RRB NTPC CBT-I Official Paper (Held On: 2 Feb 2021 Shift 2) (Previous Year Paper)

The correct answer is Executive Senior System.

Key Points

• The Executive Support System (ESS) belongs to software which allows users to interchange enterprise data into fast accessible and executive-level reports, such as those used by billing, accounting and staffing departments.
• The ESS improves decision-making for executives.
• ESS is also called Executive Information System (EIS).

Additional Information

• Advantages of ESS(Executive support system):
• ​Easy for upper level executive to use.
• Ability to analyze trends.
• Augmentation of managers' leadership capabilities.
• Enhance personal thinking and decision-making.
• Contribution to strategic control flexibility.
• Enhance organizational competitiveness in the market place.
• Instruments of change.

The correct answer is Hindustan Newsprint Limited (HNL).

Key Points

• Hindustan Newsprint Ltd. is a government company i Central Public Sector.
• This industrial unit is renamed as Kerala Paper Products Limited.
• HNL was established under the Companies Act, 1956, on 7 June 1983, in Kerala.
• The GOI(Government of India) announced the privatization of Hindustan Newsprint On 28 October 2017.

Additional Information

• Indian Government has approved the Maharatna status for NTPC, IOC, ONGC and SAIL.
• Indian Oil Corporation Limited is an Indian government-owned oil and gas explorer and producer, The headquarter of IOCL is located in New Delhi.
• The Oil and Natural Gas Corporation is an Indian oil and gas explorer and producer, The headquarter of ONGC is Located in New Delhi.
• Bharat Heavy Electricals Limited is an Indian govt. owned engineering and manufacturing enterprise which is based in New Delhi, India.
• It is under the of Ministry of Heavy Industries, Government of India

Given: 

Explanation:

Logic : Multiply all outer numbers = Inner number

First jar

7 × 2 × 9 = 126

Similarly,

Second jar

6× 5× 8 = 240 

Hence, "240" is the correct answer.

The correct answer is Greater Noida.

Key Points

• Prime Minister inaugurates the Pandit Deendayal Upadhyaya Institute of Archaeology at Greater Noida in Uttar Pradesh.
• The Institute's aims is to provide a supportive and enthusiastic academic atmosphere to help students achieve their full potential in the field of archaeology.
• “The institute will provide modern amenities for research scholars and students from India and also from all over the world."
• The institute was inaugurated on 9 March 2019.

Additional Information

• List of Top Archaeology Colleges In India based on 2022 Ranking
• ​BAMU, Aurangabad.
• BHU, Varanasi.
• Panjab University - [PU], Chandigarh.
• SPPU, Pune.
• Guru Gobind Singh Indraprastha University - [GGSIPU], New Delhi.
• B.K Birla College Of Arts Science & Commerce, Thane.
• University of Calcutta, Kolkata.
• Mumbai University, Mumbai.

Given:

Number of days taken by 18 skilled workers to do a task = 12 days

Number of days taken by 24 semi-skilled workers to do a task = 15 days

Number of workers left from skilled workers = 3

Concept Used:

Total Efficiency = Total Number of workers × Number of days taken

Calculation:

⇒ Let the efficiency of skilled workers be a and semi-skilled workers be b.

⇒ Total Efficiency for skilled workers = 18a × 12

⇒ So, Total Efficiency for semi-skilled workers = 24b × 15

⇒ According to the question, efficiencies will be same for both types of workers.

⇒ $18a\times 12=24b\times 15$

⇒ 3a = 5b

⇒ This means efficiency of 3 skilled workers is equals to the efficiency of 5 semi-skilled workers.

⇒ If 12 skilled workers started the work and 3 of them left,

⇒ We have already derived the equation,

⇒ So, Number of semi-skilled workers who will replace 3 skilled workers = 5

Therefore, 5 semi-skilled workers will replace the 3 skilled ones who left the task.

The correct answer is 1857.

Key Points

• Indian Mutiny, which is also called Sepoy Mutiny, widespread but unsuccessful rebellion against British rule in India in the year 1857–59.
• The present cause of the Indian Revolt of 1857, or Sepoy Mutiny, was a seemingly change in the weapons used by the British East India Company's army.
• The Company had updated to the new Pattern Enfield Rifle in the year 1853, which used greased paper cartridges.
• On 29 March 1857 at the Barrackpore parade ground, near Calcutta, 29-year-old Mangal Pandey of the 34th BNI, angered by the recent actions of the East India Company, declared that he would rebel against his commanders.

Additional Information

• The Battle of Plassey was a victory of the British East India Company over the Nawab of Bengal, on 23 June 1757, under the leadership of Robert Clive
• Texas Revolution, which is also known as War of Texas Independence, fought from October 1835 to April 1836 between Mexico and Texas colonists that resulted in Texas's independence from Mexico and the founding of the Republic of Texas

Given:

Lengths of chords = x and y

Angles subtended = 60º and 90º

Calculation:

⇒ In $\triangle COD$, we have

⇒ All the radius length will be equal.

⇒ So, OA = OB = OC = OD = r

⇒ Applying Pythagoras theorem,

⇒ Hypotenuse = (Base² + Height²)^1/2

⇒ $y=\sqrt{r^2+r^2}=\sqrt2r$

⇒ $r=\frac{y}{\sqrt2}$

⇒ So, x = r because $\triangle AOB$ is an equilateral triangle.

⇒ Replacing the values, we get

⇒ $x=\frac{y}{\sqrt2}$

⇒ $y=\sqrt2x$

Therefore, the condition which is satisfied for the given chords is $y=\sqrt2x$

The correct answer is 2015.

Key Points

• Indian PM Shri Narendra Modi on 15 July 2015, SKILL INDIA MISSION aims to train over 40 crore people in India in different skills by 2022.
• The National Skill Development Mission was Approved by the Union Cabinet in the year 2015.
• The main aim of the Skill India program is to provide adequate training in market-relevant skills to over 40 crore youth by 2022.
• It also aims to create opportunities for the development of talent in the country and improve the scope and space for undeveloped sectors.

Additional Information

• National Missions
• ​National semiconductor mission for a new era in electronics.
• National mission on natural language translation.
• Smart Cities Mission.
• National Skill Development Mission (NSDM).
• Digital India.
• Ayushman Bharat -National Health Protection Mission (AB-NHPM).
• Atal Innovation Mission.

The correct answer is Patiyali.

Key Points

• Amīr Khusrau was born in Patiyali, presently located in Kasganj district, in modern-day Uttar Pradesh.
• Amir Khusrau was born on 19^th May 1253.
• He was a classical poet associated with the royal courts of the Delhi Sultanate.
• He is also associated with the courts of Alauddin Khilji the ruler of Khilji Dynasty.

Additional Information

• Famous Books are written by Amir Khusro:
• Ghazal.
• Masnavi.
• Qata.
• Rubai.
• Do-baiti.
• Tarkib-band.
• Excerpts of the works done by him are
• Tughluq Nama.
• Wast-ul-Hayat.
• Nuh Sipihr.
• Ashiqa.
• Khamsa.
• Baqia-Naqia.

Given:

LCM of x and y = 2079

HCF of x and y = 27

x = 189

Concept Used:

HCF × LCM = Product of two numbers

Calculation:

⇒ HCF × LCM = Product of two numbers

⇒ 27 × 2079 = 189 × y

⇒ 56133 = 189y

⇒ $y=\frac{56133}{189}=297$

Therefore, the value of y is 297.

Explanation:

Logic : Second number × Third number =  A/first number  = Answer

9 × 5 = 45/15 = 3

6 × 4 = 24/12 = 2

4 × 9 = 36/2 = 18

Hence, 18 is the correct answer.

Given:

X can work as fast as Y and Z together.

X and Y together can finish the task 3 times as fast as Z.

All three working together finishes the work in 15 days.

Calculation:

⇒ Let x, y and z be the per day work rate of X, Y and Z respectively.

⇒ According to the question,

⇒ x = y + z               → (1)

⇒ x + y = 3z             → (2)

⇒ x + y + z = $\frac{1}{15}$            → (3)

⇒ Putting the value of Equation (2) into (3), we get

⇒ 3z + z = $\frac{1}{15}$

⇒ $z=\frac{1}{15\times 4}=\frac{1}{60}$

Therefore, the time Z will take to finish the task is 60 days.

Given:

The population affected with asthma = 20%

Out of these 20%, patients who work in flour mills = 90%

The population working in flour mills = 30%

Concept Used:

Basic Percentage 

Calculation:

⇒ Let the total population be 100

⇒ Number of people affected with asthma = 20% of 100 = $\frac{20}{100}\times 100$ = 20

⇒ Number of asthma patients working in flour mills = 90% of 20 = $\frac{90}{100}\times 20$ = 18

⇒ Number of people working in flour mills = 30% of 100 = $\frac{30}{100}\times 100$ = 30

⇒ Percentage of people working in mills who are suffering from asthma = $\frac{18}{30}\times 100$ = 60%

Therefore, 60% of the people working in mills are suffering from asthma.

Given:

Sum of cost prices of two bikes = Rs 1,00,000

Profit on selling of first bike = 20%

Loss on selling of second bike = 20%

Selling prices of both the bikes are same.

Concept Used:

Selling Price = $\frac{100+Gain\%}{100}\times CP$

Selling Price = $\frac{100-Loss\%}{100}\times CP$

Calculation:

⇒ Let the cost price of first bike be Rs x.

⇒ So, Cost price of second bike = Rs (100000 – x)

⇒ For first bike, Profit = 20%

⇒ So, SP of first bike = $\frac{100+20}{100}\times x=\frac{6x}{5}$ Rs

⇒ Now, for second bike, Loss = 20%

⇒ So, SP of second bike = $\frac{100-20}{100}\times (100000-x)=\frac{4(100000-x)}{5}$

⇒ According to the question,

⇒ SP of first bike = SP of second bike

⇒ $\frac{6x}{5}=\frac{400000-4x}{5}$

⇒ 6x + 4x = 400000

⇒ 10x = 400000

⇒ $x=\frac{400000}{10}=40000$

Therefore, the cost price of the first bike is Rs 40,000

Given:

$\cos \theta + \sec \theta = \sqrt 3$

Concept Used:

(a + b)³ = a³ + b³ + 3ab(a + b)

$cos\theta=\frac{1}{sec\theta}$

Calculation:

⇒ We have, $\cos \theta + \sec \theta = \sqrt 3$

⇒ Cubing both the sides, we get

⇒ $cos^3\theta+sec^3\theta+3\times cos\theta \times sec\theta(cos\theta+sec\theta)=3\sqrt3$

⇒ Putting the given values,

⇒ $cos^3\theta+sec^3\theta+3\times \frac{1}{sec\theta}\times sec\theta\times \sqrt3=3\sqrt3$

⇒ $cos^3\theta+sec^3\theta+3\sqrt3=3\sqrt3$

⇒ $cos^3\theta+sec^3\theta=3\sqrt3-3\sqrt3=0$

Therefore, the required value of $cos^3\theta+sec^3\theta$ is 0.

Given:

Liquid solution = 50 L

Spirit percentage in liquid solution = 20%

Amount of water = 10 L

Calculation:

⇒ Amount of spirit in liquid solution = 20% of 50 L

⇒ Amount of spirit in liquid solution = $\frac{20}{100}\times 50$ = 10 L

⇒ If liquid solution is added with 10 L of water,

⇒ Resulting solution = 50 + 10 = 60 L

⇒ Percentage of spirit in resulting solution = $\frac{10}{60}\times 100=\frac{50}{3}=16\frac{2}{3}\%$

Therefore, the percentage of spirit in resulting mixture is $16\frac{2}{3}\%$.

Explanation:

The possible Venn diagram is : 

Conclusion I . All eggs are blue 

False ( because some eggs are onion ) 

Conclusion II. All onions are eggs.

False ( as shown in  the above venn diagram )

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

Given:

Sum of three numbers = 0

Concept Used:

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

Calculation:

⇒ Let the three numbers be a, b and c.

⇒ According to the question, a + b + c = 0

⇒ Using the formula, we get

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

⇒ Putting the value of given sum,

⇒ a3 + b3 + c3 – 3abc = 0 × (a2 + b2 + c2 – ab – bc – ca) = 0

⇒ a³ + b³ + c³ = 3abc

Therefore, the value of the sum of cubes of three numbers is equals to "three times the product of the three numbers".

The correct answer is John Maynard Keynes.

 Key Points

• John Maynard Keynes's influential work was The General Theory of Employment, Interest and Money.
• He detailed these ideas in his magnum, The General Theory of Employment, Interest and Money, which was published in late 1936.
• British economist John Maynard Keynes, He was regarded as the founder of modern macroeconomics.

Additional Information

• David Ricardo was a classical economist, He was known for his theory on wages and profit, the labor theory of value, the theory of comparative advantage, and the theory of rents.
• The Harrod–Domar model is a model of economic growth. Which is used in the development of economics to explain an economy's growth rate.
• Lewis Carroll was a novelist and poet.
• He was known as the author of the children's book Alice's Adventures in Wonderland (1865) and its sequel Through the Looking-Glass

Explanation:

The logic followed here is : 

Train : Travel : The purpose of train is that it is used for traveling and transport.

Similarly, 

Pen : Write : The purpose of a pen is to write.

Hence, Pen: Write is the correct answer.

The correct answer is Redwood.

Key Points

• The world's largest tree is Hyperion, which is a coastal redwood tree and It is located in the Redwood National Park in California.
• The coastal redwood was discovered by Chris Atkins and Michael Taylor (both belonging to the USA) on 25 August 2006 and its location is kept a closely guarded secret to try and protect it.
• The height of this tree is approx 379 feet or 115 meters.
• The king of these giants tree is known as Hyperion, as per the Guinness book of World Records.

Additional Information

• Deodar Forests are forests dominated by Cedrus deodara, Which is also known as Deodar Cedars tree.
• These types of trees are found naturally in Western Himalayas from the Gandaki river in central Nepal to the Hindukush Mountain range in Afghanistan.
• The oak is a tree or shrub. There are approximately 500 extant species of oaks.
• Eucalyptus which is also known as southern blue gum or blue gum, is a species of tall, evergreen tree endemic to southeastern Australia.

The correct answer is Alexander.

Key Points

• The Battle of Hydaspes was a battle fought between Alexander the Great and the King Porus in 326 BC.
• It ended in a victory for Alexander's Macedonian Army.
• The Battle of the Hydaspes was also the most costly battle fought by the Macedonians.
• Sikandar is the Persian rendition of the name Alexander.

Additional Information

• The battle of Hydaspes resulted in a victory and the surrender of King Porus.
• The Kalinga War was fought in ancient India between the Mauryan Ruler Ashoka the great and the state of Kalinga, an independent kingdom located on the east coast of Odisha.
• Important Battle fought by Babur.
• ​Battle of Khanwa.(1527).
• Battle of Ghaghra.(1529).
• 1^st Battle of Panipat(1526).

The correct answer is Article 326.

Key Points

• Article 326 of the Indian Constitution allows that the elections to the House of the People and to the Legislative Assembly for every Indian State will be on the basis of adult suffrage.
• As per Universal Adult Suffrage, women are not eligible to vote. Article 326 of the Indian Constitution is associated with Universal Adult Suffrage.
• Universal suffrage gives the right to vote to all adult Indian citizens, regardless of wealth, income, gender, social status, race, political stance, or any other restriction.

Additional Information

• Article 327: Power of Parliament allows making provision with respect to elections to legislature.
• Article 325: No person to be ineligible for inclusion or to claim to be included in a special electoral roll on grounds of religion, race, caste or sex.
• The validity of any law relating to the delimitation of constituencies or the allotment of seats to such constituencies, made or purporting to be made under Article 327 or Article 328, shall not be called in question in any court;

Explanation :

Ganga is a river and a river is a water body.

Hence option 3 is the correct answer.

Given:

Calculation:

⇒ In 1993, value of 110 kg of an item = Rs 230

⇒ Value of 1 kg item = $\frac{230}{110}$ = 2.1 Rs

⇒ In 1994, value of 95 kg of an item = Rs 210

⇒ Value of 1 kg item = $\frac{210}{95}$ = 2.21 Rs

⇒ In 1995, value of 125 kg of an item = Rs 340

⇒ Value of 1 kg item = $\frac{340}{125}$ = 2.72 Rs

⇒ In 1996, value of 130 kg of an item = Rs 430

⇒ Value of 1 kg item = $\frac{430}{130}$ = 3.3 Rs

Therefore, the maximum value of a given item per kg out of given years is Rs 3.3.

The correct answer is Yuri Gagarin.

Key Points

• Yuri Gagarin, a Soviet astronaut, became the first person to fly into space on April 12, 1961.
• Orbited Earth aboard Vostok 1 for about 108 minutes.
• His flight marked a milestone in space exploration.
• Established the Soviet Union's lead in the space race.
• Inspired global advancements in space technology.
• Symbolizes humanity's capability for space exploration.

Additional Information

• Yelena Serova:
• Yelena Serova is a Russian cosmonaut who flew to the International Space Station (ISS) in 2014.
• She became the fourth Russian woman in space and the first Russian woman to visit the ISS since 1997.
• Valentina Tereshkova:
• First woman to fly into space.
• Launched aboard Vostok 6 on June 16, 1963.
• Completed 48 orbits around the Earth during her three-day mission.
• Became a symbol of women's achievements in space exploration.
• Neil Armstrong:
• Neil Armstrong was an American astronaut and the first person to walk on the moon on July 20, 1969, during NASA's Apollo 11 mission.
• His iconic words, "That's one small step for a man, one giant leap for mankind," were broadcast worldwide.

Shortcut Trick

For two objects on the same side of a tower of height (h), the distance (d) between them is given by:

d = h × (cot θ_smaller − cot θ_larger)

Here, h = 200 m, θ_smaller = 30°, and θ_larger = 45°.

d = 200 × (cot 30° − cot 45°) = 200 × (√3 − 1) m.

∴ The correct answer is 200(√3 − 1) m.

Alternate Method

Given:

Height of the watch tower (AB) = 200 m

Angle of depression of first cliff (C) = 45° → Angle of elevation at C = 45°

Angle of depression of second cliff (D) = 30° → Angle of elevation at D = 30°

In right-angled triangle ABC:

⇒ tan 45° = AB / BC

⇒ 1 = 200 / BC

⇒ BC = 200 m

In right-angled triangle ABD:

⇒ tan 30° = AB / BD

⇒ 1 / √3 = 200 / BD

⇒ BD = 200√3 m

The distance between the two cliffs (CD) is:

⇒ CD = BD − BC

⇒ CD = 200√3 − 200

⇒ CD = 200(√3 − 1) m

∴ The correct answer is 200(√3 − 1) m.

Additional Information

Angle Relationship

The angle of depression from a point is numerically equal to the angle of elevation from the observed object to that point because they are alternate interior angles.

Opposite Sides Formula

If objects are on opposite sides of the tower, the distance between them is d = h(cot θ₁ + cot θ₂).

Trigonometric Values

Standard values used: tan 45° = 1, tan 30° = 1/√3, cot 45° = 1, and cot 30° = √3 (where √3 ≈ 1.732).

The correct answer is EM Forster.

Key Points

• Edward Morgan Forster was an English author, He was best known for his novels, particularly A Room with a View, Howards End, and A Passage to India.
• He also wrote various short stories, essays, speeches and broadcasts, as well as limited number of biographies and some plays.
• It is widely known as Forster's finest work and it became his last novel, the fact that he remained active as a writer and critic for more than four decades after its publication.
• A Passage to India was published in the year 1924.

Additional Information

• Karl Gunnar Myrdal was a Swedish economist and sociologist.
• In 1974, he received the Nobel Memorial Prize in Economic Sciences.
• Nirad Chandra Chaudhuri was an Indian writer.
• In the year 1990, Oxford University awarded Nirad Chandra Chaudhuri, by then a long-time resident of the city of Oxford, an Honorary Degree in Letters.
• In the year 1992, he was made an honorary Commander of the Order of the British Empire.

The correct answer is Article 50.

Key Points

• Article 50: According to this Article the State shall take steps to separate the judiciary from the executive.
• In India, separation of functions rather than of powers is followed. Unlike in the US, in India, the concept of separation of powers is not adhered to strictly.
• Most of the constitutional systems do not have a separation of powers between the various organs in the classical sense because it is impractical.
• The purpose of separation of powers is to prevent abuse of power by a single person or a group of individuals.

Additional Information

• Separation of Powers
• ​This concept was first seen in the works of Aristotle, in the 4th century BCE, wherein he described the three agencies of the government as General Assembly, Public Officials and Judiciary.
• In the Ancient Roman Republic too, a similar concept was followed.
• In modern times, it was 18th-century French philosopher Montesquieu who made the doctrine a highly systematic and scientific one, in his book De l’esprit des lois (The Spirit of Laws).
• His work is based on an understanding of the English system which was showing a propensity towards a greater distinction between the three organs of government.
• The idea was developed further by John Locke.

Given:

$\frac{7}{9} - \frac{{11}}{{12}} + \frac{{13}}{{16}} - \frac{1}{8}$

Calculation:

⇒ Taking the LCM of denominators 9, 12, 16 and 8,

⇒ LCM of 9, 12, 16, and 8 = 144

⇒ $\frac{7}{9} - \frac{{11}}{{12}} + \frac{{13}}{{16}} - \frac{1}{8}$ = $\frac{7\times 16-11\times 12+13\times 9-18}{144}$

⇒ $\frac{112-132+117-18}{144}=\frac{79}{144}$

Therefore, the required value of the given expression is $\frac{79}{144}$.

The correct answer is Paris.

Key Points

• The Organisation for Economic Co-operation and Development (OECD) is a group of 37 member countries that discuss and develop economic and social policy.
• 12 OECD members are typically democratic countries that support free-market economies.
• The OECD's headquarters are at the in Paris, France.
• India is now the 27th member of the Centre, joining many OECD countries as well as Argentina, Brazil and Chile.

Additional Information

• International organizations have been formed with the aim of helping to set the international agenda, strengthen political relationships, providing a place for developmental initiatives, etc.
• The city of Geneva itself is host to 39 international institutions, organizations, bodies as well as a secretariat established under a treaty.
• Some Important Organization and there Headquartes:
• ​United Nations University (UNU)- Tokyo, Japan.
• World Food Programme (WFP)- Rome, Italy.
• International Maritime Organisation (IMO)- London, United Kingdom.
• United Nations Educational Scientific and Cultural Organisation (UNESCO)-Paris, France.

The correct answer is Denis Mukwege and Nadia Murad.

Correct answer is Nile.

Key Points

• The Nile River is roughly 4,100 miles long and was factually thought to be the longest river in the world.
• There is many of discussion surrounding this, however, for many believe the Amazon River in South America might be longer.
• The Nile River flows through south to north through eastern Africa.
• It starts in the rivers that flow into Lake Victoria, and empties into the Mediterranean Sea more than 6,600 kilometers (4,100 miles) to the north, making it one of the longest river in the world.

Additional Information

• ​The River Ganges emerges in the western Himalayas and flows down over northern India into Bangladesh, where it empties into the Bay of Bengal.
• The Amazon is the significant river of South America and the largest drainage system in the world in terms of the volume of its flow and the area of its basin.
• Yangtze is the country's chief waterway, and its basin is China's great granary and contains nearly one-third of the national population.

The correct answer is Oxygen.

Key Points

• Carbon dioxide is released during photosynthesis.
• During photosynthesis, plants take in carbon dioxide (CO2) and water (H2O) from the air and soil.
• The raw materials required for photosynthesis are carbon dioxide, water and sunlight primarily.
• Oxygen is given out as a waste product during photosynthesis.

Additional Information

• Photosynthesis is a process used by plants and other organisms to convert light energy into chemical energy that, through cellular respiration, can later be released to fuel the organism's activities.
• Within the plant cell, the water is oxidized, meaning it loses electrons, while the carbon dioxide is reduced, meaning it gains electrons.
• This transforms the water into oxygen and the carbon dioxide into glucose.

Given:

Distance travelled by train before accident = 30 km

Reduced speed = Four-fifth of the original speed

Delayed time = 45 min

If accident would have happened 18 km farther, then delayed time = 36 min

Concept Used:

Speed = Distance ÷ Time

Calculation:

⇒ Let the original speed of train be x.

⇒ Reduced speed of train after accident = $\frac{4x}{5}$

⇒ Time difference in covering extra 18 km due to change in speed = 45 – 36 = 9 min

⇒ According to the question,

⇒ $\frac{18}{\frac{4x}{5}}-\frac{18}{x}=\frac{9}{60}$

⇒ $\frac{18\times 5}{4x}-\frac{18}{x}=\frac{3}{20}$

⇒ $\frac{90-72}{4x}=\frac{3}{20}$

⇒ 3 × 4x = 20 × 18

⇒ $x=\frac{360}{12}$ = 30 km/h

Therefore, the original speed of the train is 30 km/h.

The correct answer is Speaker.

Key Points

• The speaker of the Lok Sabha is that the leader and also the highest authority of the Lok Sabha, the lower house of the Parliament of India.
• The speaker is elected generally whithin the first meeting of the Lok Sabha following general elections.
• Serving for a term of 5 years, the speaker chosen from sitting members of the Lok Sabha.
• Parliament is that the supreme legislative body of India.

Additional Information

• The President is liable for implementing and enforcing the laws written by Congress and, to it end, appoints the heads of the federal agencies, including the Cupboard.
• The Vice President is additionally a part of the chief Branch, able to assume the Presidency should the requirement arise.
• The Prime minister acts because the leader of the house of the chamber of parliament—generally the Lok Sabha—they belongs to.
• The Prime minister is tasked with representing the manager whithin the legislature, announces important legislation, and is further expected to reply to the opposition's concerns.

The correct answer is Angel.

Key Points

• The highest or tallest waterfall in the world is Angel Falls, which means 'waterfall of the deepest place', is known in Venezuela.
• It is the world's tallest uninterrupted waterfall, with a height of 979 meters and a plunge of 807 m.
• The waterfall drops from the Auyán-tepui mountain in the Canaima National Park, a UNESCO World Heritage site in the Gran Sabana region of Bolívar State.
• Angel Falls exists as the highest continuous waterfall in the world.

Additional Information

• The Gavarnie Falls is a waterfall located in France. with the height of 422 meters, it is the highest waterfall in France.
• Jog is located in Siddapur taluk in Uttara Kannada district of Karnataka state, India.
• Ribbon Fall, which is located in Yosemite National Park in California, flows off on the west side of Capitan and is the longest single-drop waterfall in North America

The correct answer is Sedimentation.

Key Points

• The process of separating insoluble substances which are heavier than liquid by allowing them to settle down on their own due to gravity is called sedimentation.
• Sedimentation is the process of deposition of sediments.
• It tooks place when particles in suspension are settled out of the fluid in which they are entrained and come to rest against a barrier.
• The particles which settled out from the suspension become sediment, and in water treatment is called as sludge.

Additional Information

• Evaporation is a procedure of vaporization which occurs on the surface of a liquid as it changes into the gas phase.
• Decantation is the process of separation of liquid from solid and other non-merging liquids.
• The process in which solid particles in a liquid or gaseous fluid are removed by the use of a filter medium that permits the fluid to pass through but retains the solid particles.

Given:

Divisors of 120

Calculation:

⇒ We have to find the divisors of 120

⇒ Divisors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

⇒ Total divisors = 16

Therefore, the total number of divisors of 120 is 16.

Given:

Selling price of two articles = Rs 4,000 each

Profit percentage on first article = 15%

Loss percentage on second article = 15%

Concept Used:

Cost Price = $\frac{100}{100+Gain\%}\times SP$

Cost Price = $\frac{100}{100-Loss\%}\times SP$

Calculation:

⇒ For the first article with profit of 15%,

⇒ Cost Price = $\frac{100}{100+15}\times 4000=\frac{100}{115}\times 4000$

⇒ Cost Price = Rs 3,478.26

⇒ For the second article with loss of 15%,

⇒ Cost Price = $\frac{100}{100-15}\times 4000=\frac{100}{85}\times 4000$

⇒ Cost Price = Rs 4,705.88

⇒ Total Selling Price = Rs 8000

⇒ Total Cost Price = 3478.26 + 4705.88 $\approx$ Rs 8,184

⇒ Loss = CP – SP = 8184 – 8000 = Rs 184

Therefore, the loss on the selling of both articles costs to Rs 184.

Explanation:

Logic :√ (1^st number) +√ (2^nd number)  = Third number

√25 = 5, √64 = 8

5 + 8 = 13

√144 = 12, √36 = 6

12 + 6 = 18

√121 = 11, √81 = 9

11 + 9 = 20

Hence, Option 3 is the correct answer.

The correct answer is Raja J Chelliah.

Key Points

• The government constituted the Tax Reforms Committee (TRC) in August 1991, under the chairmanship of Professor Raja J. Chelliah to recommend measures for the reform of Central taxes.
• This TRC came up with three reports in 1991, 1992 and 1993 with several measures, which can be summarized in these points.
• Reforming the personal taxation system by reducing the marginal tax rates.
• Reduction in the corporate tax rates.
• Reducing the cost of imported inputs
• Reforming the personal taxation system by reducing the marginal tax rates.
• by lowering the customs duties.

Additional Information

• Raghuram Govindarajan is an Indian economist and the Katherine Dusak Miller Distinguished Service Professor of Finance at the University of Chicago Booth School of Business.
• Between 2003 and 2006 he was Chief Economist and director of research at the International Monetary Fund.
• Vijay L. Kelkar is an Indian economist and academic, who is currently the Chairman of the Forum of Federations, Ottawa & India Development Foundation, New Delhi.
• Pamulaparthi Venkata Narasimha Rao was an Indian lawyer and politician who served as the 9th Prime Minister of India from 1991 to 1996. He is often referred to as the "Father of Indian Economic Reforms"

The correct answer is Subhash Chandra Bose.

Key Points

• The Indian Struggle, 1920–1942, is a two-division book by the Indian leader Netaji Subhash Chandra Bose.
• This book covers 1920–1942, this part elaborates the history of the Indian independence movement to end British imperial rule over India.
• The book analyzes a period of the Indian independence struggle from the Non-Cooperation and Khilafat Movements of the early 1920s to the Quit India and Azad Hind movements of the early 1940s.
• The first part of The Indian Struggle covers the years 1920–1934 and was published in London in 1935 by Lawrence and Wishart.

Additional Information

• India wins Freedom is a book written by Maulana Abul Kalam Azad.
• The Discovery of India and A letter from a father to his daughter  are the books given by Pandit Jawaharlal Nehru.
• The Story of My Experiments with Truth  is the autobiography of Mahatma Gandhi, covering his life from early childhood through to 1921.

The correct answer is Mineral.

Key Points

• The compounds of metals in which the metals forms occur naturally are called minerals.
• Most pure metals on the earth come from the earth's crust.
• They are found in ores, which is a solid materials that minerals and metals can be taken from.
• The most valuable ore contains metals to industry and trade, like copper, gold, and iron.

Additional Information

• The fused material formed during the melting or refining of metals by combining the flux with gangue, impurities in the metal, etc is known as Slag.
• A naturally occurring mineral containing a valuable constituent (such as metal) for which it is mined and worked is known as Ore.
• Flux is the presence of a force field in a specified physical medium, or the flow of energy through a surface.

Given:

Increase in length of rectangle = 70%

Concept Used:

Area of rectangle = Length × Breadth

Calculation:

⇒ Let the length of rectangle be x and breadth be y.

⇒ Area of rectangle = xy

⇒ New length after increase = x + 70% of x

⇒ New length after increase = $x+\frac{70}{100}\times x=x+\frac{7x}{10}=\frac{17x}{10}$

⇒ As the area is same, the breadth will be,

⇒ Breadth = $\frac{xy}{\frac{17x}{10}}=\frac{10xy}{17x}=\frac{10y}{17}$

⇒ So, Percentage decrease in width = $\frac{7y}{17}\times \frac{1}{y}\times 100=\frac{700}{17}=41.17\%$

Therefore, the percentage decrease in the width to maintain the same area is 41.17 %.

Explanation:

STEP1. The one who wrote first gave it to Riya so Riya becomes the second to receive novel.

STEP2.  The one who wrote last took it from Priya so Priya becomes 4th out of 5 girls to receive the novel.

STEP3.Tina was not the first or the last to write. Here Riya and Priya have already been placed at 2nd and 4th position respectively so Tina will be the 3rd girl to receive the novel.

STEP4. There were two writers in between Usha and Priya and to follow this logic we will place Usha at 1st and the remaining 5th posotion will be taken by Shreya.

Hence, Shreya is the correct answer.

Given:

Function = 4a³ – 12a² + 14a – 3

Divisor = a – $\frac{1}{2}$

Calculation:

⇒ To get the value of a, equate the equation equals to 0.

⇒ So, a – $\frac{1}{2}$ = 0

⇒ a = $\frac{1}{2}$

⇒ Putting the value of a, in the function to get the remainder.

⇒ $f(\frac{1}{2})$ = 4 × $\left(\frac{1}{2}\right)^3$– 12 × $\left(\frac{1}{2}\right)^2$ + 14 × $\left(\frac{1}{2}\right)$ – 3

⇒  $f(\frac{1}{2})$ = 4 × $\frac{1}{8}$ – 12 × $\frac{1}{4}$ + 7 – 3

⇒  $f(\frac{1}{2})$ = $\frac{1}{2}$ – 3 + 7 – 3

⇒ $f(\frac{1}{2})=\frac{1+2}{2}=\frac{3}{2}$

Therefore, the remainder of the given function when divided by $a-\frac{1}{2}$ is $\frac{3}{2}$.

Given:

Amount = Rs 175

Time = 8 years

Rate = 5% per annum

Concept Used:

Simple Interest = $\frac{P\times R\times T}{100}$

Amount = Principal + Simple Interest

Calculation:

⇒ Let the sum invested be Rs x.

⇒ So, $175=x+\frac{x\times 5\times 8}{100}=\frac{100x+40x}{100}$

⇒ 140x = 17500

⇒ $x=\frac{17500}{140}$ = 125

Therefore, the sum invested was Rs 125

Explanation :

Argument (ii) is valid because parents play biggest role in development and separation over long period of time damages children's relationship with them, leaving the children feeling anxious or alone.

Argument (i) is a baseless argument because separation from their homes is not beneficial

Hence, Only argument (ii) is strong is the correct answer.

The correct answer is Germany.

Key Points

• The Axis powers (Germany, Italy, Japan) were opposed by the Allied Powers (led by Great Britain, the U.S, and also the Soviet Union).
• Five other nations joined the Axis during Warfare II: Hungary, Romania, Bulgaria, Slovakia, and Croatia.
• The decline and fall of the Axis alliance began in 1943.
• The Axis Powers ruled much of Europe,geographical area and Africa.

 Additional Information

• ​World War II or the Second World War, was a global war that lasted from 1939 to 1945.
• It involved the overwhelming majority of the world's countries—including all of the nice powers—forming two opposing military alliances: the Allies and therefore the Axis powers.
• Hitler's invasion of Poland in September 1939 drove Great Britain and France to declare war on Germany, marking the starting of World War II.

Given:

$\frac{1}{{36.18}}$ = 0.0276

Calculation:

⇒ $\frac{1}{{36.18}}=0.0276$

⇒ We have to find the value of $\frac{1}{{0.0003618}}$,

⇒ To get this value, we will divide by 100000,

⇒ $\frac{1}{\frac{36.18}{100000}}$ = 0.0276 × 100000

⇒ $\frac{1}{{0.0003618}}$ = 2760

Therefore, the value of $\frac{1}{{0.0003618}}$ is 2760.

The correct answer is Maharaja Sawai Pratap Singh.

Key Points

• The Hawa Mahal is a palace in the city of Jaipur, Located in India.
• It is Built from red and pink sandstone.
• It is on the edge of the City Palace, Jaipur, and It can be extended to the Zenana.
• The structure was built in the year 1799 by Maharaja Sawai Pratap Singh, Who was the grandson of Maharaja Sawai Jai Singh, the Founder of the city of Jaipur, India.

Additional Information

• The Jantar Mantar was constructed in the year 1724, by King Sawai Jai Singh, the Raja of Jaipur.
• The Jantar Mantar in Delhi was the first to be built and was one of five-Jaipur, Ujjain, Varanasi, and Mathura.
• The memorial is a life-sized bronze statue of Maharana Pratap balanced on his loyal and favorite horse**, Chetak.**
• It is believed that Chetak was a faithful horse.

Given:

(6 + 4) × $\frac{4}{2}$ + 5 – 3

Concept Used:

BODMAS = Bracket, Of, Division, Multiplication, Addition, Subtraction

Calculation:

⇒ (6 + 4) × $\frac{4}{2}$ + 5 – 3

⇒ 10 × 2 + 5 – 3

⇒ 20 + 2 = 22

Therefore, the required value of the expression is 22.

Correct answer is ATP.

Key Points

• Adenosine triphosphate, or ATP, is the chief molecule for storing and transferring energy in cells.
• The structure of ATP is a nucleoside triphosphate, made up of a nitrogenous base (adenine), a ribose sugar, and three serially bonded phosphate groups.
• ATP is generally mentioned as the "energy currency" of the cell, as it provides readily releasable energy in the bond between the second and third phosphate groups.
• ATP plays an important role in the transport of macromolecules such as proteins and lipids into and out of the cell.

Additional Information

• Adenosine monophosphate (AMP) is one of the components of RNA and also the organic component of the energy-carrying molecule ATP.​
• Ribonucleic acid (RNA) is a nucleic acid present in all living cells that has structural similarities to DNA.
• DNA, or deoxyribonucleic acid, is the hereditary material in humans and nearly all other organisms.

Given:

23 × 33 × 54 × 72

Divisor = 50

Calculation:

⇒ We can write 50 as 2 × 5²,

⇒ Extracting this term, we get

⇒ 2 × 5² × 2² × 3³ × 5² × 7²

⇒ Excluding 2² because multiplying any power of 2 with 50 will be divisible by 100

⇒ Now, the total factors will be +1 in each remaining terms power.

⇒ Factors of 23 × 33 × 54 × 7² which are divisible by 50 but not by 100 = (3 + 1) × (2 + 1) × (2 + 1) = 4 × 3 × 3 = 36

Therefore, total factors of 23 × 33 × 54 × 7² which are divisible by 50 but not by 100 equals to 36.

Explanation :

17 - 16 = 1 , 14 - 13 = 1

17 - 12 = 5 , 9 - 4 = 5

Similarly,

32 - 29 = 3 , 20 - 17 = 3

Hence, 20 is the correct answer.

Correct answer is Loan to small businessmen from 50 thousand up to 5 lakhs.

Key Points

• Pradhan Mantri MUDRA Yojana (PMMY) is a scheme launched by the Hon'ble Prime Minister on April 8, 2015, for providing loans up to 10 lakh to non-corporate, non-farm small/micro enterprises.
• Anyone who runs a small business enterprise is eligible to try for a Mudra Loan.
• The scheme offers a sanction that ranges from Rs. 50,000 to Rs. 5 lakh at the Mudra interest rate decided by the lending institution in question.
• In Kishore Mudra Yojana, the interest rate may range from 8.60% to 11.15% or more and is based on the scheme's guidelines and your credit history.

Additional Information

• Pradhan Mantri Jan-Dhan Yojana (PMJDY) is a National assignment for Financial Inclusion to make sure access to financial services, namely, basic savings & deposit accounts, remittance, credit, insurance, and pension in an affordable manner.​
• Pradhan Mantri Awas Yojana (PMAY) to provide affordable housing to all citizens by 2022.
• The Government of India started the Stand Up India scheme on April 5, 2016, as part of efforts to support entrepreneurship among women and Scheduled Caste & Scheduled Tribe (SC & ST) communities.

Correct answer is 2 years, 11 months and 18 days.

Key Points

• The Constitution process took 2 years, 11 months, and 18 days—at a total expenditure of ₹6.4 million to finish.
• The Republic is ruled in terms of the Constitution of India which was adopted by the Constituent Assembly on 26th November 1949 and effective on 26th January 1950.
• The Constitution of India is the supreme law of India.
• A constitution is a set of fundamental principles according to which a country can be governed.

Additional Information

​ Qualities of the Indian Constitution are given below:

• World's Longest Constitution
• Independent and Integrated Judicial System
• Directive Principles of State Policy
• Federal System with Unitary Features

Correct answer is Manipur.

Key Points

• The sangai, endemic to Manipur, is found only at the Keibul Lamjao National Park (KLNP), the world's only floating national park.
• It is largely seen over the floating biomass, locally known as “phumdi” in the South Eastern part of Loktak Lake inside the park.
• The park covers an area of 40 km² and the home range of the deer in the park is confined to 15–20 km².
• Sangai, also known as the brow-antlered deer or the dancing deer.

Additional Information

• ​Periyar Wildlife Sanctuary is the biggest wildlife sanctuary in Kerala which is Spread over an area of approximately 777 sq km.
• The Kaziranga National Park is a famous wildlife sanctuary in Assam.
• Nauradehi Wildlife Sanctuary, covering about **1,197 km² **is the largest wildlife sanctuary in Madhya Pradesh state in India.

Explanation:

The name written in the blue boxes refer to women's names and the remaining are the name of males.The bold vertical line represents parents‐  children while the bold horizontal line represents the relationship of siblings. The blue horizontal line represents wife-husband relations. Naming the mother of Walter 'Mother' we get to know that Skyler is Mother's Husband's sister.

Hence, Husband's sister is the  correct answer.

The correct answer is 1942.

Key Points

• On 8 August 1942 at the All-India Congress Committee session in Bombay, Mohandas Karamchand Gandhi start the 'Quit India' movement.
• A while later, Gandhi, Nehru, and many other leaders of the Indian National Congress were arrested by the British Government.
• The Quit India Movement was announced by the Indian National Congress after the failure of the Cripps Mission.
• The movement began in a speech in Bombay, where Mahatma Gandhi asked Indians to Do or Die.

Additional Information

• ​The Khilafat movement (1919-1924) was a trouble by Indian Muslims allied with Indian nationalism in the years following World War I.
• Dandi March was a 24-day non-violent march conduct by Mahatma Gandhi.
• Champaran has been the starting point of India's independence movement began by Gandhi.

Correct answer is 1858.

Key Points

• Queen Victoria's Proclamation of 1 November 1858 announced that then India would be governed by and in the name of the British Monarch through a Secretary of State.
• Government of India Act, 1858 is also famous as the act of good governance.
• Parliament to hand over administrative control of British India from the East India Company.
• The act made India a direct British Colony and scraped the dual government proposed by Pitt's India Act of 1784.

Additional Information

• Pitt's India Act established the system of dual control of India and these changes continued through 1858.
• The Government of India Act 1919 was an act of the British Parliament that sought to increase the participation of Indians in the administration of their country.
• The Government of India Act, of 1935 was an Act adapted from the Parliament of the United Kingdom.​

Given:

Volume of cube = 324 cm³

Ratio of length, width and height of cuboid = 3 : 2 : 2

Concept Used:

Volume of Cuboid = l × b × h

Calculation:

⇒ Let the length, breadth and height of cuboid be 3x, 2x and 2x respectively.

⇒ Even if cube is moulded into cuboid, the volume remains same.

⇒ Volume of cuboid = 324 cm³

⇒ 3x × 2x × 2x = 324

⇒ 12x³ = 324

⇒ x³ = $\frac{324}{12}$ = 27

⇒ So, x = 3

⇒ Length of cuboid = 3x = 3 × 3 = 9 cm

Therefore, the length of cuboid is 9 cm.

Correct answer is Khushi Chindaliya.

Key Points

• Khushi Chindaliya, a 17-year-old girl from Surat has been scheduled as Regional Ambassador for India by the United Nations Environment Programme - Tunza Eco-Generation.
• She says**, "Impassioned about conserving the environment, I appeal to everyone to spread awareness to safeguard it."**
• Brand ambassadors are additionally hired by the government or a private entity to affect the mindset of targeted customers or societies.

Additional Information

• The United Nations Environment Programme (UNEP) is the main environmental authority in the United Nations system.
• UNEP works on delivering transformational change for people and nature by dessert on the root causes of the three planetary crises of climate change, nature and biodiversity loss, and pollution and waste.

​

Given:

Number = 367892141

Calculation:

⇒ Place value of 3 in 367892141 = 3 × 100000000

⇒ Place value of 3 in 367892141 = 3 × 10⁸

Therefore, the place value of 3 in 367892141 is 3 × 10⁸.

Correct answer is Sunil Arora.

Key Points

• Sunil Arora was the 23rd Chief Election Commissioner of India.
• Sunil Arora is as well the chairman of the Association of World Election Bodies (A-WEB).
• He is a retired 1980-batch Indian Administrative Service (IAS) officer of the Rajasthan cadre.

Additional Information

• Syed Nasim Ahmad Zaidi served as the 20th Chief Election Commissioner of India.​
• Om Prakash Rawat is a retired 1977 batch Indian Administrative Service (IAS) officer of the Madhya Pradesh cadre as 22nd Chief Election Commissioner of India.
• Achal Kumar Jyoti is a retired 1975 IAS officer of Gujarat cadre as 21st Chief Election Commissioner of India.

Given:

Dividend = 13, 26 and 39

Remainders = 1, 2 and 3

Calculation:

⇒ Let the HCF of the numbers be x.

⇒ In order to make 13, 26 and 39 completely divisible by x, we need to deduct the remainders from them respectively.

⇒ Required number = 12, 24 and 36

⇒ Factors of 12 = 2 × 2 × 3

⇒ Factors of 24 = 2 × 2 × 2 × 3

⇒ Factors of 36 = 2 × 2 × 3 × 3

⇒ HCF = Common factors = 2 × 2 × 3 = 12

Therefore, the greatest number which divides 13, 26 and 39 and gives remainders as 1, 2 and 3 respectively is 12.

Explanation:

The logic followed here is sum of all the number given in the circle will be equal to 70.

15 + 13 +17 + 25 = 70

21+ 26 + 10 + 13 = 70

49 + 3 + 7 + 11 = 70

10 + 32 +10 + 18 = 70

Hence, 10 is the correct answer.

Explanation :

Argument (i) and (ii) both are valid because it presents the fact that on one side war- type games helps in developing strategy and planning skills in children on the other side such games do not teach children good values.

so, both arguments are strong

Hence, Option 3 is the correct answer.

Correct answer is 2010.

Key Points

• The National Green Tribunal was established in 2010.
• The National Green Tribunal Act is a specialised judicial body equipped with skill simply for the motive of adjudicating environmental cases in the country.
• The National Green Tribunal was set up under the National Green Tribunal Act, 2010 (NGT Act).
• The objective of the NGT Act is to provide effective and expeditious disposal of cases relating to the protection of the environment.

Additional Information

• The NGT has five places for sittings, New Delhi is the chief place of sitting, and Bhopal, Pune, Kolkata, and Chennai are the other four.​
• The NGT act directs and gives authority to the central government to form an NGT to deal with environmental issues.
• It is a trained body begin for the effective and timely resolution of matters involving environmental protection.

Correct answer is One-horn rhino.

Key Points

• The Kaziranga National Park hosts two-thirds of the world's great one-horned rhinoceroses, is a World Heritage Site.
• Kaziranga National Park is a national park in the Golaghat and Nagaon districts of the state of Assam, India.
• Kaziranga is regarded as one of the finest wildlife refuges in the world.
• Kaziranga National Park is also known as an important birdlife area by Birdlife International for conserving varied species of birdlife.

Additional Information

• The largest tiger reserve in India is the Nagarjunsagar-Srisailam Tiger Reserve.
• ​The Darrah National Park is one of the most popular national parks in Rajasthan.
• Gir forests of Gujarat is the only place where this race of lions i.e. Asiatic lion is found in its natural habitat.

Shortcut Trick

We need exactly 1 white ball and 1 non-white ball from 21 total balls (7 white, 14 non-white).

Probability = P(First is White, Second is Non-White) + P(First is Non-White, Second is White)

P = (7/21 × 14/20) + (14/21 × 7/20)

P = (1/3 × 7/10) + (2/3 × 7/20)

P = 7/30 + 7/30 = 14/30 = 7/15

∴ The correct answer is 7/15.

Alternate Method

Given:

Number of blue balls = 9

Number of white balls = 7

Number of black balls = 5

Number of balls drawn = 2

Formula Used:

Probability = Number of Favorable Outcomes ÷ Total Possible Outcomes

Combination formula: ⁿC_r = n! ÷ [r! × (n−r)!]

Calculations:

⇒ Total number of balls = 9 + 7 + 5 = 21

⇒ Total possible outcomes when drawing 2 balls = ²¹C₂

⇒ ²¹C₂ = (21 × 20) ÷ (2 × 1) = 210

⇒ Number of non-white balls = 9 (blue) + 5 (black) = 14

⇒ We need exactly one white ball, which implies drawing 1 white ball AND 1 non-white ball.

⇒ Number of favorable outcomes = ⁷C₁ × ¹⁴C₁

⇒ Favorable outcomes = 7 × 14 = 98

⇒ Required Probability = 98 ÷ 210

⇒ Divide numerator and denominator by 14: 98 ÷ 14 = 7 and 210 ÷ 14 = 15

⇒ Required Probability = 7/15

∴ The correct answer is 7/15.

Additional Information

Combinations in Probability

When drawing multiple items simultaneously, combinations (ⁿC_r) are used to find the number of ways to select r items from a total of n items without regard to order.

Mutually Exclusive Events

Events that cannot occur at the same time. The probability of either event A or event B occurring is the sum of their individual probabilities: P(A or B) = P(A) + P(B).

Multiplication Rule for Dependent Events

When drawing items one after another without replacement, the outcome of the first draw affects the probabilities of the second draw: P(A and B) = P(A) × P(B after A).

Given:

Ratio of speeds of three cars = 2 : 3 : 4

Concept Used:

Speed is inversely proportional to time taken.

Speed = Distance / Time

Calculation:

⇒ Let the distance be 1.

⇒ LCM of 2,3 and 4 = 12

⇒ Ratio of time taken = $\frac{1}{2}\times 12:\frac{1}{3}\times 12:\frac{1}{4}\times 12$ = 6 : 4 : 3

Therefore, the ratio of time taken by these cars is 6 : 4 : 3