RRB NTPC CBT-I Official Paper (Held On: 15 Feb 2021 Shift 2) (Previous Year Paper)

The correct answer is August 09, 2019

Key Points

• The Jammu and Kashmir Reorganization Bill, 2019 received the assent of the President on August 09, 2019.
• This act of Parliament reorganized the state of Jammu and Kashmir into two Union Territories: Jammu and Kashmir, and Ladakh.
• The reorganization aimed to provide better governance and ensure the integration of the region with the rest of India.
• The bill was introduced in the Rajya Sabha by the Minister of Home Affairs, Mr. Amit Shah.

Additional Information

• The reorganization came into effect on October 31, 2019, the birth anniversary of Sardar Vallabhbhai Patel, who is remembered for his role in the integration of India.
• The Jammu and Kashmir Reorganization Act, 2019, also led to the abrogation of Article 370, which granted special autonomy to the region.
• This decision was met with various political reactions and has had significant implications for the region's governance and administration.

The correct answer is Navratna

Key Points

• Oil India Limited is a Central Public Sector Enterprise (CPSE).
• It is classified as a Navratna company.
• Navratna status is a recognition given by the Government of India to public sector enterprises that have comparative advantages and greater autonomy to compete in the global market.
• This status allows the company to invest up to a certain limit without seeking government approval.
• Oil India Limited is engaged in the business of exploration, development, and production of crude oil and natural gas, transportation of crude oil, and production of LPG.

Additional Information

• Oil India Limited was established in 1959 and is headquartered in Duliajan, Assam, India.
• It is the second-largest hydrocarbon exploration and production (E&P) company in India.
• In addition to India, Oil India Limited has operations in countries like Libya, Gabon, Nigeria, Sudan, Venezuela, Mozambique, Bangladesh, and the USA.
• The company has received several awards for its performance and contribution to the oil and gas sector.
• Oil India Limited plays a significant role in the energy security of India.

The logic followed here is:

Logic: Tool and its Function.

Here,

Pen : Writing → Pen is a tool used for Writing.

Similarly,

EVM : Voting → EVM is a tool used for Voting.

Hence, the correct answer is "Option 3".

Given:

Numbers: 108, 288, 360

Formula Used:

To find the H.C.F of multiple numbers, we use the prime factorization method.

Calculation:

Prime factorization of 108:

108 = 2² × 3³

Prime factorization of 288:

288 = 2⁵ × 3²

Prime factorization of 360:

360 = 2³ × 3² × 5

To find the H.C.F, we take the lowest power of all common prime factors:

Common prime factors: 2 and 3

Lowest power of 2: 2²

Lowest power of 3: 3²

⇒ H.C.F = 2² × 3²

⇒ H.C.F = 4 × 9

⇒ H.C.F = 36

The H.C.F of 108, 288, and 360 is 36.

Shortcut Trick

In a rhombus, the diagonals are perpendicular to each other, so the angle at the intersection point is 90º (∠AOD = 90º).

Since opposite sides of a rhombus are parallel (AD || BC), the alternate interior angles are equal:

⇒ ∠DAC = ∠ACB = 40º

In the right-angled triangle AOD, the sum of acute angles is 90º:

⇒ ∠ADB = 90º − ∠DAC = 90º − 40º = 50º.

∴ The correct answer is 50º.

Alternate Method

Given:

In a rhombus ABCD, the angle ∠ACB = 40º.

Properties Used:

1. The diagonals of a rhombus bisect each other at right angles (90º).
2. Opposite sides of a rhombus are parallel (AD || BC).

Calculations:

Let the diagonals AC and BD intersect each other at point O.

⇒ ∠AOD = 90º (Diagonals are perpendicular)

Since AD || BC and AC is a transversal line:

⇒ ∠DAC = ∠ACB (Alternate interior angles)

Given that ∠ACB = 40º:

⇒ ∠DAC = 40º

Now, in triangle AOD, the sum of all interior angles is 180º:

⇒ ∠ADB + ∠DAC + ∠AOD = 180º

⇒ ∠ADB + 40º + 90º = 180º

⇒ ∠ADB + 130º = 180º

⇒ ∠ADB = 180º − 130º

⇒ ∠ADB = 50º

∴ The correct answer is 50º.

Additional Information

Properties of Rhombus Diagonals

The diagonals of a rhombus bisect each other at right angles (90º) and also bisect the internal angles of the vertices they connect.

Area of a Rhombus

The area of a rhombus can be calculated using the lengths of its diagonals: Area = (1 ÷ 2) × d₁ × d₂, where d₁ and d₂ are the diagonals.

Relation between Sides and Diagonals

The sum of the squares of the diagonals is equal to four times the square of any side: d₁² + d₂² = 4 × a², where a is the side length.

Given:

Mean of the first r odd natural numbers = $r^2\over16$

Formula used:

Mean of the first r odd natural numbers = Sum of the first r odd natural numbers / r

Sum of the first r odd natural numbers = r²

Calculation:

Mean of the first r odd natural numbers:

⇒ r²/r = r

Given:

⇒ r = r²/16

Multiplying both sides by 16:

⇒ 16r = r²

⇒ r² - 16r = 0

⇒ r(r - 16) = 0

⇒ r = 16 (since r cannot be 0)

∴ The value of r is 16.

The correct answer is Brazil

Key Points

• Brazil is the only country that has participated in every FIFA Football World Cup since its inception in 1930.
• The FIFA World Cup is an international football competition contested by the men's national teams of the member associations of FIFA.
• Brazil is known for its rich football history and has won the World Cup a record five times.
• The country has produced many legendary football players, including Pelé, Zico, Romário, Ronaldo, and Neymar.

Additional Information

• The first FIFA World Cup was held in 1930 in Uruguay, and it is held every four years.
• Brazil won its first World Cup in 1958, followed by victories in 1962, 1970, 1994, and 2002.
• The World Cup is one of the most widely viewed and followed sporting events in the world, with an estimated 3.5 billion people tuning in to watch the 2018 tournament.
• The tournament format involves a qualification phase, which takes place over the preceding three years, to determine which teams qualify for the tournament phase.
• The current format of the tournament involves 32 teams competing for the title at venues within the host nation(s) over a period of about a month.

Given,

Statement:

Most of the people like old songs.

Conclusions:

I. Old songs are less costly as compared to new songs - False (Because the statement does not provide any information regarding the cost of old songs compared to new songs).

II. Old songs touch listener's feelings better compared to new songs - True (Because the statement mentions that most people like old songs, which can imply that old songs resonate more with listeners' emotions).

So, Only conclusion II follows.

Hence, the correct answer is "Option 3".

Given:

We have to find the difference between the biggest and the smallest fraction among $\dfrac{2}{3}$, $\dfrac{3}{4}$, $\dfrac{4}{5}$ and $\dfrac{5}{6}$

Calculation:

The denominator of all fractions are 3, 4, 5 and 6

LCM of 3, 4, 5 and 6 is 60

Now equation all denominators with 60 get,

$2 \over 3$ → ${2 \times 20} \over {3 \times 20}$ = $40 \over 60$

$3 \over 4$ → ${3 \times 15} \over {4 \times 15}$ = $45 \over 60$

$4 \over 5$ → ${4 \times 12} \over {5 \times 12}$ = $48 \over 60$

$5 \over 6$ → ${5 \times 10} \over {6 \times 10}$ = $50 \over 60$

Now, 50 > 48 > 45 > 40

⇒ 50/60 > 48/60 > 45/60 > 40/60

⇒ 5/6 > 4/5 > 3/4 > 2/3

The biggest number is 5/6 and the smallest number is 2/3

The difference between the biggest and smallest number is (5/6) - (2/3) = 1/6

The correct answer is Sulphur

Key Points

• Sulphur is a non-metallic mineral, distinguishing it from metals like iron, silver, and platinum.
• Non-metallic minerals are those minerals that do not contain metal elements in their inorganic chemical formula.
• They are typically used in a variety of industries including construction, agriculture, and chemical manufacturing.
• Sulphur is commonly used in the production of fertilizers, chemicals, and in the vulcanization of rubber.

Additional Information

• Iron, Silver, and Platinum are all metallic minerals, characterized by their ability to conduct electricity, heat, and their malleability.
• Metallic minerals are essential for various industrial applications including construction, electronics, and transportation.
• Non-metallic minerals, like sulphur, are typically more abundant and less expensive compared to metallic minerals.
• The distinction between metallic and non-metallic minerals is crucial for their respective applications and industries.

The correct answer is GPS Aided Geo Augmented Navigation

Key Points

• GAGAN stands for GPS Aided Geo Augmented Navigation.
• It is a satellite-based augmentation system (SBAS) developed by the Indian Space Research Organisation (ISRO) and the Airports Authority of India (AAI).
• The primary objective of GAGAN is to provide accurate and reliable navigation services over the Indian airspace, which is crucial for civil aviation.
• GAGAN improves the accuracy, integrity, and availability of GPS signals to meet the stringent requirements for civil aviation and other applications.
• It is the first SBAS system in the world to serve the equatorial region.

Additional Information

• GAGAN is interoperable with other international SBAS systems such as the US Wide Area Augmentation System (WAAS), European Geostationary Navigation Overlay Service (EGNOS), and Japan's Multi-functional Satellite Augmentation System (MSAS).
• The system enhances the accuracy of GPS to within 1.5 meters, compared to the 20-meter accuracy provided by unaugmented GPS.
• GAGAN is also intended to support a range of other applications including surveying, marine navigation, and disaster management.
• The system covers the entire Indian Flight Information Region (FIR) and extends beyond into neighboring regions.

The correct answer is Bhopal

Key Points

• Indore has been awarded the cleanest city in India for the third consecutive time from 2017 to 2019.
• Indore is located in the state of Madhya Pradesh.
• The capital of Madhya Pradesh is Bhopal.
• Bhopal is known for its historical significance and beautiful lakes, earning it the nickname "City of Lakes".

Additional Information

• Swachh Survekshan is an annual survey of cleanliness, hygiene, and sanitation in cities and towns across India.
• It was launched as part of the Swachh Bharat Abhiyan, a campaign by the Government of India to clean the streets, roads, and infrastructure of the country's cities and rural areas.
• Indore has consistently ranked at the top due to its effective waste management systems and public engagement in cleanliness initiatives.
• Madhya Pradesh, with its capital at Bhopal, has several other cities like Gwalior and Jabalpur that also participate actively in the Swachh Bharat Abhiyan.

The correct answer is Sabarmati

Key Points

• Sabarmati is one of the rivers that flows into the Arabian Sea.
• The Sabarmati River originates in the Aravalli Range of the Udaipur District of Rajasthan and flows through the state of Gujarat before emptying into the Arabian Sea.
• Other major rivers that flow into the Arabian Sea include the Narmada and the Tapi.
• The Arabian Sea is part of the northern Indian Ocean and is situated between the Indian subcontinent and the Arabian Peninsula.

Additional Information

• The Godavari is the second-longest river in India but it flows into the Bay of Bengal.
• The Luni is an endorheic river, meaning it does not flow into any sea or ocean but ends in the Rann of Kutch.
• The Krishna River is one of the longest rivers in India, flowing into the Bay of Bengal.
• Rivers play a crucial role in the geography, economy, and culture of the regions they flow through, providing water for irrigation, drinking, and industrial purposes.

Given:

Sum of five consecutive multiples of 2 = 660

Formula Used:

Sum of an arithmetic sequence = n/2 × (first term + last term)

Calculation:

Let the five consecutive multiples of 2 be 2n, 2(n+1), 2(n+2), 2(n+3), and 2(n+4).

Sum = 2n + 2(n+1) + 2(n+2) + 2(n+3) + 2(n+4)

Sum = 2n + 2n + 2 + 2n + 4 + 2n + 6 + 2n + 8

Sum = 10n + 20

Given Sum = 660

⇒ 10n + 20 = 660

⇒ 10n = 660 - 20

⇒ 10n = 640

⇒ n = 64

The five consecutive multiples of 2 are 2×64, 2×65, 2×66, 2×67, 2×68

⇒ 128, 130, 132, 134, 136

The largest number is 136.

The correct answer is option 1.

The correct answer is Afghanistan

Key Points

• Afghanistan became the 164^th member of the World Trade Organization (WTO) on 29 July 2016.
• The WTO is an international organization that regulates trade between nations with the aim of ensuring that trade flows as smoothly, predictably, and freely as possible.
• As a member, Afghanistan is expected to benefit from the global trading system which includes access to international markets and the ability to participate in the formulation of global trade rules.
• Afghanistan's accession to the WTO was seen as a significant step towards integrating the country into the global economy and promoting economic growth and development.

Additional Information

• The World Trade Organization (WTO) was established on 1 January 1995 and is the successor to the General Agreement on Tariffs and Trade (GATT).
• The WTO provides a framework for negotiating trade agreements and a dispute resolution process aimed at enforcing participants' adherence to WTO agreements.
• As of now, the WTO has 164 member countries and is headquartered in Geneva, Switzerland.
• Membership in the WTO is seen as a sign of a country's commitment to the principles of open trade and economic reform.

Given:

8 boys and 12 girls together can finish a project work in 5 days.

It takes 50 days for one boy alone to finish the same project.

Formula Used:

Work Rate of one boy = 1 / Days taken by one boy

Work Rate of one girl = 1 / Days taken by one girl

Combined Work Rate = Sum of individual work rates

Work Rate × Time = Total Work

Calculation:

Work Rate of one boy = 1 / 50

Let the number of days required for one girl alone to complete the project be x.

Work Rate of one girl = 1 / x

Combined Work Rate of 8 boys and 12 girls = 8 × (1/50) + 12 × (1/x)

Combined Work Rate of 8 boys and 12 girls = (8/50) + (12/x)

Total Work = 1 (since one complete project is considered as 1 unit of work)

Work Rate × Time = Total Work

[(8/50) + (12/x)] × 5 = 1

⇒ (8/50) + (12/x) = 1/5

⇒ 8/50 + 12/x = 1/5

⇒ 8x + 600 = 10x

⇒ 600 = 2x

⇒ x = 600 /2

⇒ x = 300

One girl alone can complete the project in  300 days.

Given:

The number leaves no remainder when divided by 5.

The number leaves a remainder of 1 when divided by 4.

The number leaves a remainder of 5 when divided by 6 or 7.

Formula Used:

Let the number be x .

From the given conditions:

$x \equiv 0 \pmod{5}$

$x \equiv 1 \pmod{4}$

$x \equiv 5 \pmod{6}$

$x \equiv 5 \pmod{7}$

Calculation:

Start by considering the smallest number that satisfies x $\equiv 0 \pmod{5}$ :

Let x = 5k .

Since $x \equiv 1 \pmod{4}$ :

$5k \equiv 1 \pmod{4}$

⇒ m

⇒ $k \equiv 1 \pmod{4}$

Let n .

Therefore, x = 5(4n + 1) = 20n + 5 .

Now, $x \equiv 5 \pmod{7}$.

So, $20n + 5 \equiv 5 \pmod{7}$ .

These are always true for all integers n .

We need to find the smallest n = 0 :

⇒ x = 20(0) + 5 = 5 (This does not satisfy all conditions)

Check for n = 1 :

⇒ x = 20(1) + 5 = 25 (This does not satisfy all conditions)

Check for n = 2 :

⇒ x = 20(2) + 5 = 45 (This does not satisfy all conditions)

Check for n = 3 :

⇒ x = 20(3) + 5 = 65 (This does not satisfy all conditions)

Continue this process until we find the correct x .

Check for n = 20 :

⇒ x = 20(20) + 5 = 405 (This does not satisfy all conditions)

Check for n = 21 :

⇒ x = 20(21) + 5 = 425 (This satisfies all conditions)

The least number is 425.

The correct answer is He or she must have qualified for elections as a member of the Rajya Sabha

Key Points

• According to the Constitution of India, the eligibility criteria for the appointment of a state Governor include:
• He or she must not hold any other office of profit.
• He or she must be a citizen of India.
• He or she must have completed 35 years of age.
• The criteria that is NOT required is that the individual must have qualified for elections as a member of the Rajya Sabha.

Additional Information

• The Constitution of India does not specify that a Governor must have qualified for elections as a member of the Rajya Sabha.
• The Governor is appointed by the President of India and holds office at the President's pleasure.
• The role of the Governor includes being the constitutional head of the state and acting on the advice of the state's Council of Ministers.
• The Governor also has certain discretionary powers that can be exercised in specific situations.

Given:

Final sale price of the laptop = ₹18,000

Initial discount = 25%

Additional discount = 20%

Formula Used:

Final Sale Price = Labelled Rate × (1 - Initial Discount) × (1 - Additional Discount)

Calculation:

Let the labelled rate be ₹L.

Initial Discount = 25% = 0.25

Additional Discount = 20% = 0.20

Final Sale Price = Labelled Rate × (1 - 0.25) × (1 - 0.20)

₹18,000 = ₹L × 0.75 × 0.80

₹18,000 = ₹L × 0.60

⇒ ₹L = ₹18,000 / 0.60

⇒ ₹L = ₹30,000

The labelled rate of the laptop was ₹30,000.

Given:

We need to find the least perfect square that is exactly divisible by each of 2, 5, 7, 8, and 10.

Formula Used:

To find the least perfect square divisible by given numbers, we need to find the Least Common Multiple (LCM) of those numbers and then make sure the result is a perfect square.

Calculation:

Prime factorization of the given numbers:

2 = 2¹

5 = 5¹

7 = 7¹

8 = 2³

10 = 2¹ × 5¹

LCM is found by taking the highest powers of all prime numbers:

LCM = 2³ × 5¹ × 7¹

LCM = 8 × 5 × 7

LCM = 280

To make 280 a perfect square, we need to balance the powers of all primes:

280 = 2³ × 5¹ × 7¹

We need even powers for a perfect square:

2³ needs one more 2 to become 2⁴

5¹ needs one more 5 to become 5²

7¹ needs one more 7 to become 7²

So, we multiply LCM by 2¹ × 5¹ × 7¹ = 70

⇒ Least perfect square = 280 × 70

⇒ Least perfect square = 19600

The least perfect square, which is exactly divisible by each of 2, 5, 7, 8, and 10 is 19600.

The correct answer is a condition in which the small intestines are unable to break down the sugars found in dairy products

Key Points

• Lactose intolerance is a condition where the small intestines cannot effectively break down lactose, the sugar found in dairy products.
• This occurs due to a deficiency of lactase, the enzyme responsible for digesting lactose.
• Symptoms of lactose intolerance include bloating, diarrhea, and abdominal pain after consuming dairy products.
• It is different from a milk allergy, which involves the immune system reacting to proteins in milk.
• Management of lactose intolerance often involves dietary adjustments, such as reducing or eliminating dairy intake or using lactose-free products.

Additional Information

• Lactase persistence is the continued activity of the lactase enzyme into adulthood, which is genetically determined and varies among populations.
• Populations with historically high dairy consumption, such as those in Northern Europe, have higher rates of lactase persistence.
• Non-dairy calcium sources include leafy green vegetables, fortified plant-based milks, and supplements.
• Some individuals with lactose intolerance can tolerate small amounts of dairy or certain dairy products like hard cheeses and yogurt.
• Consulting with a healthcare provider or a dietitian can help in managing lactose intolerance effectively.

The correct answer is IIT Delhi

Key Points

• The first India International Science Festival (IISF) was held in December 2015 at IIT Delhi.
• The IISF is a celebration to promote science and technology and demonstrate how science could lead India towards a developed nation.
• It aims to engage the public with science, celebrate the joy of science and show how science, technology, engineering, and mathematics (STEM) provide solutions to improve lives.
• The festival includes various events such as lectures, workshops, exhibitions, and competitions to foster scientific temper among people.

Additional Information

• The India International Science Festival is organized annually by the Ministry of Science and Technology and Earth Sciences in association with Vijnana Bharati (VIBHA).
• The festival aims to highlight India’s contributions in the field of science and technology over the years.
• It provides a platform for young scientists to showcase their work and interact with eminent scientists from across the globe.
• The IISF also aims to bridge the gap between science and society by bringing scientific advancements closer to the public.
• Each year, the festival is hosted in different cities across India to reach a wider audience.

The correct answer is Sunlight

Key Points

• Sunlight is considered an inexhaustible resource because it is abundant and continuously available.
• In contrast, resources like Petroleum and Natural Gas are exhaustible as they are finite and can be depleted.
• Forests, although renewable, can be exhausted if not managed sustainably.
• Inexhaustible resources are crucial for sustainable development and long-term energy solutions.

Additional Information

• Solar energy harnessed from sunlight is one of the cleanest and most sustainable forms of energy.
• It plays a significant role in reducing the dependency on fossil fuels and mitigating climate change.
• Technological advancements have made solar power more accessible and cost-effective.
• Investments in solar energy infrastructure continue to grow globally as part of green energy initiatives.

The correct answer is Kolkata

Key Points

• The Botanical Survey of India (BSI) is headquartered in Kolkata.
• BSI was founded on 13 February 1890, and it is an institution under the Ministry of Environment, Forest and Climate Change.
• The primary objectives of BSI are to explore plant resources of the country and to identify plant species with economic virtues.
• BSI also conducts research in taxonomy and provides a database of plants in India.
• The organization plays a crucial role in the conservation of plant diversity and the sustainable utilization of plant resources.

Additional Information

• The Botanical Survey of India has several regional centers across the country, including in Dehradun, Pune, Shillong, and Coimbatore.
• BSI publishes various research journals and books, such as the "Flora of India" series.
• The institution also collaborates with international botanical research organizations to enhance knowledge and conservation efforts.
• BSI's herbarium, the Central National Herbarium (CNH), is one of the largest herbaria in the world, housing over 2 million plant specimens.
• BSI is actively involved in the documentation and preservation of endangered plant species in India.

Given:

Lengths to measure: 220 cm, 260 cm, and 300 cm.

Formula Used:

Greatest possible length = HCF (Highest Common Factor) of the given lengths

Calculation:

Find the HCF of 220, 260, and 300.

Prime factorization of 220: 2² × 5 × 11

Prime factorization of 260: 2² × 5 × 13

Prime factorization of 300: 2² × 3 × 5²

Common factors: 2² and 5

HCF = 2² × 5

HCF = 4 × 5

HCF = 20

The greatest possible length which can be used to measure exactly the lengths 220 cm, 260 cm, and 300 cm is 20 cm.

The correct answer is 150^th

Key Points

• 2 October 2019 marks the 150^th birth anniversary of Mahatma Gandhi.
• Mahatma Gandhi, also known as the "Father of the Nation," was born on 2 October 1869.
• His birth anniversary is commemorated every year as Gandhi Jayanti, a national holiday in India.
• Gandhi's principles of non-violence and truth had a significant impact on India's independence movement and continue to inspire movements for civil rights and freedom across the world.

Additional Information

• In 2007, the United Nations General Assembly declared 2 October as the International Day of Non-Violence, acknowledging Gandhi's role in promoting peace and non-violence worldwide.
• Gandhi's philosophy and leadership played a crucial role in India's struggle for independence from British rule.
• He led nationwide campaigns for easing poverty, expanding women's rights, building religious and ethnic amity, ending untouchability, and achieving Swaraj or self-rule.
• His autobiography, "The Story of My Experiments with Truth," provides an insight into his life and principles.

The correct answer is Mozilla Firefox

Key Points

• Mozilla Firefox is an open-source web browser, which means it is not proprietary software.
• Proprietary software refers to software that is owned by an individual or a company and its source code is usually not available to the public.
• Examples of proprietary web browsers include Safari, Internet Explorer, and Opera.
• Mozilla Firefox is developed by the Mozilla Foundation, a non-profit organization, and its source code is freely available for anyone to view, modify, and distribute.
• This open-source nature of Mozilla Firefox allows for greater transparency and community involvement in its development.

Additional Information

• Safari is a web browser developed by Apple Inc. and is proprietary software.
• Internet Explorer is a web browser developed by Microsoft and is proprietary software.
• Opera is a web browser developed by Opera Software and is proprietary software.
• Open-source software like Mozilla Firefox often benefits from contributions and improvements from a global community of developers.

The correct answer is Astra

Key Points

• The Astra missile is the indigenously developed Beyond-Visual-Range Air-to-Air Missile (BVRAAM) by India.
• It was successfully test-fired by the Indian Air Force in September 2018.
• The Astra missile is designed to engage and destroy highly maneuvering supersonic aircraft.
• It is capable of engaging targets at varying ranges and altitudes.
• The successful test-firing of Astra showcases India’s prowess in developing advanced weaponry and strengthens the country’s defense capabilities.

Additional Information

• BrahMos is a medium-range ramjet supersonic cruise missile that can be launched from submarines, ships, aircraft, or land.
• Prahaar is a short-range ballistic missile developed for quick strikes against tactical targets.
• Dhanush is a variant of the surface-to-surface or ship-to-ship Prithvi missile.
• The development and successful testing of indigenous missiles like Astra are crucial for India's strategic and defense autonomy.

The correct answer is Pro-Active and Responsive facilitation by Interactive, Virtuous and Environmental single-window Hub

Key Points

• PARIVESH stands for Pro-Active and Responsive facilitation by Interactive, Virtuous and Environmental single-window Hub.
• It was launched in August 2018 as a single window integrated system for obtaining various environmental, forest, wildlife, and CRZ (Coastal Regulation Zone) clearances.
• The system aims to streamline the process of granting clearances to projects, ensuring efficiency and transparency.
• It integrates various stages of environmental clearance processes, making it easier for project proponents to track their applications.
• PARIVESH enhances the ease of doing business by providing a platform for single-window clearance.

Additional Information

• Environmental clearances are essential for ensuring that projects comply with environmental regulations and do not harm the ecosystem.
• The system is part of the government's efforts to promote ease of doing business and ensure sustainable development.
• PARIVESH is also integrated with the Geographic Information System (GIS) to provide spatial analysis and decision support.
• The initiative reflects the government's commitment to improving environmental governance and facilitating responsible project development.
• The system helps in reducing the time taken for granting clearances and enhances transparency and accountability.

Given:

$x^2 - 1$ is a factor of $ax^4 + bx^3 + cx^2 + dx + e$

Formula used:

If $x^2 - 1$ is a factor, then $x^2 - 1 = (x - 1)(x + 1)$

The polynomial should be divisible by both $x - 1$ and $x + 1$

Calculations:

Substituting $x = 1$ in $ax^4 + bx^3 + cx^2 + dx + e$:

⇒ $a(1)^4 + b(1)^3 + c(1)^2 + d(1) + e = a + b + c + d + e = 0$  .....................(1)

Substituting $x = -1$ in $ax^4 + bx^3 + cx^2 + dx + e$:

⇒ $a(-1)^4 + b(-1)^3 + c(-1)^2 + d(-1) + e = a - b + c - d + e = 0$ .............(2)

Adding both equations(1) &(2) :

⇒ $2(a + c + e) = 0 \Rightarrow a + c + e = 0$

Subtracting (2) equation from the (1):

⇒ $2(b + d) = 0 \Rightarrow b + d = 0$

∴ The possible relations is a + c + e = b + d.

Given:

Expression: $2\sin^2\theta + 3 \cos^2\theta$

Formula used:

We know that $\sin^2\theta + \cos^2\theta = 1$

Calculations:

Let $x = \sin^2\theta$. Then, $\cos^2\theta = 1 - x$.

Substituting in the given expression:

⇒ $2x + 3(1 - x) = 2x + 3 - 3x = 3 - x$

The expression is $3 - x$, where the maximum value of $x$ is 1 and the minimum value is 0.

For the minimum value of the expression, $x = 1$:

⇒ $3 - 1 = 2$

∴ The least value is 2.

The correct answer is Harshavardhana

Key Points

• Harshavardhana was the author of the literary work 'Ratnavali'.
• Harshavardhana, also known as Harsha, was an Indian emperor who ruled North India from 606 to 647 CE.
• He was a patron of arts and literature, and his court was adorned with scholars such as Banabhatta and Mayura.
• Harsha himself wrote three Sanskrit plays: 'Nagananda', 'Ratnavali', and 'Priyadarsika'.
• 'Ratnavali' is a significant work in the realm of classical Sanskrit literature and reflects Harsha's literary prowess.

Additional Information

• Harshavardhana was a ruler from the Vardhana dynasty and was known for his administrative capabilities and military conquests.
• He shifted his capital from Thanesar to Kannauj and ruled over a vast territory including parts of present-day Punjab, Haryana, Uttar Pradesh, and Bihar.
• Harsha's reign is often considered a period of peace and prosperity, and he is remembered for his contributions to culture and religion.
• He was a devotee of Buddhism and organized the Kanauj Assembly and the Prayag Assembly to discuss religious matters.
• His biography, 'Harshacharita', was written by the court poet Banabhatta and provides a detailed account of his life and times.

The correct answer is Clock Speed.

Key Points

• Clock Speed is the speed at which a microprocessor executes instructions.
• It is measured in Hertz (Hz), typically in megahertz (MHz) or gigahertz (GHz).
• Higher clock speed indicates a faster processor, capable of performing more operations per second.
• Clock speed is a critical factor in determining the overall performance of a microprocessor.

Additional Information

• Microprocessors use a clock signal to synchronize operations.
• Other factors such as the number of cores, cache size, and architecture also impact a processor's performance.
• Modern processors often use techniques like overclocking to increase clock speed beyond the base rate for enhanced performance.
• Clock speed alone does not determine overall system performance; it should be considered alongside other specifications.

The logic followed here is,

DOOR is written as FRSW,

Similarly, FAN can be written as,

Hence, the correct answer is "HDR".

Given:

Let the positive number be x.

According to the question,

x + 15 = 100 × (1/x)

Formula used:

x + 15 = 100/x

Calculations:

Multiply both sides by x to eliminate the denominator:

⇒ x² + 15x = 100

Rearrange the equation:

⇒ x² + 15x - 100 = 0

Use the quadratic formula: x = [-b ± √(b² - 4ac)] / 2a

Here, a = 1, b = 15, c = -100

⇒ x = [-15 ± √(15² - 4 × 1 × (-100))] / 2

⇒ x = [-15 ± √(225 + 400)] / 2

⇒ x = [-15 ± √625] / 2

⇒ x = [-15 ± 25] / 2

⇒ x = (25 - 15)/2 = 10/2 = 5 (positive solution)

∴ The positive number is 5.

The correct answer is India Brand Equity Foundation

Key Points

• India Brand Equity Foundation (IBEF) is an initiative by the Ministry of Commerce and Industry, Government of India.
• IBEF aims to promote and create international awareness of the "Made in India" label in markets overseas and to facilitate the dissemination of knowledge of Indian products and services.
• The 'India Lounge' at international trade fairs and events showcases India's strengths in various sectors.
• The foundation plays a crucial role in communicating India's growth story and leveraging its economic potential globally.

Additional Information

• The 'Make in India' initiative was launched by Prime Minister Narendra Modi in September 2014 to encourage national and multinational companies to manufacture their products in India.
• The initiative is aimed at transforming India into a global design and manufacturing hub.
• IBEF supports this initiative by promoting Indian brands and products across the world.
• The foundation works closely with stakeholders, including industry associations, export promotion councils, and Indian missions abroad.

Given Statement: Nowadays, Indian cricket team plays very well.

Now, 

Assumptions:

1. The teams of other countries are not interested towards cricket - Not Implicit (The statement only mentions the performance of the Indian cricket team and does not imply anything about the interest level of teams from other countries) 2. It is happening by chance - Not Implicit (The statement does not suggest that the Indian team's good performance is happening by chance. It simply states that they are playing well)

Here, Neither assumptions I nor II are implicit.

Hence, the correct answer is "Option 3".

The correct answer is opaque

Key Points

• Opaque objects are those that do not allow light to pass through them.
• When light encounters an opaque object, it is either absorbed or reflected, but not transmitted.
• This interaction of light with opaque objects results in the formation of shadows.
• Shadows are areas where light is blocked by the opaque object, creating a dark shape on a surface opposite the light source.

Additional Information

• Luminous objects are those that emit their own light, such as the sun or a light bulb.
• Transparent objects allow light to pass through them completely, like clear glass or clean water.
• Translucent objects allow some light to pass through but scatter it, such as frosted glass or thin paper.
• The study of light and shadows is a fundamental aspect of physics, specifically in the branch of optics.

Shortcut Trick

In a parallelogram, if the angle bisector of one angle meets the midpoint of the opposite side, the triangle formed is always isosceles.

Here, AP is the bisector of ∠A and P is the midpoint of BC.

Since AD || BC, the alternate interior angle ∠BPA = ∠DAP.

Thus, in ΔABP, ∠BAP = ∠BPA, making AB = BP.

Since BP = BC/2 = AD/2, we get AB = 10/2 = 5 cm.

Opposite sides are equal: CD = AB = 5 cm.

∴ The correct answer is 5 cm.

Alternate Method

Given: ABCD is a parallelogram, P is the midpoint of BC, ∠BAP = ∠DAP, and AD = 10 cm.

Formula Used: In a parallelogram, opposite sides are parallel and equal. Base angles of an isosceles triangle are equal.

⇒ In parallelogram ABCD, AD = BC = 10 cm (Opposite sides are equal).

⇒ P is the midpoint of BC, ∴ BP = PC = 10 ÷ 2 = 5 cm.

⇒ Since AD || BC and AP is a transversal, ∠DAP = ∠BPA (Alternate interior angles).

⇒ Given ∠BAP = ∠DAP, ∴ ∠BAP = ∠BPA.

⇒ In ΔABP, sides opposite to equal angles are equal, ∴ AB = BP.

⇒ AB = 5 cm.

⇒ In parallelogram ABCD, CD = AB (Opposite sides are equal).

⇒ CD = 5 cm.

∴ The correct answer is 5 cm.

Additional Information

Properties of a Parallelogram

Opposite sides are parallel and equal (AB = CD, BC = AD). Adjacent angles are supplementary (sum = 180°).

Alternate Interior Angles

When two parallel lines are cut by a transversal, the pairs of angles on opposite sides of the transversal and between the parallel lines are equal.

Isosceles Triangle Property

If two angles of a triangle are equal, the sides opposite to those angles are also equal (Converse of Isosceles Triangle Theorem).

The logic followed here is,

Hence, the correct answer is "S".

According to the given information,

1) Indiana makes the blue paint and the pink is for automobiles.

2) The green, which is not for interiors, is from Hartley.

3) The exterior paint is produced by Finesse.

Here, we can see that Finesse company manufactures the tan paint.

Hence, the correct answer is "Finesse".

The logic followed here is:

 

Knife, Fork, Spoon all are used for eating,

Whereas,

Pan is used for cooking.

Hence, the correct answer is "Pan".

The correct answer is State Private Sector Enterprises (SPSEs)

Key Points

• State Private Sector Enterprises (SPSEs) is not a classification of Public Sector Undertakings (PSUs).
• Public Sector Undertakings (PSUs) are government-owned corporations or state-owned enterprises created by the Government of India.
• The common classifications of PSUs include Public Sector Banks (PSBs), Central Public Sector Enterprises (CPSEs), and Public Sector Enterprises (PSEs).
• These classifications help in the management and operation of these entities, ensuring they serve the public interest effectively.

Additional Information

• Public Sector Banks (PSBs) are banks where the majority stake is held by the government.
• Central Public Sector Enterprises (CPSEs) are companies in which the direct holding of the Central Government or other CPSEs is 51% or more.
• Public Sector Enterprises (PSEs) refer to government-owned corporations that can be at both the central and state levels.
• The objective of PSUs is to accelerate economic growth and industrial development in the country.
• PSUs play a crucial role in the economic development of India by providing infrastructure, creating jobs, and contributing to the GDP.

The correct answer is 31.15%

Key Points

• According to the 2011 Census of India, approximately 31.15% of the Indian population resides in urban areas.
• The Census of India is conducted every ten years and provides vital statistics on the demographic profile of the country.
• Urban areas are defined by the Census as places with a minimum population of 5,000, at least 75% of the male working population engaged in non-agricultural activities, and a population density of at least 400 persons per square kilometer.
• The increase in urban population indicates the rapid urbanization and migration trends within the country.

Additional Information

• The Census of India is conducted by the Office of the Registrar General and Census Commissioner, India, under the Ministry of Home Affairs, Government of India.
• The first complete census of India was conducted in 1881, and since then, it has been conducted every decade.
• Data collected from the census is crucial for planning and implementation of various governmental policies, schemes, and programs aimed at the development of the country.
• The census provides comprehensive data on various parameters such as population size, distribution, density, growth rate, and various socio-economic indicators.
• Urbanization trends observed in the census data help in understanding the changing demographic patterns and the needs of urban infrastructure and services.

Given:

Find the two-digit number such that:

• The sum of its digits is 8.
• The digits of the number get reversed when 36 is added to it.

Formula Used:

Let the number be 10x + y, where x and y are its digits.

Given:

x + y = 8

10x + y + 36 = 10y + x

Calculation:

From the given conditions:

x + y = 8 ..........(1)

Now,

⇒  10x + y + 36 = 10y + x

⇒ 10x - x + 36 = 10y - y 

⇒ 9x + 36 = 9y 

⇒ 9(x - y) = 36 

⇒ x - y = 4 ...........(2)

From equation (1) and (2) we get :

x = 6 & y = 2 

Hence two digit number is 26.

Given :-

$0.5×0.5+0.09-0.15\over0.125+0.027$

Concept Used :- 

a³ + b³ = (a + b)(a² + b² - ab)

Calculation :-

$0.5\times0.5+0.09-0.15\over0.125+0.027$

⇒ $0.5\times0.5+0.3\times0.3-0.5\times0.3\over0.5^3+0.3^3$

⇒ $0.5^2+0.3^2-0.5\times0.3\over(0.5 + 0.3)(0.5^2+0.3^2-0.5\times0.3)$

⇒ 1/(0.5 + 0.3)

⇒ 1/0.8

⇒ 10/8 = 5/4

∴ The correct answer is option (4).

The correct answer is Nairobi, Kenya.

Key Points

• United Nations Environment Programme (UNEP)
• UNEP was established in 1972,
• Since 1972 it is dealing with critical environmental challenges.
• Its headquarters are located in Nairobi, Kenya.
• UNEP is one of the leading global voices on the environment.
• The United Nations Environment Programme (UNEP) is the global authority.
• It sets the environmental agenda and promotes the coherent implementation of the environmental dimension of sustainable development within the United Nations system.
• It serves as an authoritative advocate for the global environment.
• In March 2022, UNEP celebrated its 50^th anniversary.
• Reports published by UNEP
• Emission Gap Report
• Adaptation Gap Report
• Global Environment Outlook
• Frontiers

Additional Information

• World Environment Day
• It is held annually on 5 June since 1974
• It  was led by the United Nations Environment Programme (UNEP)
• World Environment Day is the largest global platform for environmental public outreach and is celebrated by millions of people across the world.

The correct answer is Green plants

Key Points

• Green plants are a biotic factor of an ecosystem.
• Biotic factors are living components of an ecosystem, which include plants, animals, and microorganisms.
• These factors interact with abiotic factors such as temperature, carbon dioxide, and atmospheric humidity to create a balanced ecosystem.
• Green plants play a crucial role in ecosystems by producing oxygen through photosynthesis and serving as a primary food source for herbivores.

Additional Information

• The United Nations Environment Programme (UNEP) was established in 1972 and has been addressing critical environmental challenges since then.
• UNEP's headquarters are located in Nairobi, Kenya.
• UNEP is a leading global voice on the environment and sets the environmental agenda within the United Nations system.
• In March 2022, UNEP celebrated its 50^th anniversary.

The correct answer is Udaipur

Key Points

• Udaipur is known as the 'Venice of the East'.
• The City Palace is located in Udaipur.
• Udaipur is famous for its lakes, palaces, and rich cultural heritage.
• The city is a popular tourist destination in the state of Rajasthan, India.
• It was founded by Maharana Udai Singh II in 1559.
• Udaipur is also known as the 'City of Lakes' due to its sophisticated lake system.

Additional Information

• The City Palace in Udaipur is a complex of palaces situated on the eastern banks of Lake Pichola.
• It was built over a period of nearly 400 years, with contributions from several rulers of the Mewar dynasty.
• The architecture of the City Palace is a fusion of Rajasthani and Mughal styles.
• Udaipur's Lake Palace, located on the Jag Niwas Island in Lake Pichola, is another iconic landmark of the city.
• The city hosts several cultural festivals, including the Mewar Festival, which showcases the region's cultural heritage.
• Udaipur is also an educational hub, with several universities and colleges offering a range of courses.

The logic followed here is:

Logic: The letters are coded with their positional values.

PEN is written as 16514,

Similarly, 'INK' can be written as,

Hence, the correct answer is "91411".

The correct answer is Arabic

Key Points

• Al-Biruni wrote his famous book 'Kitab-ul-Hind' in the Arabic language.
• Al-Biruni was a Persian scholar and polymath who made significant contributions to various fields such as astronomy, mathematics, and history.
• 'Kitab-ul-Hind' is an in-depth study of Indian culture, philosophy, science, and religion during the early 11^th century.
• The book provides a comprehensive account of Indian knowledge and practices, showcasing Al-Biruni's dedication to understanding and documenting different cultures.

Additional Information

• In addition to 'Kitab-ul-Hind', Al-Biruni wrote numerous other works on subjects ranging from astronomy to pharmacology.
• He traveled extensively and learned several languages, which helped him in his scholarly pursuits and in understanding various cultures.
• Al-Biruni's works are considered valuable resources for understanding the scientific and cultural history of the medieval Islamic world and beyond.

The correct answer is 100^th Constitutional Amendment Bill, 2015

Key Points

• The 100^th Constitutional Amendment Bill, 2015 facilitated the implementation of the India-Bangladesh Land Boundary Agreement (LBA).
• This amendment involved the exchange of enclaves and the demarcation of the boundary between India and Bangladesh, which had been pending since the agreement was signed in 1974.
• The amendment aimed to resolve long-standing border disputes and improve bilateral relations between the two countries.
• As part of the agreement, India and Bangladesh exchanged 162 enclaves, with 51 enclaves being transferred to Bangladesh and 111 to India.

Additional Information

• The Land Boundary Agreement was first signed in 1974 between the then Prime Minister of India, Indira Gandhi, and the Prime Minister of Bangladesh, Sheikh Mujibur Rahman.
• The agreement aimed to address the issue of enclaves and adverse possessions along the India-Bangladesh border.
• The 100^th Amendment Bill was passed by the Indian Parliament in May 2015 and received the President's assent in the same month.
• This historic agreement was seen as a significant step towards enhancing the diplomatic and strategic relationship between India and Bangladesh.

Given:

X > 1

X + 1/X = √29

Formula used:

(X + 1/X)² = X² + 2 + 1/X²

To find X - 1/X: (X + 1/X)² - 4 = (X - 1/X)²

Calculations:

(X + 1/X)² = (√29)²

⇒ X² + 2 + 1/X² = 29

⇒ (X - 1/X)² = 29 - 4 = 25

⇒ X - 1/X = √25 = 5

∴ The correct answer is 5.

The correct answer is 1995

Key Points

• The Gandhi Peace Prize awards were instituted in 1995.
• The awards recognize individuals and institutions for their contributions to social, economic, and political transformation through non-violence and other Gandhian methods.
• The prize is an annual award named after Mahatma Gandhi, the leader of the Indian independence movement and an advocate of non-violence.
• Recipients of the award include notable figures and organizations who have made significant contributions to peace and harmony.

Additional Information

• The Gandhi Peace Prize includes a monetary award, a citation, and a plaque.
• It is open to all persons regardless of nationality, race, language, caste, creed, or gender.
• The award aims to perpetuate Mahatma Gandhi’s legacy and inspire future generations to follow his path of peace and non-violence.
• Some of the notable recipients of the Gandhi Peace Prize include Nelson Mandela, Grameen Bank of Bangladesh, and Archbishop Desmond Tutu.

Given:

radius is $\frac{r}{4}$ and slant height is 4l 

Concept Used:

TSA of cone = π r(r + l)

Solution:

According to the question, 

⇒ π (r/4)(r/4 + 4l)

⇒ π r(l + r/16)

∴ The TSA of Cone is  π r(l + r/16)

Given:

45% of the students qualified.

Number of students not qualified = 79750.

Formula Used:

Total students appeared = Number of qualified students + Number of not qualified students

Number of qualified students = 45% of Total students appeared

Calculation:

Let the total number of students appeared be xxxxx

  .

Number of qualified students = 0.45x

Number of not qualified students = 79750

Therefore,

x - 0.45x = 79750

⇒ 0.55x = 79750

⇒ x = 79750 / 0.55

⇒ x = 145000

The total number of students who appeared for the examination is 145000.

The correct answer is Aloke Singh

Key Points

• Aloke Singh was appointed as the CEO of Air India Express in November 2020.
• He took over the position during a critical phase for the airline industry, which was heavily impacted by the COVID-19 pandemic.
• Aloke Singh has extensive experience in the aviation sector, having held various leadership roles in airlines and related businesses.
• His appointment is aimed at steering the low-cost carrier towards better operational efficiency and service quality.

Additional Information

• Air India Express is a wholly owned subsidiary of Air India, focusing on short-haul international flights, primarily to the Middle East and Southeast Asia.
• The airline was established in 2005 and operates a fleet of Boeing 737 aircraft.
• Air India Express is known for its low-cost structure while providing essential services to expatriates and tourists.
• In recent years, the airline has been expanding its network and enhancing its service offerings to compete more effectively in the low-cost carrier market.

According to the given information,

1) The Kerala player is not a bowler.

2) David is from Kerala.

3) Two of them are bowlers and two are batsmen.

4) One of the batsmen is a Maharashtrian but Vijay is neither.

5) Rashid is not from Punjab, but he is a bowler.

Here, we can see that David-Vijay is a batsmen-bowler pair.

Hence, the correct answer is "David-Vijay".

The least possible Venn diagram for the given statement is:

Conclusions:

A. No fly is a rhino - False (Because all rhinos are pigs and some flies are pigs. As no direct relation between rhino and fly is given so, it is possible but not definitely true.)

B. Some flies are rhinos - False (Because all rhinos are pigs and some flies are pigs. As no direct relation between rhino and fly is given so, it is possible but not definitely true.)

Both the conclusions are wrong but Conclusion A and B form a complementary pair.

So, "Either A or B" follows.

Hence, the correct answer is "Option 4".

Additional Information

Conditions of Either-or case: 

1. The elements should be same in both statements.
2. Individually both the conclusions should be false.
3. One conclusion should be positive and one conclusion should be negative (Complementary pair).

The two complementary pairs are:

1. All + Some not

2. No + Some

The correct answer is Due to limited oxygen the covered candle got extinguished after some time.

Key Points

• Oxygen is essential for combustion. When a lit candle is covered with a glass tumbler, the oxygen inside the tumbler is gradually consumed by the flame.
• As the oxygen level decreases, the flame's ability to sustain combustion diminishes.
• Eventually, the oxygen level drops below the required threshold to support the flame, causing the candle to extinguish.
• This process demonstrates the principle that a continuous supply of oxygen is necessary for maintaining combustion.

Additional Information

• Combustion is a chemical reaction that typically involves the rapid combination of a fuel with oxygen, producing heat and light.
• The flame of a candle is a result of the combustion of the wax, which is the fuel, in the presence of oxygen from the air.
• In an enclosed space, once the available oxygen is depleted, combustion cannot continue, leading to the extinguishment of the flame.
• This principle is also why fire safety protocols emphasize the importance of controlling oxygen availability to manage and extinguish fires.

The logic followed here is: Position value according to the English alphabetic series is written.

So,

• SHOES : 19815519

Similarly,

• SHIRT : ?

Hence, "Option - (3)" is the correct answer.

The correct answer is 3 Only.

Key PointsChronology of Historical Events:

• Humayun regains lost territories (C): This event occurred in 1555 when Humayun, the Mughal Emperor, regained the territories he had lost to Sher Shah Suri.
• Nadir Shah invades India and attacks Delhi (A): This event took place in 1739 when Nadir Shah of Persia invaded India and sacked Delhi.
• Ahmad Shah Abdali defeats the Marathas in the third battle of Panipat (D): This event occurred in 1761 when Ahmad Shah Abdali (also known as Ahmad Shah Durrani) defeated the Marathas in the third battle of Panipat.
• The Diwani of Bengal is transferred to the East India Company (B): This event happened in 1765 when the Mughal Emperor granted the East India Company the right to collect revenue in Bengal, Bihar, and Orissa.

Therefore, the correct chronological order is: C, A, D, B

Given:

sin 78° + cos 132°

Formula used:

Use the identity: cos(θ) = sin(90° - θ)

Calculation:

cos 132° = sin(90° - 132°) = sin(-42°)

sin(-42°) = -sin 42°

sin 78° + cos 132° = sin 78° - sin 42°

Using the identity: sin(A) - sin(B) = 2 cos[(A + B)/2] × sin[(A - B)/2]

⇒ sin 78° - sin 42° = 2 cos[(78° + 42°)/2] × sin[(78° - 42°)/2]

⇒ = 2 cos 60° × sin 18°

⇒ = 2 × (1/2) × sin 18°

⇒ = sin 18°

∴ The value of sin 78° + cos 132° is sin 18°.

Shortcut Trick

Gold parts in the ratio = 8

Total parts in the mixture = 8 + 12 = 20

Weight of 8 parts = 30 Kg

Weight of 1 part = 30 ÷ 8 = 3.75 Kg

Weight of 20 parts = 20 × 3.75 = 75 Kg

∴ The correct answer is 75 Kg.

Alternate Method

Given:

Ratio of Gold and Silver in the mixture = 8 : 12

Quantity of Gold consumed = 30 Kg

Gold: 8 parts

Silver: 12 parts

30 Kg

Total Mixture = 20 parts = ?

Calculation:

⇒ Let the quantity of Gold and Silver in the mixture be 8x and 12x respectively.

⇒ According to the given data, 8x = 30 Kg

⇒ x = 30 ÷ 8 = 3.75 Kg

⇒ Total weight of the mixture = Quantity of Gold + Quantity of Silver

⇒ Total weight = 8x + 12x = 20x

⇒ Total weight = 20 × 3.75

⇒ Total weight = 75 Kg

∴ The correct answer is 75 Kg.

Additional Information

Ratio Definition

A ratio is the comparison of two homogeneous quantities. If quantities A and B are in the ratio x:y, then their actual values can be represented as kx and ky respectively.

Mixture Concepts

When elements are mixed in a specific ratio, the total weight or volume of the mixture is always the sum of the individual parts forming the whole mixture.

Unitary Method

In proportional relationships, determining the equivalent value of a single unit allows you to multiply and easily calculate the value for any larger group of units.

Given:

Series: $\frac{1}{5 \times 6} + \frac{1}{6 \times 7} + \frac{1}{7 \times 8} + \ldots$

Number of terms (n) = 20

Formula used:

The general term of the series is $\frac{1}{r(r+1)}$

It can be simplified as:

$\frac{1}{r(r+1)} = \frac{1}{r} - \frac{1}{r+1}$

Calculations:

The sum of the first 20 terms:

$\sum_{r=5}^{24} \left(\frac{1}{r} - \frac{1}{r+1}\right)$

⇒ $\left(\frac{1}{5} - \frac{1}{6}\right) + \left(\frac{1}{6} - \frac{1}{7}\right) + \ldots + \left(\frac{1}{24} - \frac{1}{25}\right)$

All intermediate terms cancel out:

⇒ $\frac{1}{5} - \frac{1}{25}$

⇒ $\frac{5 - 1}{5 \times 25} = \frac{4}{25} = 0.16$

∴ The sum of the first 20 terms is 0.16.

Shortcut Trick

Suresh's 1 day work = 1/10 and Ramesh's 1 day work = 1/12.

Combined 1 day work = 1/10 + 1/12 = 11/60.

Work done together in 4 days = 4 × (11/60) = 44/60 = 11/15.

Remaining work = 1 − 11/15 = 4/15.

∴ The correct answer is 4/15.

Alternate Method

Given:

Time taken by Suresh to finish the job = 10 days

Time taken by Ramesh to finish the job = 12 days

Days they worked together = 4 days

Calculations:

We take Total Work as the LCM of 10 and 12.

⇒ Total efficiency of Suresh and Ramesh = 6 + 5 = 11 units/day

⇒ Work completed in 4 days = 11 × 4 = 44 units

⇒ Remaining work = Total Work − Work Completed

⇒ Remaining work = 60 − 44 = 16 units

⇒ Fraction of work remaining = 16 ÷ 60 = 4/15

∴ The correct answer is 4/15.

Additional Information

Combined Work Formula

If person A can do a piece of work in x days and person B can do it in y days, their combined 1 day work is (1/x + 1/y) and total time taken together is (x × y) / (x + y) days.

Work and Wages

Total wages are always distributed in proportion to the total work done by each person. If the time worked is identical for all, wages are distributed directly in the ratio of their efficiencies.

Alternate Days Work

If two individuals work on alternate days, find the collective work done in a cycle of 2 days. Then multiply the cycle to get close to the total work and add the remaining sequence days manually.

Given:

Speed from hostel to college = 4 Km/h

Speed from college to hostel = 3 Km/h

Total time taken = 7 h

Formula used:

Total time = $\dfrac{Distance}{Speed1} + \dfrac{Distance}{Speed2}$

Calculations:

Let the distance between hostel and college be D.

⇒ $\dfrac{D}{4} + \dfrac{D}{3} = 7$

⇒ $\dfrac{3D + 4D}{12} = 7$

⇒ $\dfrac{7D}{12} = 7$

⇒ D = 12 Km

∴ The distance between the college and hostel is 12 Km.

The logic followed here is:

 

Bus, Airplane, TV all require a specific person (Driver, Pilot, Remote) to operate them,

Whereas,

Mechanic repairs the Car.

Hence, the correct answer is "Option 1".

The logic followed here is: Position value according to the English alphabetic series is written.

So,

​

Hence, "N" is the correct answer.

Given:

√(80) + 4√5

2√5 + √(125) = 7X

Formula Used:

Simplify both sides and solve for X.

Calculation:

First, simplify the given expressions:

√(80) = √(16×5) = √16 × √5 = 4√5

So, √(80) + 4√5 = 4√5 + 4√5 = 8√5

Now, simplify the second equation:

√(125) = √(25×5) = √25 × √5 = 5√5

So, 2√5 + √(125) = 2√5 + 5√5 = 7√5

We have:

7√5 = 7X

⇒ X = √5

Now, substitute X in the simplified form of √(80) + 4√5:

8√5 = 8X

The correct answer is option 2**.**

Shortcut Trick

SI for (7 − 5) = 2 years = ₹9,200 − ₹7,500 = ₹1,700.

SI for 1 year = 1700 ÷ 2 = ₹850.

Principal (P) = Amount after 5 years − SI for 5 years = 7500 − (850 × 5) = ₹3,250.

Rate % = (SI for 1 year ÷ P) × 100 = (850 ÷ 3250) × 100.

Rate % = 340 ÷ 13 ≈ 26.15% ≈ 26.2%.

∴ The correct answer is 26.2%.

Alternate Method

0 Years 5 Years 7 Years

P = ?

₹7,500

₹9,200

SI for 5 yrs

SI = ₹1,700 Timeline of Amount Growth

Given:

Amount after 5 years (A₅) = ₹7,500

Amount after 7 years (A₇) = ₹9,200

Formula Used:

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

Amount (A) = P + SI

Calculations:

⇒ SI for 2 years = A₇ − A₅ = 9200 − 7500 = ₹1,700

⇒ SI for 1 year = 1700 ÷ 2 = ₹850

⇒ SI for 5 years = 850 × 5 = ₹4,250

⇒ Principal (P) = A₅ − SI for 5 years = 7500 − 4250 = ₹3,250

⇒ Rate of Interest (R) = (SI for 1 year × 100) ÷ P

⇒ R = (850 × 100) ÷ 3250

⇒ R = 85000 ÷ 3250 = 8500 ÷ 325 = 340 ÷ 13

⇒ R ≈ 26.1538% ≈ 26.2%

∴ The correct answer is 26.2%.

Additional Information

Simple Interest Amount Formula

The total amount after T years at rate R is given by A = P[1 + (R × T) ÷ 100].

Difference Between CI and SI

For 2 years, the difference between Compound Interest and Simple Interest on the same principal is D = P(R ÷ 100)².

Principal from Direct Amount Formula

If Amount A is known for time T and rate R, the Principal P = (100 × A) ÷ (100 + R × T).

The correct answer is rotation of the earth

Key Points

• The movement responsible for the drifting of the continents was caused by the polar-fleeing force and tidal force.
• The polar-fleeing force is related to the rotation of the earth.
• The rotation of the earth generates centrifugal force, which is referred to as the polar-fleeing force.
• This force acts outward from the axis of rotation, contributing to the movement of the continental plates.

Additional Information

• The concept of continental drift was first proposed by Alfred Wegener in 1912.
• Continental drift theory was later supported by the theory of plate tectonics, which explains the movement of Earth's lithospheric plates.
• Other forces involved in plate tectonics include mantle convection, slab pull, and ridge push.
• The Earth's rotation also affects ocean currents and atmospheric circulation, further influencing geological and climatic processes.

The correct answer is Pawan Kumar Chamling

Key Points

• Pawan Kumar Chamling has been the longest-serving chief minister of an Indian state.
• He served as the Chief Minister of Sikkim from December 12, 1994, to May 27, 2019.
• His tenure lasted for more than 24 years, making him the longest-serving chief minister in the history of India.
• Chamling is the founder of the Sikkim Democratic Front (SDF) political party.
• Under his leadership, Sikkim saw significant progress in various sectors, including education, healthcare, and tourism.

Additional Information

• Mulayam Singh Yadav served as the Chief Minister of Uttar Pradesh for three non-consecutive terms but did not surpass Chamling's tenure.
• Narendra Modi served as the Chief Minister of Gujarat from 2001 to 2014 before becoming the Prime Minister of India.
• Shivraj Singh Chouhan has served multiple terms as the Chief Minister of Madhya Pradesh but his cumulative tenure is less than that of Chamling.
• Other chief ministers have had long tenures, but none have exceeded Chamling's record.

The correct answer is compiler

Key Points

• A high level source program must be translated first into a form that the machine can understand.
• This translation is done using a software called the compiler.
• The compiler converts the entire program into machine code before execution.
• It performs syntax analysis, semantic analysis, and optimizations during the translation process.

Additional Information

• An assembler is used to convert assembly language code into machine code.
• A debugger is used to test and debug programs by allowing the programmer to step through the code and inspect variables.
• A controller is a generic term and is not specifically related to the translation of high-level source code.