologize to your neighbour for the inconvenience and offer to repair or replace the broken window. If necessary, discuss how the repair costs will be covered.

This demonstrates accountability and shows respect for your neighbour's property, which is important in maintaining good relationships in the community.

Thus, the most appropriate action is: Apologize to your neighbour and offer to repair or compensate for the broken window.

Hence, the correct answer is "Option 4".

Calculation:

Statement I: The government has banned fishing in the lake.

Statement II: High amount of hazardous toxins were found in the lake water.

Analysis:

Statement I suggests a government action (banning fishing) which may be a response to some problem in the lake. Statement II mentions hazardous toxins found in the water, which can be a reason for the government to take such an action to protect public health or the environment.

This shows that the presence of hazardous toxins (Statement II) is likely the cause, and the government’s decision to ban fishing (Statement I) is the effect of that cause.

Hence, the correct option is 2) Statement II is the cause and statement I is its effect.

The correct answer is Lord Mountbatten.

Key Points

• Lord Louis Mountbatten was the last Viceroy of British India and the first Governor-General of independent India.
• He served as the Viceroy from February 1947 to August 1947 and oversaw the partition of India into two nations, India and Pakistan.
• After India's independence on 15 August 1947, Lord Mountbatten became the first Governor-General of India and held this position until June 1948.
• Mountbatten was the only British Governor-General of independent India, after which the role was assumed by Indian leaders starting with Chakravarti Rajagopalachari in 1948.
• Mountbatten's tenure was marked by significant events, including the communal violence during partition and the accession of princely states to the Indian Union.

Additional Information

• Viceroy of India:
• The Viceroy was the head of the British administration in India, representing the British Crown.
• The position was established in 1858 after the abolition of the East India Company's rule and continued until 1947.
• Governor-General of India:
• The Governor-General was originally the head of the British administration in India before the creation of the Viceroy position in 1858.
• Post-independence, the Governor-General became the representative of the British monarch in India until India became a republic in 1950.
• Partition of India:
• The partition was a significant event in Indian history, leading to the creation of two independent nations, India and Pakistan, on 15 August 1947.
• It resulted in massive communal violence, displacement, and loss of lives, affecting millions of people.
• Chakravarti Rajagopalachari:
• He was the first and only Indian Governor-General of independent India, serving from June 1948 to January 1950.
• He played a crucial role in the Indian independence movement and was a close associate of Mahatma Gandhi.

The correct answer is Morley-Minto Reforms.

Key Points

• The Indian Councils Act of 1909 is commonly referred to as the Morley-Minto Reforms.
• The Act was named after the Secretary of State for India, John Morley, and the Governor-General of India, Lord Minto.
• It introduced the concept of separate electorates for Muslims, allowing them to elect their representatives independently.
• The Act significantly expanded the legislative councils both at the central and provincial levels.
• It marked the beginning of communal representation in Indian politics, which later became a contentious issue.

Additional Information

• Separate Electorates:
• Separate electorates allowed specific communities, such as Muslims, to vote for their representatives exclusively.
• This system was meant to address the political concerns of minorities but led to divisive politics in the long run.
• Expansion of Legislative Councils:
• The Act increased the number of members in legislative councils at both central and provincial levels.
• Members could now discuss the budget and suggest amendments, though their powers remained limited.
• John Morley's Role:
• John Morley, as the Secretary of State for India, believed in reforms to address Indian demands for representation.
• He emphasized the importance of including Indians in governance while maintaining British control.
• Lord Minto's Contribution:
• Lord Minto, the Governor-General, played a key role in implementing the reforms on the ground.
• His policies earned him the title "Father of Communal Electorates" due to his role in introducing separate electorates.
• Impact on Indian Politics:
• The Morley-Minto Reforms were a response to growing demands for Indian representation in governance.
• Although they introduced reforms, they also sowed seeds of communalism, which influenced later political developments.

The correct answer is Mahatma Gandhi.

Key Points

• Mahatma Gandhi attended the Second Round Table Conference held in London in 1931 as the sole official representative of the Indian National Congress.
• The Second Round Table Conference was convened from September 7, 1931, to December 1, 1931.
• Gandhi's participation was part of the Gandhi-Irwin Pact, signed earlier in March 1931, which temporarily halted the Civil Disobedience Movement.
• The main agenda of the conference was to discuss constitutional reforms in India, but it failed to achieve significant agreements due to conflicting interests among participants.
• The conference saw representation from British officials, princely state rulers, and communal groups, but the lack of consensus frustrated Gandhi's efforts to secure a unified demand for Indian self-rule.

Additional Information

• Round Table Conferences:
• A series of three conferences held between 1930 and 1932 in London to discuss constitutional reforms in India.
• The conferences were initiated by the British government under the Viceroyship of Lord Irwin.
• The first conference (1930) was boycotted by the Indian National Congress, while the second (1931) saw Gandhi's participation.
• Gandhi-Irwin Pact (1931):
• An agreement between Mahatma Gandhi and Lord Irwin, the then Viceroy of India, signed on March 5, 1931.
• It resulted in the suspension of the Civil Disobedience Movement and agreed on the release of political prisoners.
• In return, Gandhi agreed to attend the Second Round Table Conference as the representative of the Congress.
• Outcome of the Second Round Table Conference:
• The conference ended without any substantial agreement due to fundamental differences among Indian representatives.
• Communal representation and separate electorates were major points of contention, particularly advocated by Dr. B.R. Ambedkar for Dalits.
• The lack of British commitment to self-rule for India deeply disheartened Gandhi.
• Civil Disobedience Movement:
• Launched by the Indian National Congress in 1930 under Gandhi's leadership to protest against British rule.
• The movement included nonviolent resistance, refusal to pay taxes, and boycotts of British goods.
• It was temporarily suspended following the Gandhi-Irwin Pact but resumed after the Second Round Table Conference's failure.

The correct answer is 7417 km.

Key Points

• India's coastline has a total length of 7,417 kilometers, encompassing both the mainland and its islands.
• The mainland coastline covers approximately 5,422 kilometers, while the remaining length belongs to the Andaman and Nicobar Islands and the Lakshadweep Islands.
• The coastline touches nine Indian states: Gujarat, Maharashtra, Goa, Karnataka, Kerala, Tamil Nadu, Andhra Pradesh, Odisha, and West Bengal.
• India’s coastal areas are strategically important for trade, tourism, biodiversity, and national security.
• The coastline plays a critical role in supporting marine ecosystems and livelihoods of millions of people dependent on fishing and related industries.

Additional Information

• Exclusive Economic Zone (EEZ):
• India has an Exclusive Economic Zone (EEZ) of approximately 2.37 million square kilometers, extending up to 200 nautical miles from the coastline.
• The EEZ is crucial for marine resource exploration, energy production, and fishing rights.
• Coastal Biodiversity:
• India’s coastline is home to diverse ecosystems, including mangroves, coral reefs, estuaries, and lagoons.
• The Sundarbans in West Bengal is the largest mangrove forest in the world and a UNESCO World Heritage Site.
• Ports in India:
• India has 13 major ports and over 200 minor and intermediate ports along its coastline.
• Some of the major ports include Mumbai, Chennai, Kolkata, Visakhapatnam, and Cochin.
• Coastal Protection Initiatives:
• The Indian government has launched initiatives like the Integrated Coastal Zone Management (ICZM) program to protect coastal and marine ecosystems.
• Efforts are being made to mitigate coastal erosion, which affects approximately 36% of India's coastline.

The correct answer is Narmada.

Key Points

• Narmada River is one of the major rivers in India that flows westward and drains into the Arabian Sea.
• The Narmada originates from the Amarkantak Plateau in Madhya Pradesh and flows through the states of Madhya Pradesh, Maharashtra, and Gujarat.
• It is also referred to as the "Lifeline of Madhya Pradesh and Gujarat" due to its significant contribution to irrigation, drinking water, and hydroelectric power generation.
• The river flows for approximately 1,312 kilometers before merging into the Arabian Sea.
• It forms the traditional boundary between North and South India and is one of the few rivers in India that flows westward, unlike most other major rivers that flow eastward.

Additional Information

• Westward-Flowing Rivers of India
• Rivers like Narmada, Tapi, Mahi, and Sabarmati flow westward and drain into the Arabian Sea.
• These rivers are exceptions as most Indian rivers flow eastward into the Bay of Bengal.
• The westward flow is attributed to the geological tilting of the Indian subcontinent towards the west during its formation.
• Significance of the Narmada River
• The river is home to several important dams, including the Sardar Sarovar Dam and the Indira Sagar Dam, which are vital for water supply, irrigation, and hydroelectric power.
• The Narmada Valley is known for its fertile soil, supporting agriculture in the region.
• Religious and Cultural Importance
• The Narmada is considered a sacred river in Hinduism, and it is believed that a parikrama (circumambulation) of the river can cleanse sins.
• It is associated with several mythological legends and is revered in texts like the Puranas.
• Geological Features
• The Narmada River flows through the rift valley formed due to the faulting of the Indian Plate.
• Its course features picturesque landscapes, including marble rocks near Bhedaghat in Madhya Pradesh.

The correct answer is 42^nd Amendment.

Key Points

• The 42^nd Amendment Act of 1976 added the Fundamental Duties to the Indian Constitution under Article 51A.
• This amendment was enacted during the tenure of Prime Minister Indira Gandhi.
• The Fundamental Duties were inspired by the Constitution of the Soviet Union and were introduced based on recommendations from the Swaran Singh Committee.
• Initially, there were 10 Fundamental Duties; later, the 86^th Amendment in 2002 added the 11^th duty related to education.
• Fundamental Duties are non-justiciable, meaning they cannot be enforced by law, but they serve as moral obligations for citizens.

Additional Information

• Article 51A: It lists the Fundamental Duties of Indian citizens and emphasizes their role in promoting harmony, protecting heritage, and contributing to national development.
• Swaran Singh Committee: Established in 1976, it recommended the inclusion of Fundamental Duties in the Indian Constitution to instill civic responsibility among citizens.
• 42^nd Amendment (1976): Known as the "Mini-Constitution," this amendment brought significant changes, including the addition of Fundamental Duties, and expanded the scope of Directive Principles of State Policy.
• Non-Justiciability: Fundamental Duties are non-enforceable by courts but act as ethical guidelines for citizens to uphold the spirit of the Constitution.
• The 11^th Fundamental Duty, added by the 86^th Amendment in 2002, obligates parents/guardians to provide opportunities for education to their children aged 6 to 14 years.

The correct answer is Article 356.

Key Points

• Article 356 of the Indian Constitution provides provisions for imposing President's Rule in a state due to the failure of constitutional machinery.
• Under this article, if the Governor of a state submits a report indicating that the state government cannot function according to constitutional provisions, the President can intervene.
• President's Rule is imposed when there is a breakdown of governance or law and order, or if elections cannot be conducted.
• During President's Rule, the state legislature is either dissolved or suspended, and the central government assumes control of the state.
• The imposition of President's Rule is subject to approval by both houses of Parliament within two months of its declaration.

Additional Information

• Constitutional Emergency:
• It refers to a situation where the governance of a state cannot be carried out in accordance with the Constitution.
• It is also called "President's Rule" or "State Emergency."
• Article 356 allows the President to assume control of the state's administration during such emergencies.
• Procedure for Imposition:
• The Governor sends a report to the President citing reasons for failure of constitutional machinery.
• The President may issue a proclamation imposing President's Rule in the state.
• Parliamentary approval is required within two months of the proclamation.
• Duration and Extension:
• Initially, President's Rule can be imposed for six months.
• It can be extended up to a maximum of three years with parliamentary approval every six months.
• Judicial Review:
• The imposition of President's Rule is subject to judicial review to ensure it is not misused.
• The landmark case of S.R. Bommai v. Union of India (1994) established guidelines for its application.

The correct answer is Ganesh Vasudev Mavalankar.

Key Points

• Ganesh Vasudev Mavalankar, often referred to as "Dadasaheb," was the First Speaker of the Lok Sabha after India gained independence.
• He served as the Speaker from 1952 to 1956, during the First Lok Sabha.
• Mavalankar was a prominent figure in India's freedom struggle and was associated with the Indian National Congress.
• He played a key role in shaping parliamentary procedures and strengthening democratic practices in India.
• Before becoming the Speaker of the Lok Sabha, he was the Speaker of the Central Legislative Assembly under British India.

Additional Information

• Role of the Speaker:
• The Speaker of the Lok Sabha is responsible for maintaining order and decorum in the House during debates.
• The Speaker represents the Lok Sabha to the President of India and communicates its resolutions.
• They ensure impartiality and fair conduct in the proceedings of the House.
• Lok Sabha:
• The Lok Sabha is the lower house of India's Parliament, consisting of representatives directly elected by the people.
• The First Lok Sabha was constituted in 1952 following the general elections held under the Indian Constitution.
• It has a maximum strength of 552 members, with 530 representing the states, 20 from Union territories, and 2 nominated by the President.
• Ganesh Vasudev Mavalankar's Legacy:
• Mavalankar was instrumental in establishing parliamentary norms and traditions in newly independent India.
• He authored several works on parliamentary practices and procedures.
• His leadership laid the foundation for India's robust parliamentary democracy.
• Central Legislative Assembly:
• The Central Legislative Assembly was the precursor to the Lok Sabha during British rule in India.
• It was established under the Government of India Act, 1919, and had limited legislative powers.
• Ganesh Vasudev Mavalankar served as the Speaker of this Assembly before India's independence.

The correct answer is Cabinet Committee on Economic Affairs.

Key Points

• The Cabinet Committee on Economic Affairs (CCEA) is responsible for approving the Minimum Support Prices (MSP) for various crops in India.
• MSP is a form of market intervention by the government to ensure agricultural producers are protected against any sharp fall in farm prices.
• The CCEA takes decisions based on the recommendations of the Commission for Agricultural Costs and Prices (CACP).
• MSP is announced for 22 mandated crops and an additional bonus for some crops in certain cases.
• The primary objective of MSP is to ensure a remunerative price to farmers and encourage them to adopt modern farming practices.

Additional Information

• Commission for Agricultural Costs and Prices (CACP):
• CACP is an attached office of the Ministry of Agriculture and Farmers' Welfare.
• It recommends MSPs for crops based on factors like cost of production, demand-supply balance, and market price trends.
• Factors Considered for MSP:
• Cost of cultivation, including inputs like seeds, fertilizers, and labor.
• Trends in domestic and international market prices.
• Parity between crops and ensuring fair returns to farmers.
• Mandated Crops under MSP:
• Includes cereals (wheat, rice, maize, etc.), pulses (tur, moong, urad), oilseeds (soybean, mustard, groundnut), and commercial crops (cotton, sugarcane).
• Role of MSP in Agriculture:
• Encourages farmers to grow particular crops to meet food security needs.
• Acts as a safety net for farmers during market price fluctuations.
• Helps stabilize the rural economy and reduce farmer distress.

The correct answer is Rajiv Kumar.

Key Points

• Rajiv Kumar served as the Vice Chairperson of NITI Aayog from September 1, 2017, to April 30, 2022.
• He succeeded Arvind Panagariya, the first Vice Chairperson of NITI Aayog.
• The National Institution for Transforming India (NITI) Aayog is the policy think tank of the Government of India, established on January 1, 2015.
• Rajiv Kumar, an economist, has authored several books on India’s economy and has held multiple academic and administrative positions globally.
• Under his leadership, NITI Aayog focused on policy reforms and development strategies, including initiatives like "Aspirational Districts Programme" and "Atal Innovation Mission."

Additional Information

• NITI Aayog:
• It replaced the Planning Commission of India, which was operational since 1950.
• The organization operates under the chairmanship of the Prime Minister of India.
• Its core function is to foster cooperative federalism and promote sustainable development goals (SDGs) in India.
• NITI Aayog has two key hubs: Team India Hub (engages with states) and Knowledge and Innovation Hub (focuses on research and innovation).
• Functions of NITI Aayog:
• Promoting competitive and cooperative federalism among states.
• Formulating strategic and long-term policies and programs for India’s development.
• Providing technical advice to the central and state governments.
• Monitoring and evaluating the implementation of government programs and initiatives.
• Key Initiatives by NITI Aayog:
• Aspirational Districts Programme: Aims to transform underdeveloped districts through rapid progress in health, education, and infrastructure.
• Atal Innovation Mission: Promotes entrepreneurship and innovation across India through initiatives like Atal Tinkering Labs and Atal Incubation Centers.
• Digital India: Supports the government's vision of a digitally empowered India through policy frameworks.
• Health and Nutrition: Implements the National Nutrition Mission (Poshan Abhiyan) to reduce malnutrition and stunting in children.
• Rajiv Kumar’s Contributions:
• Played a key role in drafting the Three-Year Action Agenda for accelerating economic growth.
• Advocated for reforms in agriculture, education, and job creation.
• Focused on making India self-reliant through initiatives like Atmanirbhar Bharat Abhiyan.

The correct answer is Kerala.

Key Points

• Onam is the most celebrated and significant festival of Kerala, India.
• It is a harvest festival that marks the annual homecoming of the mythical King Mahabali.
• The festival is celebrated in the month of Chingam (August-September) in the Malayalam calendar.
• Onam is a 10-day-long festival featuring cultural events such as Pookalam (flower arrangements), Vallam Kali (boat races), and Onasadya (a traditional feast).
• It is considered a symbol of Kerala's rich cultural heritage and unity.

Additional Information

• King Mahabali:
• According to mythology, King Mahabali was a generous and just ruler who was sent to the underworld by Lord Vishnu's Vamana avatar.
• Onam celebrates his annual visit to his kingdom as a blessing from Lord Vishnu.
• Onasadya:
• Onasadya is a grand vegetarian feast served on banana leaves, consisting of multiple dishes like rice, sambar, avial, and payasam.
• It is an integral part of the Onam celebrations.
• Pookalam:
• Pookalam refers to intricate floral designs created on the ground as a form of decoration during Onam.
• Each day of the festival sees the addition of more flowers to the Pookalam.
• Vallam Kali:
• Vallam Kali, or snake boat races, are thrilling events held during Onam in Kerala's backwaters.
• It attracts huge crowds and showcases teamwork and traditional boat-building skills.
• Unity in Diversity:
• Onam is celebrated by people of all religions and communities in Kerala, reflecting the state's unity and harmony.
• It is a festival that transcends cultural and religious boundaries.

The correct answer is Odissi.

Key Points

• Ranjana Gauhar is a renowned Indian classical dancer and an acclaimed exponent of Odissi.
• She has been honored with the prestigious Padma Shri award in 2003 for her contributions to Indian classical dance.
• Ranjana Gauhar has performed extensively across India and abroad, promoting the rich cultural heritage of Odissi.
• She is also a mentor and has been instrumental in training the next generation of Odissi dancers through her organization, Utsav Educational and Cultural Society.
• Odissi is one of the eight classical dance forms of India, originating from the state of Odisha and characterized by its fluid movements and expressive storytelling.

Additional Information

• Odissi Dance
• Odissi is one of the oldest surviving classical dance forms, with roots dating back to 2000 years.
• It is deeply connected to temple art and the devotional traditions of Lord Jagannath in Puri, Odisha.
• The dance form is known for its intricate footwork, graceful movements, and sculpturesque poses inspired by temple carvings.
• Odissi performances are based on themes from Hindu mythology, particularly those related to Lord Krishna and Radha.
• Key Elements of Odissi
• The dance incorporates three distinct stances: Chowka (square posture), Tribhangi (three-bend posture), and Abhinaya (expressional acting).
• It combines rhythmic movements with emotive expressions (or bhava) to narrate stories.
• Recognition and Revival
• Odissi gained recognition as a classical dance form of India in the 1950s.
• Efforts by dancers and scholars such as Kelucharan Mohapatra and Sanjukta Panigrahi played a significant role in its revival and global popularity.
• Other Classical Dance Forms
• India recognizes eight classical dance forms: Bharatanatyam, Kathak, Kathakali, Kuchipudi, Manipuri, Mohiniyattam, Odissi, and Sattriya.
• Each dance form represents the cultural and artistic traditions of its region of origin.

The correct answer is Buddhism.

Key Points

• The Ajanta Caves are located in Maharashtra and were built during the period between the 2^nd century BCE and the 6^th century CE.
• The paintings and sculptures found in the Ajanta Caves are primarily related to Buddhism, depicting the life and teachings of Gautama Buddha.
• The caves are renowned for their intricate frescoes, murals, and carvings, showcasing scenes from the Jataka tales, which narrate stories of Buddha's previous lives.
• Ajanta Caves served as a monastic retreat for Buddhist monks and were used for meditation, study, and the propagation of Buddhist principles.
• The site is recognized as a UNESCO World Heritage Site and is considered a masterpiece of ancient Indian art and architecture.

Additional Information

• Buddhism:
• Buddhism is a spiritual tradition founded by Gautama Buddha in the 5^th-6^th century BCE in India.
• It emphasizes the Four Noble Truths and the Eightfold Path to achieve liberation from suffering and attain Nirvana.
• The religion spread across Asia and influenced art, culture, and philosophy in regions like China, Japan, Sri Lanka, and Southeast Asia.
• Jataka Tales:
• Jataka tales are a collection of stories about the previous lives of Buddha, illustrating moral and ethical lessons.
• These stories are a prominent feature in Buddhist art, including the murals of the Ajanta Caves.
• UNESCO World Heritage Site:
• Ajanta Caves were designated as a UNESCO World Heritage Site in 1983.
• Such sites are recognized for their cultural, historical, or scientific significance and are protected under international conventions.
• Architectural Features of Ajanta Caves:
• The caves include monasteries (Viharas) and prayer halls (Chaityas), carved into the rock face.
• The murals display advanced techniques of shading, perspective, and naturalistic representations of figures.

The correct answer is 101.

Key Points

• India achieved its highest-ever medal tally of 101 medals at the 2010 Commonwealth Games held in Delhi, India.
• This tally included 39 gold, 26 silver, and 36 bronze medals, showcasing India's best performance in the history of the Commonwealth Games.
• The 2010 Commonwealth Games was the 19^th edition of the event and marked the first time India hosted the games.
• India ranked second in the medal tally, with Australia finishing first and England in third place.
• Sports such as wrestling, shooting, and athletics were key contributors to India's success in the 2010 edition.

Additional Information

• Commonwealth Games Overview:
• The Commonwealth Games is a multi-sport event held every four years involving athletes from the Commonwealth of Nations.
• It was first held in 1930 as the British Empire Games in Hamilton, Canada.
• India has been participating in the Commonwealth Games since 1934 and has consistently improved its performance over the years.
• Highlights of the 2010 Commonwealth Games:
• Wrestler Sushil Kumar, shooter Gagan Narang, and boxer Vijender Singh were among the standout performers for India.
• India's performance in shooting and wrestling played a significant role in achieving the record-breaking medal tally.
• The event witnessed participation from 71 nations and territories.
• India's Best Performances in Commonwealth Games:
• India's second-best performance occurred during the 2018 Gold Coast Commonwealth Games, where the country secured 66 medals.
• India has consistently performed well in sports like shooting, wrestling, weightlifting, and badminton.
• Significance of the 2010 Commonwealth Games:
• The 2010 Games helped India establish itself as a major sporting nation in the Commonwealth.
• It also highlighted India's organizational capabilities, despite challenges in preparation and controversies.

The correct answer is 5.

Key Points

• India has won a total of 5 Olympic medals in Wrestling as of June 2018.
• The medal tally includes 1 gold, 2 silver, and 2 bronze medals.
• India's first Olympic medal in wrestling was won by Khashaba Dadasaheb Jadhav in the 1952 Helsinki Olympics (bronze).
• Sushil Kumar is the only Indian wrestler to have won two Olympic medals: a bronze in the 2008 Beijing Olympics and a silver in the 2012 London Olympics.
• Yogeshwar Dutt (bronze in 2012) and Sakshi Malik (bronze in 2016) are other notable Indian wrestlers who have brought Olympic glory to the country.

Additional Information

• Khashaba Dadasaheb Jadhav: India's first individual Olympic medalist in wrestling, he paved the way for future wrestlers by winning bronze in 1952.
• Sushil Kumar: He holds the distinction of being India's most decorated wrestler in the Olympics, with two medals to his name (bronze in 2008 and silver in 2012).
• Sakshi Malik: She became the first Indian woman wrestler to win an Olympic medal (bronze in 2016), inspiring a new generation of female wrestlers.
• Wrestling is a traditional sport in India, with its roots in Pehlwani (a form of traditional Indian wrestling practiced in mud pits called "akhadas").
• The Freestyle and Greco-Roman wrestling formats are the two disciplines contested in the Olympics, with India specializing mainly in freestyle wrestling.

The correct answer is CO2.

Key Points

• Carbon dioxide (CO2) is considered one of the best fire extinguishers, especially for electrical and oil fires, as it does not conduct electricity and does not leave residue.
• CO2 extinguishes fire by displacing oxygen in the surrounding area and suffocating the flames.
• CO2 is a non-flammable and inert gas, making it an ideal choice for extinguishing fires without causing damage to sensitive equipment.
• It is widely used in fire extinguishers and fixed fire suppression systems, particularly in areas like server rooms, laboratories, and industrial facilities.
• CO2 extinguishers are highly effective for Class B (flammable liquids) and Class C (electrical) fires.

Additional Information

• Types of Fire Classes:
• Class A: Fires involving ordinary combustibles like wood, paper, and cloth.
• Class B: Fires involving flammable liquids like gasoline, oil, and paints.
• Class C: Fires involving electrical equipment.
• Class D: Fires involving combustible metals like magnesium and sodium.
• Class K: Fires involving cooking oils and fats.
• Fire Extinguishing Methods:
• Cooling: Reducing the temperature to below ignition point (e.g., water).
• Smothering: Cutting off the oxygen supply (e.g., CO2).
• Starvation: Removing the fuel source.
• Limitations of CO2 Extinguishers:
• Not suitable for Class A fires involving solid combustibles.
• Can pose a risk of asphyxiation in enclosed spaces due to oxygen displacement.
• Other Types of Extinguishing Agents:
• Water: Effective for Class A fires but not for electrical fires.
• Foam: Effective for Class B fires but can damage equipment.
• Dry Chemical Powder: Versatile and effective for Class A, B, and C fires.

The correct answer is 195.

Key Points

• UNESCO (United Nations Educational, Scientific and Cultural Organization) is an international organization established in 1945.
• As of June 2023, UNESCO has 195 Member States and 11 Associate Members.
• UNESCO aims to build peace through international cooperation in education, sciences, culture, and communication.
• The United States and Israel formally withdrew from UNESCO in 2019 but rejoined later.
• UNESCO's headquarters is located in Paris, France.

Additional Information

• UNESCO's Key Activities:
• Promotes education worldwide, including initiatives like Education for All.
• Encourages the protection of cultural heritage through programs like the World Heritage Sites.
• Advances scientific research and collaboration, particularly in sustainability and climate change.
• Supports press freedom and media development under the Communication and Information sector.
• Associate Members:
• Associate Members are territories or regions not fully sovereign but participate in UNESCO's activities.
• Examples include Hong Kong and Macau.
• UNESCO's Governance Structure:
• Governed by the General Conference, which meets every two years to set policies and approve budgets.
• Executive Board comprises representatives from Member States and oversees day-to-day operations.
• UNESCO's Major Programs:
• Man and the Biosphere Programme (MAB): Promotes sustainable development through ecosystem conservation.
• International Geoscience and Geoparks Programme (IGGP): Supports geological heritage and sustainable tourism.
• Memory of the World Programme: Preserves documentary heritage globally.

The correct answer is -0.016.

Key Points

• India's crude oil production growth rate in March 2018 was -0.016, reflecting a decline in production compared to the previous year.
• The negative growth rate indicates a contraction in crude oil production output, which has implications for energy security and the industrial sector.
• Crude oil production is a critical indicator of the energy sector, influencing import dependency and domestic energy prices.
• India imports a significant portion of its crude oil requirements, making domestic production trends crucial for economic planning.
• Factors such as aging oil fields, technical challenges, and infrastructure issues often contribute to declining production rates.

Additional Information

• Crude Oil Production:
• Crude oil is a naturally occurring liquid fossil fuel extracted from underground reservoirs.
• It serves as a primary source for producing petroleum products such as gasoline, diesel, and jet fuel.
• India's key crude oil production regions include offshore fields like Bombay High and onshore fields in Assam and Gujarat.
• Energy Import Dependency:
• India imports over 80% of its crude oil needs, making it highly dependent on international markets.
• Fluctuations in global oil prices directly impact India's trade deficit and inflation rates.
• Challenges in Domestic Production:
• Declining output from mature oil fields due to depletion of reserves and technical challenges.
• Delays in exploration and development of new oil fields.
• Inadequate investment in advanced extraction technologies.
• Government Initiatives:
• Policies to promote exploration and production under the Hydrocarbon Exploration and Licensing Policy (HELP).
• Strategic petroleum reserves have been established to ensure energy security in case of supply disruptions.

The correct answer is TCS (Tata Consultancy Services).

Key Points

• TCS became India’s first IT company to achieve a market capitalization of $100 billion on April 23, 2018.
• The milestone was achieved due to consistent growth in its revenue, expansion in global markets, and strong client retention.
• TCS is part of the Tata Group, one of India's largest and most respected business conglomerates.
• As of the landmark achievement, TCS was among the top global IT services companies in terms of market capitalization.
• The company's focus on digital transformation, automation, cloud computing, and AI contributed significantly to its valuation.

Additional Information

• Market Capitalization:
• It refers to the total value of a company’s outstanding shares of stock, calculated as the share price multiplied by the number of shares.
• Market capitalization is a key indicator of a company's size and financial stability.
• Tata Consultancy Services (TCS):
• Founded in 1968, TCS is headquartered in Mumbai, India.
• It is a leading provider of IT services, consulting, and business solutions globally.
• The company operates in over 50 countries and has a diversified client base across industries.
• Factors Behind TCS's Success:
• TCS’s emphasis on innovation and adoption of emerging technologies like AI, machine learning, and blockchain.
• Strong execution capabilities and robust client relationships.
• Expansion into key global markets, including the US, Europe, and Asia-Pacific.
• Indian IT Industry:
• The Indian IT industry is one of the largest and fastest-growing sectors globally, contributing significantly to the country's GDP.
• Key services include IT consulting, software development, and BPO (Business Process Outsourcing)$.

The correct answer is Chandigarh.

Key Points

• Chandigarh has NOT been listed among the world's 20 most polluted cities in terms of PM2.5 particulate matter levels as per global air quality studies.
• PM2.5 refers to fine particulate matter with a diameter of 2.5 micrometers or less, which is linked to serious health risks.
• According to the World Health Organization (WHO) and IQAir reports, cities like Patna, Agra, and Gurgaon have been identified as highly polluted in terms of PM2.5 levels.
• Chandigarh, known for its planned urban design and greenery, generally fares better in air quality compared to other major Indian cities.
• Efforts to maintain sustainable urban development and cleaner air contribute to Chandigarh’s relatively lower pollution levels.

Additional Information

• Particulate Matter (PM2.5):
• PM2.5 particles are tiny and can penetrate deep into the lungs and bloodstream, causing respiratory and cardiovascular problems.
• Sources of PM2.5 include vehicle emissions, industrial activities, construction dust, and burning of fossil fuels.
• Air Pollution and Health:
• Exposure to high levels of air pollution can lead to asthma, bronchitis, heart diseases, and reduced life expectancy.
• Children and the elderly are especially vulnerable to air pollution effects.
• Global Air Quality Reports:
• Organizations like IQAir and WHO release annual reports ranking cities based on air pollution levels.
• India often features prominently in these rankings due to industrial emissions, vehicular pollution, and agricultural burning.
• Steps to Reduce Pollution:
• Promoting renewable energy, public transport, and afforestation can help mitigate air pollution.
• Government initiatives like the National Clean Air Programme (NCAP) aim to improve air quality in Indian cities.

Given:

Let x and y be the largest four-digit and the smallest five-digit numbers, respectively, that when divided by 789 leave a remainder of 7.

Formula used:

Number = Divisor × Quotient + Remainder

Calculation:

Largest four-digit number: 9999

⇒ Find x such that 9999 = 789 × Quotient + 7

⇒ Quotient = ⌊(9999 - 7) ÷ 789⌋ = ⌊9992 ÷ 789⌋ = 12

⇒ x = 789 × 12 + 7

⇒ x = 9468 + 7 = 9475

Smallest five-digit number: 10000

⇒ Find y such that 10000 = 789 × Quotient + 7

⇒ Quotient = ⌊(10000 - 7) ÷ 789⌋ = ⌊9993 ÷ 789⌋ = 13

⇒ y = 789 × 13 + 7

⇒ y = 10257 + 7 = 10264

⇒ |x - y| = |9475 - 10264|

⇒ |x - y| = 789

∴ The correct answer is option (2).

Given:

a = 1.01, b = 0.01, x = 7.85, y = 2.15

Formula used:

$a^3+b^3=(a+b)(a^2-ab+b^2)$

$x^2-y^2=(x+y)(x-y)$

Calculations:

For 1^st term : $\frac{(1.01)^3+0.000001}{1.0201-(0.01)^2}$

⇒ a + b = 1.01 + 0.01 = 1.02 

⇒ a − b = 1.01 − 0.01 = 1

⇒ a² = 1.0201, ab = 1.01 × 0.01 = 0.0101, b² = 0.0001

⇒ a² − ab + b² = 1.0201 − 0.0101 + 0.0001 = 1.0101

⇒ $\frac{a^3+b^3}{a^2-b^2}=\frac{(a+b)(a^2-ab+b^2)}{(a+b)(a-b)}=\frac{a^2-ab+b^2}{a-b}=\frac{1.0101}{1}=1.0101$

For 2^nd term: $\frac{(7.85)^2-4.6225}{7.85-2.15}$

⇒ x + y = 7.85 + 2.15 = 10

⇒ x − y = 5.7

⇒ $\frac{x^2-y^2}{x-y}=\frac{(x+y)(x-y)}{x-y}=x+y=10$

⇒ Result=1.0101 × 10 = 10.101

∴ The value of the expression is 10.101.

Given:

Expression: $\frac{(625)^{6.25} × (\sqrt5)^{10.4}}{(\sqrt5)^{54} × 5^{1.2} × (25)^{0.5}}$

Formula used:

Power of a power: $(a^m)^n = a^{m×n}$

Roots as fractional exponents: $\sqrt5=5^{1/2},;25=5^2$

Calculations:

⇒ $625=5^4$

⇒ $(5^4)^{6.25}=5^{4×6.25}=5^{25}$

⇒ $(\sqrt5)^{10.4}=(5^{1/2})^{10.4}=5^{10.4/2}=5^{5.2}$

⇒ Numerator = $5^{25}×5^{5.2}=5^{30.2}$

⇒ $(\sqrt5)^{54}=5^{54/2}=5^{27}$

⇒ $(25)^{0.5}=(5^2)^{0.5}=5^{2��0.5}=5^1$

⇒ Denominator exponent = 27 + 1.2 + 1 = 29.2 ⇒ Denominator = $5^{29.2}$

⇒ Fraction = $5^{30.2−29.2}=5^1$ = 5

∴ The expression simplifies to 5.

Given:

$\frac{5}{7}\ of\ \left[\frac{1}{1\frac{3}{7}}+\frac{6}{5}\ of\ \frac{3\frac{1}{3}-2\frac{1}{2}}{2\frac{5}{21}-2}\right]+\left[\frac{7}{5-2\frac{2}{3}}\div \frac{3-\frac{2}{3-1\frac{1}{2}}}{4-1\frac{1}{2}}\right]$

Calculations:

$\frac{5}{7}\ of\ \left[\frac{1}{1\frac{3}{7}}+\frac{6}{5}\ of\ \frac{3\frac{1}{3}-2\frac{1}{2}}{2\frac{5}{21}-2}\right]+\left[\frac{7}{5-2\frac{2}{3}}\div \frac{3-\frac{2}{3-1\frac{1}{2}}}{4-1\frac{1}{2}}\right]$

⇒ $\frac{5}{7} \times \left[\frac{1}{\frac{10}{7}}+\frac{6}{5}\times \frac{\frac{10}{3}-\frac{5}{2}}{\frac{47}{21}-2}\right]+\left[\frac{7}{5-\frac{8}{3}}\div \frac{3-\frac{2}{3-\frac{3}{2}}}{4-\frac{3}{2}}\right]$

⇒ $\frac{5}{7} \times \left[\frac{7}{10}+\frac{6}{5}\times \frac{\frac{20}{6}-\frac{15}{6}}{\frac{47 - 42}{21}}\right]+\left[\frac{7}{\frac{15 - 8}{3}}\div \frac{3-\frac{2}{\frac{6 -3}{2}}}{\frac{ 8 - 3}{2}}\right]$

⇒ $\frac{5}{7} \times \left[\frac{7}{10}+\frac{6}{5}\times \frac{\frac{5}{6}}{\frac{5}{21}}\right]+\left[\frac{7}{\frac{7}{3}}\div \frac{3-\frac{4}{3}}{\frac{5}{2}}\right]$

⇒ $\frac{5}{7} \times \left[\frac{7}{10}+\frac{6}{5}\times \frac{21}{6}\right]+\left[3\div \frac{\frac{5}{3}}{\frac{5}{2}}\right]$

⇒ $\frac{5}{7} \times \left[\frac{7}{10}+\frac{21}{5}\right]+\left[3\div \frac{2}{3}\right]$

⇒ $\frac{5}{7} \times \left[\frac{7}{10}+\frac{42}{10}\right]+\left[3\times \frac{3}{2}\right]$

⇒ $\frac{5}{7} \times \left[\frac{49}{10}\right]+\left[\frac{9}{2}\right]$

⇒ $\frac{5}{7} \times \left[\frac{49}{10}\right]+\left[\frac{9}{2}\right]$

⇒ $\left[\frac{7}{2}\right]+\left[\frac{9}{2}\right]$

⇒ $\frac{16}{2}$

⇒ 8

∴ The correct answer is option 3.

Given:

Fraction of students less than 10 years = $\frac{1}{5}$ of total students.

Number of girls more than 10 years = 60.

Number of girls more than 10 years = $\frac{3}{2}$ × Number of boys more than 10 years.

Calculation:

Let the total number of students in the school be 'T'.

60 girls are more than 10 years of age, and this number is equal to $\frac{3}{2}$ of the number of boys who are more than 10 years of age.

60 = $\frac{3}{2}$ × (Number of boys > 10 years)

⇒ Number of boys > 10 years = 60 × $\frac{2}{3}$

⇒ Number of boys > 10 years = 40

Total students > 10 years = Girls > 10 years + Boys > 10 years

⇒ Total students > 10 years = 60 + 40

⇒ Total students > 10 years = 100

We know that $\frac{1}{5}$ of the total students are less than 10 years of age.

This means the remaining fraction of students are more than 10 years of age.

Fraction of students > 10 years = 1 - $\frac{1}{5}$ = $\frac{5-1}{5}$ = $\frac{4}{5}$

So, $\frac{4}{5}$ of the total students is equal to 100.

⇒ $\frac{4}{5}$ × T = 100

⇒ T = 100 × $\frac{5}{4}$

⇒ T = 25 × 5

⇒ T = 125

So, the total number of students is 125.

$\frac{3}{5}$ of the total number of students.

Required value = $\frac{3}{5}$ × T

⇒ Required value = $\frac{3}{5}$ × 125

⇒ Required value = 3 × 25

⇒ Required value = 75

∴ $\frac{3}{5}$ of the total number of students is 75.

Given:

The ratio of last year's incomes of A, B, and C = 3 : 5 : 7

The ratio of last year's income to this year's income for A, B, and C = 2 : 3, 3 : 4, and 4 : 5

Total present income = ₹83,650

Formula used:

Present income = Last year's income × Conversion ratio

Calculation:

Let last year's income of A, B, and C be 3x, 5x, and 7x respectively.

Last year's total income = 3x + 5x + 7x = 15x

Present income of A = $3x × \frac{3}{2} = \frac{9x}{2}$

Present income of B = $5x × \frac{4}{3} = \frac{20x}{3}$

Present income of C = $7x × \frac{5}{4} = \frac{35x}{4}$

Total present income = ₹83,650

⇒ $\frac{9x}{2} + \frac{20x}{3} + \frac{35x}{4} = 83,650$

⇒ $\frac{54x}{12} + \frac{80x}{12} + \frac{105x}{12} = 83,650$

⇒ $\frac{239x}{12} = 83,650$

⇒ $x = \frac{83,650 × 12}{239}$

⇒ $x = 4,200$

Present income of C = $\frac{35x}{4} = \frac{35 × 4,200}{4} = ₹36,750$

∴ The correct answer is option (4).

Given:

Number of boys is 50% more than the number of girls.

20% of boys are scholarship holders.

30% of girls are scholarship holders.

Calculation:

Let the number of girls be G.

According to the problem, the number of boys (B) is 50% more than the number of girls:

B = G + 50% of G

⇒ B = 1.5G

For ease of calculation, let's assume the number of girls (G) = 100.

Then, the number of boys (B) = 1.5 × 100 = 150.

Total number of students = Number of girls + Number of boys

⇒ Total students = 100 + 150 = 250

Number of scholarship holder boys = 20% of B

⇒ Scholarship boys = 0.20 × 150 = 30

Number of scholarship holder girls = 30% of G

⇒ Scholarship girls = 0.30 × 100 = 30

Total number of scholarship holders = Scholarship boys + Scholarship girls

⇒ Total scholarship holders = 30 + 30 = 60

Number of students who are NOT scholarship holders = Total students - Total scholarship holders

⇒ Students NOT scholarship holders = 250 - 60 = 190

Percentage of students who are NOT scholarship holders = $\left(\frac{\text{Number of students NOT scholarship holders}}{\text{Total number of students}}\right) \times 100$

⇒ Percentage = $\left(\frac{190}{250}\right) \times 100$

⇒ Percentage = $\left(\frac{19}{25}\right) \times 100$

⇒ Percentage = 19 × 4

⇒ Percentage = 76%

∴ The percentage of students who are NOT scholarship holders is 76%.

Given:

Marked Price (MP) = ₹1,600

Price after two successive discounts = ₹1,080

First Discount = 25%

Let the second discount be x%.

Final Selling Discount = 150% of the second discount

Formula used:

Price after successive discounts = MP × (1 - First Discount/100) × (1 - Second Discount/100)

Profit Percentage = $\dfrac{\text{Selling Price - Cost Price}}{\text{Cost Price}} \times 100$

Calculation:

1080 = 1600 × (1 - 25/100) × (1 - x/100)

⇒ 1080 = 1600 × (0.75) × (1 - x/100)

⇒ 1080 = 1200 × (1 - x/100)

⇒ 1 - x/100 = 1080/1200

⇒ 1 - x/100 = 0.9

⇒ x/100 = 1 - 0.9

⇒ x = 10

Second Discount = 10%

Final Selling Discount = 150% of Second Discount:

Final Selling Discount = 150% of 10 = 15%

SP = MP × (1 - Final Selling Discount/100)

⇒ SP = 1600 × (1 - 15/100)

⇒ SP = 1600 × 0.85

⇒ SP = ₹1,360

CP = ₹1,080

Profit Percentage = $\dfrac{SP - CP}{CP} \times 100$

⇒ Profit Percentage = $\dfrac{1360 - 1080}{1080} \times 100$

⇒ Profit Percentage = $\dfrac{280}{1080} \times 100$

⇒ Profit Percentage = 25.93% ≈ 26%

∴ The correct answer is option (3).

Given:

Amount after 2 years (A₂) = ₹9,680

Amount after 3 years (A₃) = ₹10,648

Time (t₂) = 2 years

Time (t₃) = 3 years

Time for calculation = 3(3/4) years = 3.75 years

Formula used:

A = P(1 + r/100)^t

Calculations:

From the given data:

A₃/A₂ = (1 + r/100)³ / (1 + r/100)²

⇒ ₹10,648/₹9,680 = (1 + r/100)

⇒ 1.1 = (1 + r/100)

⇒ r = 10%

A₂ = P$(1+\frac{r}{100})^2$

9680 = P$(1+\frac{10}{100})^2$

9680 = P$(1.1)^2$

9680 = P × 1.21

⇒ P = $\frac{9680}{1.21}$

⇒ P = ₹8,000

New rate (r') = 2 × original rate = 2 × 10% = 20%

New time (t') = $3\frac{3}{4}$ years = 3 years + $\frac{3}{4}$ year

First, calculate the amount after 3 full years with the new rate:

Amount after 3 years = P$(1+\frac{r'}{100})^3$

⇒ Amount after 3 years = 8000$(1+\frac{20}{100})^3$

⇒ Amount after 3 years = 8000$(1.2)^3$

⇒ Amount after 3 years = 8000 × 1.728

⇒ Amount after 3 years = ₹13,824

Now, The simple interest for the remaining $\frac{3}{4}$ year on this amount:

Interest for fractional year = $13824 \times \frac{20}{100} \times \frac{3}{4}$

⇒ Interest for fractional year = $13824 \times 0.20 \times 0.75$

⇒ Interest for fractional year = 13824 × 0.15

⇒ Interest for fractional year = ₹2073.6

Final Amount = Amount after 3 years + Interest for fractional year

⇒ Final Amount = ₹13,824 + ₹2073.6

⇒ Final Amount = ₹15,897.6

⇒ Final Amount ≈ ₹15,898

∴ The same sum will amount to ₹15,898 (nearest to a whole number) after $3\frac{3}{4}$ years at double the rate of interest.

Given:

Water flow rate = 5 km/h = 5000 m/h

Radius of pipe = 7 cm = 0.07 m

Length of tank = 100 m

Breadth of tank = 88 m

Rise in water level = 14 cm = 0.14 m

Formula Used:

Volume of water flowing per unit time from pipe = Area of pipe cross-section × Speed of water

Area of pipe cross-section = $\pi r^2$

Volume of water in tank = Length × Breadth × Height

Time = Total Volume required / Volume flow rate

Calculation:

Volume of water flowing through the pipe per hour:

Volume flow rate (V_pipe) = $\pi r^2 \times \text{speed}$

V_pipe = $\frac{22}{7} \times (0.07)^2 \times 5000$

V_pipe = $\frac{22}{7} \times 0.0049 \times 5000$

V_pipe = $22 \times 0.0007 \times 5000$

V_pipe = 22 × 3.5

⇒ V_pipe = 77 m³/hour

Required volume in tank (V_tank) = L × B × H

V_tank = 100 m × 88 m × 0.14 m

V_tank = 8800 × 0.14

⇒ V_tank = 1232 m³

Time = $\frac{\text{Required volume in tank}}{\text{Volume flow rate from pipe}}$

Time = $\frac{1232 \text{ m}^3}{77 \text{ m}^3/\text{hour}}$

⇒ Time = 16 hours

∴ The time in which the level of water in the tank will rise by 14 cm is 16 hours.

Given:

HCF of two numbers = 18

Product of two numbers = 5832

The numbers lie between 30 and 200.

Formula Used:

For two numbers 'a' and 'b', Product (a × b) = HCF(a, b) × LCM(a, b)

If HCF(a, b) = H, then a = Hx and b = Hy, where x and y are coprime integers.

Sum of reciprocals = $\frac{1}{a} + \frac{1}{b} = \frac{a+b}{ab}$

Calculation:

Let the two numbers be 'a' and 'b'.

We are given HCF(a, b) = 18 and a × b = 5832.

a × b = HCF(a, b) × LCM(a, b)

5832 = 18 × LCM(a, b)

⇒ LCM(a, b) = $\frac{5832}{18}$

⇒ LCM(a, b) = 324

Since HCF(a, b) = 18, we can write the numbers as:

a = 18x

b = 18y

where x and y are coprime integers (HCF(x, y) = 1).

Substitute these into the product equation:

(18x) × (18y) = 5832

324xy = 5832

⇒ xy = $\frac{5832}{324}$

⇒ xy = 18

Now, find pairs of coprime integers (x, y) whose product is 18:

If x = 1, y = 18. HCF(1, 18) = 1. (Valid pair)

If x = 2, y = 9. HCF(2, 9) = 1. (Valid pair)

If x = 3, y = 6. HCF(3, 6) = 3. (Not coprime, so not valid)

Let's check the numbers 'a' and 'b' for each valid (x, y) pair against the condition that they lie between 30 and 200.

Case 1: (x, y) = (1, 18)

a = 18 × 1 = 18

b = 18 × 18 = 324

Here, a = 18 is not > 30, and b = 324 is not < 200. So, this pair is not suitable.

Case 2: (x, y) = (2, 9)

a = 18 × 2 = 36

b = 18 × 9 = 162

Here, a = 36 (30 < 36 < 200) and b = 162 (30 < 162 < 200). This pair satisfies all conditions.

So, the two numbers are 36 and 162.

Sum of reciprocals = $\frac{1}{a} + \frac{1}{b}$

⇒ Sum of reciprocals = $\frac{1}{36} + \frac{1}{162}$

To add these fractions, find the LCM of 36 and 162.

36 = 2² × 3² = 4 × 9

162 = 2 × 3⁴ = 2 × 81

LCM(36, 162) = 2² × 3⁴ = 4 × 81 = 324

⇒ Sum of reciprocals = $\frac{9}{324} + \frac{2}{324}$

⇒ Sum of reciprocals = $\frac{9 + 2}{324}$

⇒ Sum of reciprocals = $\frac{11}{324}$

∴ The sum of their reciprocals is $\frac{11}{324}$.

Given:

The least number 'x' leaves a remainder of 7 when divided by 16, 28, 40, and 77.

The number 'x' is divisible by 19.

Formula Used:

If a number N leaves a remainder 'r' when divided by 'd', then N = qd + r, or N ≡ r (mod d).

If a number N leaves a remainder 'r' when divided by multiple numbers d₁, d₂, ..., d_n, then N = LCM(d₁, d₂, ..., d_n) × k + r, where k is an integer.

Calculation:

The LCM of 16, 28, 40, and 77.

Prime factorization of 16 = 2⁴

Prime factorization of 28 = 2² × 7

Prime factorization of 40 = 2³ × 5

Prime factorization of 77 = 7 × 11

LCM(16, 28, 40, 77) = 2⁴ × 5 × 7 × 11

⇒ LCM = 16 × 5 × 7 × 11 = 6160

The number 'x' in terms of the LCM.

Since 'x' leaves a remainder of 7 when divided by 16, 28, 40, and 77:

x = 6160k + 7 (where k is a positive integer)

The condition that 'x' is divisible by 19.

x ≡ 0 (mod 19)

6160k + 7 ≡ 0 (mod 19)

The remainder when 6160 is divided by 19:

6160 = 19 × 324 + 4

So, 6160 ≡ 4 (mod 19)

Substitute this back into the congruence:

4k + 7 ≡ 0 (mod 19)

⇒ 4k ≡ -7 (mod 19)

⇒ 4k ≡ 12 (mod 19) (Since -7 + 19 = 12)

To solve for k, we can find the multiplicative inverse of 4 modulo 19. We look for a number 'm' such that 4m ≡ 1 (mod 19). For m = 5, 4 × 5 = 20 ≡ 1 (mod 19).

Multiply both sides of 4k ≡ 12 (mod 19) by 5:

5 × 4k ≡ 5 × 12 (mod 19)

20k ≡ 60 (mod 19)

Since 20 ≡ 1 (mod 19) and 60 = 3 × 19 + 3, so 60 ≡ 3 (mod 19):

⇒ k ≡ 3 (mod 19)

The least positive integer value for k is 3.

Substitute k = 3 into x = 6160k + 7:

x = 6160 × 3 + 7

x = 18480 + 7

⇒ x = 18487

Divide 18487 by 219:

18487 ÷ 219

18487 = 219 × 84 + 91

The remainder is 91.

∴ The remainder when x is divided by 219 is 91.

Given:

The boat takes 3 hours more to travel a distance of 30 km upstream than downstream.

Speed of the boat in still water = 3 × Speed of the stream.

Distance to be traveled in still water = 180 km.

Formula used:

Time = Distance ÷ Speed

Let the speed of the stream be x km/h.

Then, speed of the boat in still water = 3x km/h.

Upstream speed = (3x - x) = 2x km/h.

Downstream speed = (3x + x) = 4x km/h.

Calculations:

Time taken upstream - Time taken downstream = 3 hours

⇒ $\frac{30}{2x} - \frac{30}{4x} = 3$

⇒ $\frac{15}{x} - \frac{7.5}{x} = 3$

⇒ $\frac{15 - 7.5}{x} = 3$

⇒ $\frac{7.5}{x} = 3$

⇒ x = $\frac{7.5}{3}$ = 2.5 km/h

Speed of the boat in still water = 3x = 3 × 2.5 = 7.5 km/h

Time taken to travel 180 km in still water = $\frac{180}{7.5}$

⇒ Time = 24 hours

∴ The correct answer is option (3).

Given:

A can complete a task in 6 more days than B takes to complete the same task.

B works for 4 days, and then A completes the task in 12 days.

Let B's time to complete the task = x days.

Therefore, A's time to complete the task = x + 6 days.

Formula used:

Work done in 1 day = 1 / (time taken to complete the task)

Total work = Work done by B in 4 days + Work done by A in 12 days

Calculation:

Work done by B in 1 day = 1/x

Work done by A in 1 day = 1/(x + 6)

Total work = 1

⇒ Work done by B in 4 days + Work done by A in 12 days = Total work

⇒ (4/x) + (12/(x + 6)) = 1

⇒ 4(x + 6) + 12x = x(x + 6)

⇒ 4x + 24 + 12x = x² + 6x

⇒ x² + 6x - 16x - 24 = 0

⇒ x² - 10x - 24 = 0

⇒ (x - 12)(x + 2) = 0

⇒ x = 12 or x = -2

Since time cannot be negative, x = 12.

∴ The time taken by B alone to complete the task is 12 days.

Given:

Total employees = 3000

Accounts = 18%, Marketing = 23%, IT = 27%, Administration = 20%

Ratios: Accounts M:F = 11:7, Marketing = 12:11, IT = 14:13, Administration = 3:2

Formula used:

Dept emp = total × % /100

Male = (M/(M + F)) × dept employees 

Female = (F/(M + F)) × dept employees 

Required ratio = male(Accounts  + IT) : female(Marketing + Admin)

Calculations:

⇒ Accounts  employees = (3000 × 18)/100 = 540

⇒ Accounts male = (11/(11 + 7)) × 540 = (11/18) × 540 = 11 × 30 = 330

⇒ IT employees = (3000 × 27)/100 = 810

⇒ IT male = (14/(14 + 13)) × 810 = (14/27) × 810 = 14 × 30 = 420

⇒ Marketing employees = (3000 × 23)/100 = 690

⇒ Marketing female = (11/(12 + 11)) × 690 = (11/23) × 690 = 11 × 30 = 330

⇒ Admin employees = (3000 × 20)/100 = 600

⇒ Admin female = (2/(3 + 2)) × 600 = (2/5) × 600 = 2 × 120 = 240

⇒ Total male = 330 + 420 = 750

⇒ Total female = 330 + 240 = 570

∴ Ratio = 750 : 570 = 25 : 19

Given:

Total employees = 3000

Dept % – Ratios:

Accounts: 18%, M:F = 11:7

Marketing: 23%, M:F = 12:11

IT: 27%, M:F = 14:13

Administration: 20%, M:F = 3:2

Others: 12%, M:F = 4:5

Formula used:

Dept emp = total × %/100

Male = (M/(M+F)) × dept emp

Female = (F/(M+F)) × dept emp

x% = ((Male_total – Female_total)/Female_total) ×100

Calculations:

⇒ Administration employees = $(3000×18)/100=540$

⇒ Administration M = $(11/18)×540=330$, F = 210

⇒ Marketing employees = $(3000×23)/100=690$

⇒ Marketing M = $(12/23)×690=360$, F = 330

⇒ IT employees = $(3000×27)/100=810$

⇒ IT M = $(14/27)×810=420$, F = 390

⇒ Admin employees = $(3000×20)/100=600$

⇒ Admin M = $(3/5)×600=360$, F = 240

⇒ Others employees = $(3000×12)/100=360$

⇒ Others M = $(4/9)×360=160$, F = 200

⇒ Male_total = 330+360+420+360+160 = 1630

⇒ Female_total = 210+330+390+240+200 = 1370

⇒ x = $(1630–1370)/1370×100 ≈18.98\%$

⇒ x ≈ 19%

∴ The correct answer is option 3.

Given:

Company A: items = 32 000, cost/100 = ₹45

Company C: items = 40 000, cost/100 = ₹50

Company E: items = 35 000, cost/100 = ₹55

Formula used:

Total cost = items × (cost/100)

Calculations:

⇒ Cost of A: $(32000×45)/100$ = $(32000×0.45)$ = 14400

⇒ Cost of C: $(40000×50)/100$ = $(40000×0.50)$ = 20000

⇒ Cost of E: $(35000×55)/100$ = $(35000×0.55)$ = 19250

∴ Total cost = ₹14400 + ₹20000 + ₹19250 = ₹53650

∴ The correct answer is option 3.

Given:

Company D: items = 50 000, cost/100 = ₹45

Company F: items = 65 000, cost/100 = ₹70

Formula used:

Total cost = items × (cost/100)

Calculations:

⇒ D items: $(50000×1.4)=70000$

⇒ D cost: $(70000×45)/100=31500$

⇒ F items: $(65000×0.6)=39000$

⇒ F cost: $(39000×70)/100=27300$

Total cost = ₹31500 + ₹27300 = ₹58800

∴ The correct answer is option 4.

Given:

City A: 2004 = 50, 2005 = 85, 2006 = 100, 2007 = 90, 2008 = 120 (lakhs)

City B: 2004 = 60, 2005 = 70, 2006 = 100, 2007 = 80, 2008 = 110 (lakhs)

Formula used:

Percentage change = ((New – Old)/Old)×100

Calculations:

⇒ City A, 2005 vs 2004: ((85 – 50)/50) × 100 = 35/50 × 100 = 0.7 × 100 = 70%

⇒ City A, 2006 vs 2005: ((100 – 85)/85) × 100 = 15/85 × 100 ≈ 17.65%

⇒ City A, 2007 vs 2006: ((90 – 100)/100) × 100 = –10/100 × 100 = –10%

⇒ City A, 2008 vs 2007: ((120 – 90)/90) × 100 = 30/90 × 100 = 33.33%

⇒ City B, 2005 vs 2004: ((70 – 60)/60) × 100 = 10/60 × 100 ≈ 16.67%

⇒ City B, 2006 vs 2005: ((100 – 70)/70) × 100 = 30/70 × 100 ≈ 42.86%

⇒ City B, 2007 vs 2006: ((80 – 100)/100) × 100 = –20/100 × 100 = –20%

⇒ City B, 2008 vs 2007: ((110 – 80)/80) × 100 = 30/80 × 100 = 37.5%

In year 2005 the percentage rise in population from the previous year was highest.

∴ The correct answer is option 2.