RPF Constable (2018) Official Paper (Held On: 02 Feb 2019) (Previous Year Paper)

Key Points

• The Gandak River is a significant tributary of the Ganges River, contributing substantially to the Ganges' flow.
• It meets the Ganges near Sonpur, close to Patna, making it strategically important for the region's hydrology and economy.
• The river originates from the Nepal Himalayas, traversing through significant parts of India and Nepal, which influences its catchment area and the volume of water it carries.
• Its confluence with the Ganges near Sonpur is a significant geographical feature, highlighting the river's importance in the northern plains of India.

Additional Information

Key Points

• Gautam Buddha received Mahaparinirvana in Kushinagar, which is located in the modern-day state of Uttar Pradesh, India.
• Mahaparinirvana refers to the death of a Buddha after which he is freed from the cycle of death and rebirth.
• Kushinagar is an important pilgrimage site for Buddhists, as it marks the site of the Buddha's passing.
• This event is considered one of the most significant moments in Buddhist history, symbolizing the end of Gautam Buddha's earthly journey.

Additional Information

The correct answer isArticle 3.

Key Points

• Article 3 of the Indian Constitution deals with the formation of new states and alteration of areas, boundaries, or names of existing states.
• This provision empowers the Parliament to legislate for the formation of new states or the reorganization of existing states without the consent of the states involved.
• The procedure for amending the boundaries or names of states under Article 3 includes a recommendation by the President of India before the bill is presented in the Parliament.
• Article 3 underscores the flexibility and adaptability of the Indian Constitution in responding to changing political, economic, and social conditions.

Additional Information

The correct answer is B. N. Rau.

Key Points

• B. N. Rau was appointed as the Constitutional Advisor (Legal Advisor) of the Constituent Assembly.
• He played a crucial role in the drafting of the Indian Constitution.
• Rau's recommendations formed the basis of many parts of the Constitution, including the Preamble.
• He also advised on the incorporation of the Fundamental Rights and the Directive Principles of State Policy.
• Rau was instrumental in framing the judicial structure of India.

Additional Information

• B. N. Rau was an Indian Civil Servant and a jurist.
• He was appointed as a Judge of the Permanent Court of International Justice after his contribution to the Indian Constitution.
• Rau was also involved in the United Nations Administrative Tribunal's formation, serving as its first President.
• His contributions extended beyond the Indian Constitution, having an impact on international law and judicial processes.
• Rau's legacy is remembered for his profound influence on India's legal and constitutional framework.

The correct answer is December 24.

Key Points

• India celebrates 'National Consumer Day' on December 24th every year.
• This day marks the enactment of the Consumer Protection Act, 1986.
• The main objective is to highlight the importance of the consumer movement and to promote the basic rights of consumers.
• It's a day to advocate for the rights and inform consumers about their responsibilities and grievances mechanisms available.

Additional Information

The correct answer is Aerobic Respiration.

Key Points

• Aerobic respiration occurs in the presence of oxygen and produces up to 38 ATP molecules from the breakdown of one glucose molecule, offering a high energy yield.
• This process takes place in the mitochondria of cells, often referred to as the powerhouse of the cell, where oxygen is used to break down organic compounds.
• Compared to anaerobic respiration, aerobic respiration is more efficient in energy production, making it crucial for high-energy-demand activities.
• In aerobic respiration, by-products such as carbon dioxide and water are produced, which are less toxic and can be easily excreted from the body.

Additional Information

The correct answer is Speaker of Lok Sabha.

Key Points

• The Speaker of the Lok Sabha is elected by the members of the Lok Sabha from amongst themselves.
• They are responsible for the conduct of business of the house, and they have the final say in all parliamentary debates.
• The Speaker ensures the discipline and decorum of the house and has the power to adjourn the house in case of any disturbance.
• Upon election, the Speaker has to remain impartial and renounce all political affiliations.

Additional Information

The correct answer is Astronomy.

Key Points

• Aryabhatiya is an ancient Indian text on astronomy and mathematics.
• It was written by the mathematician Aryabhata in the 5th century CE.
• The work is divided into four sections, covering topics such as arithmetic, algebra, trigonometry, and celestial mechanics.
• It introduced many concepts that were revolutionary for the time, including the idea that the Earth rotates on its axis.
• The Aryabhatiya also contains algorithms for finding square roots and solving linear equations.

Additional Information

The correct answer is Storm Surge.

Key Points

• The term "Storm Surge" refers to the abnormal rise of water above the normal sea level on the coast, caused by a storm.
• Storm surges are primarily caused by high winds from a cyclone pushing water towards the shore, which can lead to flooding.
• The intensity of a storm surge can vary based on the storm's strength, speed, and the shape of the coastline where it makes landfall.
• Storm surges are a significant hazard during tropical cyclones and can lead to extensive damage to coastal communities and ecosystems.

Additional Information

The correct answer is Union.

Key Points

• Part V of the Indian Constitution is dedicated to the Union, outlining the structure and functioning of the Union government.
• It encompasses articles from 52 to 151, detailing the roles and powers of the President, Vice-President, Prime Minister, Council of Ministers, Parliament, and the judiciary.
• This part is crucial for understanding how the executive, legislative, and judicial branches of the Union government operate and interact.
• It lays down the framework for the functioning of the central government and its relationship with the states.

Additional Information

The correct answer is Safe Stores (Buffer Stock).

The correct answer is Mahatma Gandhi.

Key Points

• Mahatma Gandhi was the sole representative of the Indian National Congress at the Second Round Table Conference held in 1931.
• The conference was a series of three meetings in London and was part of the constitutional reform process in India.
• It aimed to discuss the Simon Commission report and the future constitution of India.
• Gandhi attended to negotiate the terms of Indian independence and pressed for the rights of the Indian people.
• Despite his efforts, the conference did not lead to any significant breakthrough due to the lack of agreement between the British and Indian representatives.

Additional Information

The correct answer is Brazil.

The correct answer is Lord Mountbatten.

Key Points

• Lord Mountbatten was appointed as Viceroy of British India in March 1947, succeeding Lord Wavell.
• He was the last Viceroy of British India and the first Governor-General of independent India.
• Lord Mountbatten played a significant role in the partition of India, leading to the creation of India and Pakistan in August 1947.
• His tenure was marked by efforts to ensure a peaceful transfer of power amidst communal tensions.

Additional Information

The correct answer is Generator.

Key Points

• Electromagnetic induction is the process of generating electric current with a magnetic field.
• It is the fundamental operating principle behind generators, where mechanical energy is converted into electrical energy.
• In a generator, a coil of wire is rotated in a magnetic field, inducing a current along the wire.
• This phenomenon was discovered by Michael Faraday, who realized that electrical energy could be produced by moving a conductor through a magnetic field.

Additional Information

The correct answer is 35 years.

The correct answer is Resistance.

Key Points

• Resistance is a property of a material that opposes or restricts the flow of electrical current through it.
• It is measured in ohms (Ω) and varies based on the material's composition and dimensions.
• The higher the resistance, the lower the current flow for a given voltage, according to Ohm's Law (V = IR).
• Conductors have low resistance, allowing electrons to flow easily, while insulators have high resistance, hindering electron flow.

Additional Information

The correct answer is Metal Oxides.

Key Points

• When metals combine with oxygen, a chemical reaction occurs, resulting in the formation of metal oxides.
• Metal oxides are compounds composed of metal atoms and oxygen atoms. They are typically solid at room temperature.
• This process is a type of oxidation reaction, where the metal loses electrons to oxygen atoms.
• The properties of the metal oxide formed can vary widely, from being acidic or basic, to displaying different physical properties depending on the metal involved.

Additional Information

Key Points

• The Great Stupa at Sanchi is one of the oldest stone structures in India, and an important monument of Indian Architecture.
• It was originally commissioned by the emperor Ashoka the Great in the 3rd century BCE.
• The Sanchi stupa stands as a symbol of the spread of Buddhism across India.
• Over the centuries, it was expanded and decorated with gateways and railings that are richly sculpted with Buddhist motifs.

Additional Information

The correct answer is London.

Key Points

• The Wimbledon Championships in 2018 were held in London.
• Wimbledon is one of the four Grand Slam tennis tournaments, the others being the Australian Open, the French Open, and the US Open.
• Wimbledon is the oldest tennis tournament in the world and is highly prestigious.
• It was held at the All England Lawn Tennis and Croquet Club in London.
• The tournament takes place over two weeks in late June and early July.

Additional Information

Key Points

• Article 50 of the Indian Constitution deals with the separation of the judiciary from the executive. This is a directive principle of state policy.
• Its purpose is to ensure the independence of the judiciary, which is crucial for a fair and impartial justice system.
• Separation of powers is a key feature of the Constitution of India, aiming to prevent the misuse of power by any branch of the government.
• The principle helps in maintaining the checks and balances within the system of governance.

Additional Information

Key Points

• Lord Irwin was the Viceroy of India during the first Round Table Conference held in 1930.
• The first Round Table Conference was a series of peace conferences organized by the British government to discuss constitutional reforms in India.
• It marked a significant step towards the eventual independence of India, as it involved discussions on a wide range of issues related to the constitutional status of India.
• Lord Irwin played a crucial role in the conference, facilitating discussions between the British government and Indian representatives.

Additional Information

Key Points

• China was the overall champion of the 18th Asian Games 2018.
• The games were held in Jakarta and Palembang, Indonesia.
• China topped the medal tally with a total of 289 medals (132 gold, 92 silver, and 65 bronze).
• This event is recognized as the second-largest multi-sport event after the Olympics.
• The Asian Games 2018 featured 40 sports and 462 events in total.

Additional Information

Important Points

• Some key points from the 2023 Asian Games:
• India's performance
• India won 107 medals, including 28 gold, 38 silver, and 41 bronze, which was their best ever tally. India was the best-performing country in archery, kabaddi, cricket, and field hockey. They also won their first Asian Games badminton gold medal.
• New sports
• E-sports and breakdancing were introduced as medal sports for the first time.
• Olympic quotas
• India secured six Olympic quotas for Paris 2024, including four in boxing and one each in athletics and men's hockey.
• Closing ceremony
• The closing ceremony took place on October 8, 2023 at the Hangzhou Sports Park Stadium. Aichi Prefecture, Japan will host the 2026 Asian Games.
• Women's singles tennis
• Zheng Qinwen of China won the gold medal in women's singles tennis, beating compatriot Zhu Lin in the final

Key Points

• The North Eastern Monsoon, also known as the Retreating Monsoon or the Northeast Monsoon, brings rainfall to the coastal areas of Tamil Nadu during the beginning of winter.
• This monsoon typically occurs from October to early December.
• It is characterized by the movement of the monsoon winds from the land to the sea, opposite to the Southwest Monsoon.
• The North Eastern Monsoon is crucial for the agriculture of Tamil Nadu, as it provides the majority of the annual rainfall in the region.

Additional Information

Key Points

• The Maulana Abul Kalam Azad (MAKA) Trophy is awarded annually to the university which has the best all-round performance in sports across all inter-university tournaments.
• It was instituted in 1956-57 to encourage competition in sports and games among universities in India.
• The award is named after Maulana Abul Kalam Azad, the first Minister of Education in the independent India.
• The recipient university is awarded a replica of the trophy, certificates, and a cash prize.

Additional Information

Key Points

• The Gulf of Mannar is known for its rich marine biodiversity and is a key habitat for the dugong, also known as the sea cow.
• Dugongs are marine mammals that graze on underwater grasses day and night, which are found in the shallow coastal waters of the Gulf of Mannar.
• The area is part of the Gulf of Mannar Biosphere Reserve, established to protect marine life, including the vulnerable dugong population.
• Conservation efforts in the Gulf of Mannar focus on protecting the dugong's habitat from threats such as fishing nets, boat strikes, and habitat loss.

Additional Information

Key Points

• Dmitry Ivanovich Mendeleev is credited with the creation of the Periodic Table of Elements.
• He arranged the elements in order of increasing atomic mass, which allowed for the prediction of the properties of elements that had not yet been discovered.
• Mendeleev's periodic table was first published in 1869 and has been a fundamental tool in the field of chemistry.
• The periodic table not only organizes elements based on their atomic mass but also by their chemical properties, which are repeated in 'periods'.

Additional Information

Key Points

• The Danube River is the second-longest river in Europe after the Volga.
• It flows through 10 countries, more than any other river in the world.
• Budapest, the capital city of Hungary, is bisected by the Danube River, dividing the city into Buda and Pest.
• The river is a vital waterway for transport, commerce, and tourism in the region.

Additional Information

Key Points

• Sir William Jones founded the Asiatic Society of Bengal in 1784 with the objective of promoting Oriental studies.
• He was a jurist, linguist, and Indologist, deeply interested in ancient India's culture, history, and law.
• The Asiatic Society was established to encourage and support the study of the history, arts, and literature of Asia.
• Under his leadership, the society laid the foundation for Asian studies, including the discovery of the Indo-European language family.

Additional Information

Key Points

• 1929 Lahore Session: The Indian National Congress's Lahore session in December 1929 was pivotal in the history of the Indian freedom struggle.
• Pandit Jawaharlal Nehru: Presided over by Pandit Jawaharlal Nehru, it marked a decisive turn towards complete independence from British rule.
• Declaration of Purna Swaraj: It was during this session that the Congress formally adopted the resolution of 'Purna Swaraj' or complete self-rule as its ultimate goal.
• 26th January 1930: The Congress called upon the people of India to observe 26th January as the Independence Day, which was later commemorated as Republic Day post-independence.

Additional Information

• Lahore Session Significance: The Lahore Session is considered a significant milestone in India's journey towards independence. It set the stage for the Civil Disobedience Movement.
• Impact: The resolution for Purna Swaraj galvanized the Indian population across the country to actively participate in the freedom movement against British colonial rule.
• Historical Context: The decision for complete independence came after years of constitutional reform demands and participation in the colonial governance structure, which did not yield substantial progress towards self-rule.
• Legacy: The ideals and the spirit of the Lahore Session continue to inspire Indian democracy and its commitment towards sovereignty, social justice, and equality.

Key Points

• The Lok Sabha is the lower house of India's bicameral Parliament, which is elected directly by the people of India.
• Members of the Lok Sabha are elected through general elections which occur every five years or when the House is dissolved by the President.
• The Lok Sabha is responsible for making and passing laws, and its members represent the citizens of their respective constituencies.
• The direct election process ensures that the government reflects the will of the people, making the Lok Sabha a key component in India's democracy.

Additional Information

Key Points

• B.R. Ambedkar was appointed as the Chairman of the Drafting Committee of the Constitution of India on August 29, 1947.
• Under his guidance, the Drafting Committee formulated the Constitution of India.
• Ambedkar is often referred to as the "Father of the Indian Constitution" for his pivotal role in its formation.
• He advocated for civil liberties, equality, and social justice in the Constitution.

Additional Information

Key Points

• The word 'raid' is commonly associated with the sport of Kabaddi, especially in the traditional form of the game played in India.
• In Kabaddi, the term 'raid' refers to the act of raiding, where a raider enters the opposing team's half to tag as many defenders as possible and return to their half of the court.
• The strategic element of 'raid' in Kabaddi involves deception, agility, and strength, making it a critical aspect of the game.
• Unlike the sports of Badminton, Tennis, and Volleyball, Kabaddi uniquely incorporates the concept of 'red' as a fundamental part of its gameplay.

Additional Information

Key Points

• The product of mass and velocity is known as momentum, not impulse. Momentum is a vector quantity that represents the quantity of motion an object has.
• Impulse is actually the change in momentum, which is equal to the force applied on an object times the time over which it is applied.
• Force is defined as mass times acceleration (Newton's Second Law), not mass times velocity.
• Inertia is a property of matter that describes its resistance to any change in its state of motion, including a change in velocity.
• Acceleration is a measure of the change in velocity of an object per unit time and is not directly related to the product of mass and velocity.

Additional Information

Key Points

• Naziruddin Ahmed was the individual who humorously referred to the 'Drafting Committee' as the 'Drifting Committee'.
• This comment underscored his concern over the pace and direction of the committee's work in drafting the Constitution of India.
• The Drafting Committee, chaired by Dr. B.R. Ambedkar, was responsible for drafting the Constitution of India.
• Ahmed's remark was indicative of the debates and discussions that were part of the constitutional assembly debates.
• Despite his critique, the committee successfully completed the drafting of the Constitution, which was adopted on 26th November 1949.

Additional Information

Key Points

• Tropical cyclones are known in Japan as 'Taifu'.
• The term 'Taifu' is specific to the Japanese language, reflecting the local terminology for these powerful storms.
• Tropical cyclones are categorized based on their location and intensity, with names such as hurricanes, typhoons, or cyclones depending on where they occur.
• In Japan, these storms can cause significant damage, including strong winds, heavy rain, and flooding.
• Japan's geographical location makes it particularly vulnerable to typhoons, especially from July to October.

Additional Information

• Tropical cyclones are powerful storm systems characterized by a low-pressure center, a closed low-level atmospheric circulation, strong winds, and a spiral arrangement of thunderstorms that produce heavy rain.
• Depending on their location and strength, they are called hurricanes (Atlantic, Northeast Pacific), typhoons (Northwest Pacific), or cyclones (South Pacific, Indian Ocean).
• The World Meteorological Organization (WMO) has a role in the international naming of tropical cyclones to streamline communications and avoid confusion.
• Typhoons contribute to the annual rainfall in regions such as Japan, but also pose risks of flooding and landslides, necessitating advanced preparedness and response strategies.
• The intensity of a tropical cyclone is classified into five categories on the Saffir-Simpson Hurricane Wind Scale, based on the wind speed; Category 5 represents the highest intensity.

Key Points

• The newspaper "Kesari" was founded by Bal Gangadhar Tilak, a prominent leader in the Indian Independence movement.
• It was started as a Marathi weekly in 1881, serving as a mouthpiece for Tilak's views and the Indian Nationalist movement.
• "Kesari" played a crucial role in mobilizing public opinion against British rule, advocating for Swaraj, or self-rule.
• Tilak's editorial pieces in "Kesari" were known for their fierce criticism of British policies, which led to his imprisonment multiple times.

Additional Information

Key Points

• The Rural Employment Generation Programme (REGP) was started in 1995.
• It was implemented by the Khadi and Village Industries Commission (KVIC).
• The main aim of REGP was to create self-employment opportunities in rural areas and small towns.
• A significant focus was on providing financial support to establish micro-enterprises.
• It targeted to provide employment to over a million people through the establishment of about 2.5 lakh projects.

Additional Information

Key Points

• The pituitary gland is often dubbed the "master gland" because it controls several other hormone glands in the body, including the thyroid and adrenals.
• Growth hormone (GH), also known as somatotropin, plays a crucial role in cell growth, reproduction, and regeneration, making it vital for human development.
• GH is secreted by the anterior lobe of the pituitary gland, which is located at the base of the brain.
• Deficiencies or excesses of growth hormone can lead to disorders such as dwarfism or gigantism/acromegaly, respectively.

Additional Information

Key Points

• Ethanoic acid, also known as acetic acid, is a colorless liquid organic compound with the chemical formula CH₃COOH.
• It is characterized by a sour taste and pungent smell, commonly associated with vinegar, in which it is the main component.
• As a member of the carboxylic acids, it contains a carboxyl group (COOH) attached to a methyl group (CH₃), making it the simplest example of a carboxylic acid after formic acid.
• Acetic acid is widely used in the chemical industry as a precursor for the production of various chemical compounds such as vinyl acetate monomer, acetic anhydride, and acetate esters.

Additional Information

Key Points

• The Hill Area Development Program was initiated during the Fifth Five Year Plan.
• This program aimed at the development of hilly areas considering their ecological fragility, geological hazards, and socio-economic conditions.
• It focused on preserving the biodiversity and the traditional knowledge of the hill communities while promoting sustainable development.
• Projects under this program included afforestation, building infrastructure, and improving the livelihoods of people living in hill areas.

Additional Information

Key Points

• The Drafting Committee was established in 1947 to draft the Constitution of India.
• It was formed on August 29, 1947, under the chairmanship of Dr. B.R. Ambedkar.
• The committee was tasked with framing the constitution to embody the aspirations and values of the Indian people.
• It consisted of seven members, including Dr. Ambedkar.
• The committee took 2 years, 11 months, and 18 days to complete the draft Constitution.

Additional Information

Key Points

• The correct answer is option 4, which suggests Croatia reached the FIFA Men's Football World Cup for the first time in 2018.
• Croatia achieved an impressive feat by reaching the World Cup Final in 2018, which was a first for the nation.
• The 2018 FIFA World Cup was held in Russia, from June 14 to July 15.
• Croatia was defeated by France in the final, with a score of 4-2, securing the second place.
• The Croatian team's performance was celebrated globally, highlighting their skill, determination, and the quality of football in the country.

Additional Information

• FIFA World Cup is an international football competition contested by the senior men's national teams of the members of Fédération Internationale de Football Association (FIFA), the sport's global governing body.
• The tournament has been held every four years since the inaugural tournament in 1930, except in 1942 and 1946 when it was not held because of the Second World War.
• The World Cup is one of the most prestigious and widely viewed sporting events in the world, with participation from the globe's leading national teams.
• Brazil holds the record for the most World Cup titles, having won the tournament five times.
• The most recent World Cup, as of my last update, was held in 2022 in Qatar, marking the first World Cup ever to be held in November and December.

Key Points

• Arteries are the blood vessels that carry oxygen-rich blood away from the heart to all parts of the body.
• The main artery is the aorta that branches into major arteries that take blood to different limbs and organs.
• Arterial walls are thick and elastic to withstand and regulate blood pressure.
• Unlike veins, arteries carry blood at a high pressure, necessitating their strong, flexible walls.

Additional Information

Key Points

• A nebula is a giant cloud of dust and gas in space. Some nebulae (more than one nebula) come from the gas and dust thrown out by the explosion of a dying star, such as a supernova. Others are regions where new stars are beginning to form.
• For this reason, some nebulae are called "star nurseries."
• Nebulae are made of dust and gases—mostly hydrogen and helium.
• Their appearance can vary significantly, from dense patches obscuring light from background stars to glowing gas illuminated by nearby stars.

Additional Information

Given:

The selling price of the item = Rs. 425

Loss percentage = 15%

Formula:

The formula to calculate the cost price (purchase price) of an item when the selling price and loss percentage are given is:

Cost price = Selling price / (1 - Loss percentage/100)

Solution:

Substituting the given values in the above formula, we get:

Cost price = 425/(1 - 15/100)

Cost price = 425/0.85

Therefore, the purchase price of the item is Rs. 500.

Given:

LCM of two numbers = 153

HCF of two numbers = 17

One of the numbers = 17

Formula:

The formula to find the product of two numbers when their LCM and HCF are given is:

Product of two numbers = LCM x HCF

Solution:

Let the other number be x.

We know that the product of two numbers is equal to the product of their LCM and HCF, i.e.,

⇒ x × 17 = 153 × 17

Dividing both sides by 17, we get:

x = 153

Therefore, the other number is 153.

Shortcut Trick

To find the remainder when a number is divided by 9, calculate the sum of its digits.

Sum of digits of 32622 = 3 + 2 + 6 + 2 + 2 = 15.

Now, divide 15 by 9: 15 ÷ 9 → Remainder = 6.

∴ The correct answer is 6.

Alternate Method

Given:

Number = 32622

Divisor = 9

Property Used: A number and the sum of its digits leave the same remainder when divided by 9.

⇒ Sum of digits = 3 + 2 + 6 + 2 + 2

⇒ Sum = 15

⇒ Dividing 15 by 9:

⇒ 15 = (9 × 1) + 6

⇒ Final Remainder = 6

∴ The correct answer is 6.

Additional Information

Divisibility Rule of 9

A number is completely divisible by 9 if the sum of its digits is a multiple of 9 (e.g., 9, 18, 27, etc.).

Divisibility Rule of 3

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

Concept of Digital Sum

The single-digit sum obtained by repeatedly adding digits is the digital root, which represents the remainder when divided by 9 (if the sum is 9, the remainder is 0).

Given:

Principal amount (P) = 16800 rupees

Compound interest rate (r) = 10% per annum

Time (t) = 2 years

Formula:

The formula to calculate the amount (A) after a period of time with compound interest is given by:

A = P × (1 + r/100)^t

Solution:

Substituting the given values into the formula, we get:

P = 16800

r = 10

t = 2

A = 16800 × (1 + 10/100)²

Using a calculator, we can calculate the value of A.

A = 16800 × (1.10)²

A = 16800 × 1.21

A = 20328

Therefore, the amount after a period of 2 years with a compound interest rate of 10% per annum on 16800 rupees will be 20328 rupees.

Given:

Principal amount (P) = 4750 rupees

Simple interest rate (r) = 13% per annum

Time (t) = 4 years

Formula:

The formula to calculate the amount (A) after a period of time with simple interest is given by:

A = P × (1 + r × t)

Solution:

Substituting the given values into the formula, we get:

P = 4750

r = 13/100 = 0.13

t = 4

A = 4750 × (1 + 0.13 × 4)

Using a calculator, we can calculate the value of A.

A = 4750 × 1.52

A = 7220

Therefore, the amount received after 4 years at a simple interest rate of 13% per annum invested on 4750 rupees will be 7220 rupees.

Given:

Time is taken by train to cross a signal = 35 seconds

Length of the bridge = 473 meters

Time is taken by train to cross the bridge = 78 seconds

Formula:

Let's assume the length of the train as 'x'.

Speed of the train = Distance / Time

Solution:

First, we need to find the speed of the train.

When the train crosses the signal, it covers only the length of the train.

So, using the formula, speed of train = distance/time = x/35

When the train is crossing the bridge, it covers the train's length and the bridge's length.

So, using the formula, speed of train = distance / time = (x + 473) / 78

Since the speed of the train is constant, we can equate the two expressions for speed:

(x + 473)/x = 78/35

35(x + 473) = 78x

78x - 35x = 473 × 35

43x = 473 × 35

x = 11 × 35

x = 385

Therefore, the length of the train is 385 meters.

Therefore, the length of the train is 385 meters.

Given:

Germillin's average score in four exams = 75

Germillin's marks in the first three exams = 79, 75, 71

Calculation:

Let x be the score Germillin needs to achieve in the fourth test to maintain an average score of 75.

We know that the average score is calculated as the sum of all scores divided by the number of scores:

average score = (score in exam 1 + score in exam 2 + score in exam 3 + score in exam 4) / 4

Using this formula and substituting the given values, we get:

75 = (79 + 75 + 71 + x) / 4

Multiplying both sides by 4:

300 = 225 + x

Subtracting 225 from both sides:

x = 75

Therefore, Germillin needs to score 75 in the fourth exam to maintain an average score of 75.

Shortcut Trick 

Average Speed (If both the distances are equal) = 2S₁S₂ / (S₁ + S₂)

So, Average speed = (2 × 560 × 840) / (560 + 840)

⇒ (2 × 560 × 840) / 1400

⇒ 2 × 4 × 84 = 672 mph

Hence, the average speed of both laps is 672 mph.

Alternate Method

Given:

Speed of first lap = 560 mph

Speed of second lap = 840 mph

Formula:

Average speed = Total distance covered / Total time taken

To use this formula, we need to assume that both laps are of the same distance.

Calculation:

Let's say the distance of each lap is d.

The time taken to complete the first lap = d/560

The time taken to complete the second lap = d/840

The total time taken to complete both laps = (d/560) + (d/840) = (3d/1680) + (2d/1680) = (5d/1680) = (d/336)

The total distance covered in both laps = 2d

Therefore, the average speed of both laps can be calculated as:

Average speed = (Total distance covered) / (Total time taken)

= (2d)/(d/336)

= 672 mph

Hence, the average speed of both laps is 672 mph.

Given:

The average of 7 numbers is 145.

Calculation:

Let the sum of 7 numbers be S.

So, the average of 7 numbers can be written as:

S/7 = 145

S = 7 x 145

S = 1015

Now, let's say one number is removed from the 7 numbers, and the average remains the same. Let the removed number be x.

So, the sum of the remaining 6 numbers is:

S - x

And the average of these 6 numbers is still 145, so we can write:

(S - x)/6 = 145

S - x = 870

Substituting the value of S, we get:

1015 - x = 870

x = 1015 - 870

x = 145

Therefore, the extracted number is 145.

Shortcut Trick

Ratio of Price of LPG cylinder = 660 : 825 = 4 : 5.

Since Expenditure remains constant, Consumption ratio is inverse of Price ratio = 5 : 4.

Reduction in Consumption = 5 − 4 = 1 unit.

Percentage reduction = (Reduction ÷ Original Consumption) × 100 = (1 ÷ 5) × 100 = 20%.

∴ The correct answer is 20%.

Alternate Method

Given: Initial Price = ₹660, Final Price = ₹825.

Formula Used: Expenditure = Price × Consumption

⇒ Let Initial Consumption be C₁ and Final Consumption be C₂.

⇒ Constant Expenditure ⇒ 660 × C₁ = 825 × C₂

⇒ C₂ ÷ C₁ = 660 ÷ 825

⇒ C₂ ÷ C₁ = 4 ÷ 5

⇒ Reduction in Consumption = C₁ − C₂ = 5 − 4 = 1 unit

⇒ Percentage reduction = (1 ÷ 5) × 100 = 20%

∴ The correct answer is 20%.

Additional Information

Inverse Proportion Law

When the product of two variables (Price × Consumption) is constant, an increase in one variable leads to a proportional decrease in the other.

Consumption Reduction Formula

If the price increases by r%, the reduction in consumption to keep expenditure constant is [r ÷ (100 + r)] × 100%.

Percentage Change Basics

Percentage Decrease = (Original Value − New Value) ÷ Original Value × 100.

Given:

The ratio of the first part to the second part is 6:5 and the first part is 240 rupees.

Calculation:

Let's assume that the total amount is x rupees.

Then, the second part will be (5/6) times of the first part which can be expressed as:

Second part = (5/6) × first part

Second part = (5/6) × 240

Second part = 200

So, the total amount will be the sum of the first part and the second part which is:

Total amount = first part + second part

Total amount = 240 + 200

Total amount = 440

Therefore, the total amount is 440 rupees.

Calculation:

$\sqrt{(140-\sqrt{(368-\sqrt{(37+\sqrt{144})})})}$

⇒ $\sqrt{(140-\sqrt{(368-\sqrt{(37+12)}}}$

⇒ $\sqrt{(140-\sqrt{(368-\sqrt{(49)}}}$

⇒ $\sqrt{(140-\sqrt{(368-7}}$

⇒ $\sqrt{(140-\sqrt{361}}$

⇒ $\sqrt{(140-19)}$

⇒ $\sqrt{121}$

⇒ 11

∴ Option 3 is the correct answer.

Given:

Ordinary interest rate = 12% per annum

Time period = 5 years

Interest earned = Rs. 5640

Formula:

Simple Interest S.I. = (PRT)/100

where,

P = Principal amount

R = Rate of interest

T = Time period

Solution:

Let P be the principal amount invested.

Using the formula for simple interest, we have:

⇒ S.I. = (PRT)/100

⇒ 5640 = (P × 12 × 5)/100

⇒ 5640 = (60P)/100

⇒ 564000 = 60P

⇒ P = 9400

Therefore, the amount invested is Rs. 9400.

Calculation:

Difference of Y and X in 2001 = 60 - 36 = 24

Difference of Y and X in 2002 = 56 - 40 = 16

Difference of Y and X in 2003 = 66 - 48 = 18

Difference of Y and X in 2004 = 65 - 61 = 4

Difference of Y and X in 2005 = 55 - 26 = 29

Difference of Y and X in 2007 = 60 - 33 = 27

As least difference is 4 in 2004.

∴ Option 2 is the correct answer.

Given fraction = 0.3555...

CONCEPT USED:

Suppose XY is a two-digit number after the decimal 

Then, if there is a bar on the first digit i.e. $0.x\overline{y}$ =  (xy- x)/90 

CALCULATION:

Fraction = 0.355... = 0.3$\overline{5}$

 0.3$\overline{5}$ = (35 - 3)/90 = 32/90 = 16/45

Hence, option 4 is the correct answer.

Alternate Method 

Let x =  0.3555...

then 10x = 3.5555...

⇒ 10x - x = 9x = (3.5555...) - (0.3555...)

⇒ 9x = 3.2

⇒ x = 3.2/9

⇒ x = 32/90

⇒ 0.355... = 32/90 = 16/45

Option 4 is the correct answer.

Given:

Total number of detergent soaps in the box = 125

Number of detergent soaps used = 75

Formula:

Percentage = (Part / Whole) × 100

where,

Part = the value of the part being considered

Whole = the value of the whole being considered

Solution:

The number of detergent soaps left in the box is:

125 - 75 = 50

Using the formula for percentage, we can find the percentage of detergent soap left in the box:

Percentage = (Part/Whole) × 100

Percentage = (50/125) × 100

Percentage = 40%

Therefore, the percentage of detergent soap left in the box is 40%.

Given:

The ratio of alpha's age to beta's age is 2:5.

The sum of their ages is 245.

Solution:

Let the age of alpha be 2x and the age of beta be 5x (since the ratio of their ages is 2:5). Then, we can write:

2x + 5x = sum of their ages

And the difference between their ages is:

5x - 2x

Simplifying this expression, we get:

3x

Therefore, the formula to find the difference between their ages is:

Difference in ages = 3x

According to the given condition, we have:

2x + 5x = 245

Simplifying this equation, we get:

7x = 245

Dividing both sides by 7, we get:

x = 35

Therefore, alpha's age is:

2x = 2 × 35 = 70

And beta's age is:

5x = 5 × 35 = 175

The difference between their ages is:

5x - 2x = 3x = 3 × 35 = 105

Therefore, the difference between their ages is 105.

Given:

250 - [90 - (120 ÷ 10 - (30 - 60 ÷ 3) ÷ 10)]

Concept used:

Calculation:

250 - [90 - (120 ÷ 10 - (30 - 60 ÷ 3) ÷ 10)]

⇒  250 - [90 - (12 - (30 - 20) ÷ 10)]

⇒  250 - [90 - 11]

⇒ 250 - 79

⇒ 171

∴ Option 2 is the correct answer.

Given:

2 [(54 × 17 × 54 × 17) ÷ $(2(\sqrt{289\div 2}))^2$ ]

Concept used:

Calculation:

2 [(54 × 17 × 54 × 17) ÷ $(2(\sqrt{289\div 2}))^2$ ]

⇒ 2[54 × 17 × 54 × 17) ÷ $(2× \frac{17}{\sqrt2})^2$ ]

⇒ 2[54 × 17 × 54 × 17) ÷ $(\sqrt2 × 17)^2$ ]

⇒ 2[54 × 17 × 54 × 17) ÷ 2 × 17 × 17]

⇒ 54 × 54

⇒ 2916

∴ Option 2 is the correct answer.

Concept used:

A number is divisible by 12 if it is divisible by 3 and 4

A number is divisible by 3, if the sum of its digits is divisible by 3, while a number is divisible by 4, if the last two digits of the number is divisible by 4

Calculation:

Considering number 51924,

⇒ Sum of digits = 5 + 1 + 9 + 2 + 4 = 21, which is divisible by 3

⇒ Last two digits = 24, which is divisible by 4.

∴ The number 51924 is divisible by 12.

Other options can be eliminated as 51926, 34522, and 51925, their last 2 digits are divided by 4.

∴ The number 51924 is divisible by 12.

Calculation:

The total production of X = 36 + 40 + 48 + 61 + 26 + 33 = 244

The total production of Y = 60 + 56 + 66 + 65 + 55 + 60 = 362

Difference = 362 - 244 = 118

∴ Option 3 is the correct answer.

Given:

Speed of the train = 49 meters/second

Time is taken to cross a signal = 12 seconds

Formula:

Let the length of the train be L meters. Then, we can use the following formula to find the length of the train:

L = (Speed of the train × Time taken to cross the signal)

i.e., L = (49 × 12) meters

Solution:

Using the formula for the length of the train, we have:

L = (Speed of the train × Time taken to cross the signal)

L = (49 × 12) meters

L = 588 meters

Therefore, the length of the train is 588 meters.

Given:

Printed price of the book = Rs. 3,900

Discount offered = 10%

Profit earned = 20%

Formula Used:

Selling Price = Printed Price - Discount

Cost Price = Selling Price / (1 + Profit Percentage)

Calculation:

Discount = 10% of 3900

⇒ 0.10 × 3900

⇒ 390

Selling Price = Printed Price - Discount

⇒ 3900 - 390

⇒ 3510

Profit Percentage = 20%

Cost Price = Selling Price / (1 + 0.20)

⇒ 3510 / 1.20

⇒ 2925

The purchase price of the book is Rs. 2,925.

Given:

The ratio of pen, pencil, and eraser to a box is 3 ∶ 2 ∶ 1

The price of a pen is Rs. 3, the price of a pencil is Rs. 2, and the price of an eraser is Rs. 2

The amount spent on the box is Rs. 570

Calculation:

Let's use the formula to find the number of pens in the box:

Assume that the ratio of pens, pencils, and erasers to the box is expressed as 3x:2x:x, where x is a constant.

Therefore, the total number of items in the box is 3x + 2x + x = 6x.

The cost of a pen is Rs. 3, so the cost of 3x pens is 3(3x) = 9x.

The cost of a pencil is Rs. 2, so the cost of 2x pencils is 2(2x) = 4x.

The cost of an eraser is Rs. 2, so the cost of x erasers is 2x.

The total cost of the box is the sum of the cost of pens, pencils, and erasers, which is:

9x + 4x + 2x = 15x

According to the problem, the total cost of the box is Rs. 570. Therefore, we can write the equation:

15x = 570

Solving for x:

x = 38

Therefore, the number of pens in the box is 3x, which is:

3(38) = 114

Hence, there are 114 pens in the box.

Calculation:

$\rm \sqrt{(555-x)}=\sqrt{(38-\sqrt{169})}$

⇒ $\rm \sqrt{(555-x)}=\sqrt{(38-13)}$

⇒ $\rm \sqrt{(555-x)}=\sqrt{25}$

Square both sides:

⇒ 555 - x = 25

⇒ x = 530

∴ Option 1 is the correct answer.

Given:

Cost price (CP) = Rs. 400

Selling price (SP) = Rs. 320

Formula Used:

The formula for calculating the loss percentage is:

Loss Percentage = ((CP - SP) / CP) × 100%

Solution:

The cost price (CP) of the thing is Rs. 400, and the selling price (SP) of the thing is Rs. 320.

Using the formula for calculating the loss percentage, we have:

Loss Percentage = ((CP - SP) / CP) × 100%

Loss Percentage = ((400 - 320) / 400) × 100%

Loss Percentage = (80 / 400) × 100%

Loss Percentage = 0.2 × 100%

Loss Percentage = 20%

Therefore, the loss percentage of the shopkeeper is 20%.

Calculation:

The number of vehicles manufactured by the X company in 2001 and 2002 are 36 and 40 respectively.

According to the question:

⇒ 40 - 36

⇒ 4

∴ Option 3 is the correct answer.

Given:

Cost price (CP) = Rs. 212

Selling price (SP) = Rs. 265

Formula Used:

The formula for calculating the profit percentage is:

Profit Percentage = ((SP - CP) / CP) × 100%

Solution:

The cost price (CP) of the thing is Rs. 212, and the selling price (SP) of the thing is Rs. 265.

Using the formula for calculating the profit percentage, we have:

Profit Percentage = ((SP - CP)/CP) × 100%

Profit Percentage = ((265 - 212)/212) × 100%

Profit Percentage = (53 / 212) × 100%

Profit Percentage = 0.25 × 100%

Profit Percentage = 25%

Therefore, the profit percentage earned by the shopkeeper is 25%.

Given:

The ratio of arms to the quadrilateral = 2 ∶ 3 ∶ 4 ∶ 5

Perimeter of the quadrilateral = 560 cm

Solution:

Let's assume that the sides are 2x, 3x, 4x, and 5x, and the area of the quadrilateral is Ax.

So, the sum of all the sides of the quadrilateral is:

2x + 3x + 4x + 5x = 14x

According to the problem statement, the perimeter of the quadrilateral is 560 cm.

Using the formula for the perimeter of a quadrilateral, we have:

perimeter = 14x

560 cm = 14x

x = 40 cm

Therefore, the sides of the quadrilateral are 2x = 80 cm, 3x = 120 cm, 4x = 160 cm, and 5x = 200 cm.

Therefore, the smallest arm of the quadrilateral is 80 cm.

Given:

Initial value of the piece of metal = Rs. 370

The new value of the piece of metal = Rs. 444

Formula Used:

The formula for finding the percentage increase in a value is:

Percentage Increase = ((New Value - Old Value)/Old Value) × 100%

Solution:

Given that the initial value of the piece of metal is Rs. 370 and the new value of the piece of metal is Rs. 444.

Using the formula for finding the percentage increase, we have:

Percentage Increase = ((New Value - Old Value) / Old Value) × 100%

Percentage Increase = ((444 - 370)/370) × 100%

Percentage Increase = (74/370) × 100%

Percentage Increase = 0.2 × 100%

Percentage Increase = 20%

Therefore, the percentage increase in the value of the piece of metal is 20%.

Given:

The diagonal of the square = 90 cm (two different diagonals are given)

Formula Used:

The formula for finding the area of a square when the diagonal is known is:

Area = (diagonal²)/2

Solution:

Let's calculate the area of the square using the given diagonals:

Diagonal = 90 cm:

Using the formula for the area of a square, we have:

Area = (diagonal2)/2

Area = (902)/2

Area = 8100/2

Area = 4050 cm²

Therefore, the area of the square with a diagonal 90 cm is 4050 cm2

Given:

Number of players in the cricket team = 11

The average weight of the players = 102 kg

New average weight (after adding coach) = 103 kg

Formula Used:

The formula for finding the weight of the coach can be derived using the following formula for the average of n items:

Average = (sum of all items)/n

Solution:

Given that the number of players in the cricket team is 11 and the average weight of the players is 102 kg.

Let "x" be the weight of the coach.

Using the formula for the average of n items, we have:

The sum of all player weights/11 = 102 kg

sum of all player weights = 11 × 102 kg

The sum of all player weights = 1122 kg

Using the formula for finding the weight of the coach, we have:

⇒ (x + 1122 kg)/12 = 102 kg + 1 kg

⇒ x + 1122 kg = 12 × 103 kg

⇒ x + 1122 kg = 1236 kg

⇒ x = 1236 kg - 1122 kg

⇒ x = 114 kg

Therefore, the weight of the coach is 114 kg.

Given:

Side of the equilateral triangle = 94 cm

Formula Used:

The area of an equilateral triangle can be calculated using the following formula:

Area = √(3)/4) × a²

where a is the length of a side of the equilateral triangle.

Solution:

Given that the side of the equilateral triangle is 94 cm.

Using the formula for the area of an equilateral triangle, we have:

Area = √(3)/4) × a2

Substituting the value of a, we get:

Area = √(3)/4) × 942

Area = √(3) × 47 × 47

Area = 2209√3

Therefore, the area of the equilateral triangle with a side of 94 cm is 2209√3.

Given:

Width of the rectangle = 195 cm

The diagonal of the rectangle = 507 cm

Formula Used:

Let the length of the rectangle be "l".

According to the Pythagorean theorem, for any right-angled triangle, the sum of the squares of the two shorter sides equals the square of the hypotenuse (the longest side). In this case, we can use this formula to find the length of the rectangle, as follows:

l² = d² - w²

where d is the diagonal length, w is the rectangle's width.

Solution:

We know that the width of the rectangle is 195 cm.

Let the length of the rectangle be "l".

Using the Pythagorean theorem, we have:

l2 = d2 - w2

Substituting the given values, we get:

l2 = (507 cm)² - (195 cm)²

l2 = (507 +195)(507 - 195)

l2 = (702)(312)

l2 = 219024

Taking the square root of both sides, we get:

l = √(219024) cm

l = 468

Therefore, the length of the rectangle is 468 cm, and its width is 195 cm.

Given:

Percentage values: 25%, 66.67%, 75%, 80%

Solution:

Let "x" be the unknown number.

25% of 66.67% of 75% of 80% of x = 6347

⇒ [(25/100) × (66.67/100) × (75/100) × (80/100)] × x = 6347

⇒ [(1/4) × (2/3) × (3/4) × (4/5] × x = 6347

⇒ 1/10 × x = 6347

⇒ x = 63470

40% of the number x = (40/100) × 63470

⇒ 2/5 × 63470

⇒ 25388

Therefore, 40% of the unknown number is 25388.

The logic followed here is :-

Sum of digits of first number = Sum of digits of Second number 

27183 ∶ 777 

27183 → 2 + 7 + 1 + 8 + 3 = 21

777 → 7 + 7 + 7 = 21

Similarly,

34503 ∶ ?? → 3 + 4 + 5 + 0 + 3 = 15

1. 466 → 4 + 6 + 6 = 16

2. 468 → 4 + 6 + 8 = 18

3. 467 → 4 + 6 + 7 = 17

4) 465 → 4 + 6 + 5 = 15

Hence, the correct answer is "465".

i) Government of India has not taken any steps to improve this issue.

The given statement talks about the difference in the time taken to start a small business in India (90 days) compared to Australia (two days). However, it does not provide any specific information about the steps taken or not taken by the government of India to address this issue. Therefore, conclusion i) cannot be logically inferred from the given statement.

ii) Australians pay bribes to get their officers working in two days.

The given statement mentions the time taken by Australians to start a small business, but it does not provide any information about bribery or the actions of Australian officers. There is no direct evidence or logical connection between the given statement and conclusion ii). Therefore, conclusion ii) cannot be logically inferred from the given statement.

 Thus, the correct answer is (D) neither the conclusions i) nor ii) is rational.