RRB NTPC CBT-I Official Paper (Held On: 23 Jan 2021 Shift 2) (Previous Year Paper)

The correct answer is 400 km.

Key Points

• The International Space Station (ISS) orbits Earth at an average altitude of approximately 400 km.
• The ISS travels at a speed of about 28,000 km/h, completing roughly 15.5 orbits per day.
• The ISS serves as a microgravity and space environment research laboratory in which scientific research is conducted in astrobiology, astronomy, meteorology, physics, and other fields.
• The ISS is a joint project of five participating space agencies: NASA (United States), Roscosmos (Russia), JAXA (Japan), ESA (Europe), and CSA (Canada).

Additional Information

The correct answer is DRDO.

Key Points

• SAMYUKTA is an electronic warfare program developed by India.
• This program was developed jointly by the Defence Research and Development Organisation (DRDO) and the Indian Army.
• The system is designed to provide comprehensive electronic support to the Indian Army in various operational scenarios.
• DRDO is a premier research and development organization under the Ministry of Defence, India.
• The program enhances the capability of the Indian Army to carry out electronic warfare operations effectively.

Additional Information

Given:

$\frac{(3\frac{1}{4})^4 -(4\frac{1}{3})^4 }{(3\frac{1}{4})^2 - (4\frac{1}{3})^2}$

Formula Used:

a² - b² = (a - b)(a + b)

Calculation:

$\sqrt{\frac{(3\frac{1}{4})^4 -(4\frac{1}{3})^4 }{(3\frac{1}{4})^2 - (4\frac{1}{3})^2}}$

⇒ $\sqrt{\frac{[(3\frac{1}{4})^2 -(4\frac{1}{3})^2][(3\frac{1}{4})^2+(4\frac{1}{3})^2] }{(3\frac{1}{4})^2 - (4\frac{1}{3})^2}}$

⇒ $\sqrt{[(3\frac{1}{4})^2+(4\frac{1}{3})^2] }$

⇒ $\sqrt{[(\frac{13}{4})^2+(\frac{13}{3})^2] }$ 

⇒ $\sqrt{[(\frac{169}{16})+(\frac{169}{9})] }$

⇒ $\sqrt{169[(\frac{1}{16})+(\frac{1}{9})] }$

⇒ $\sqrt{169[(\frac{9 + 16}{144})] }$

⇒ $\sqrt{169[(\frac{25}{144})] }$

⇒ $13 \times \frac{5}{12}$

⇒ $\frac{65}{12}$

⇒ 5$\frac{5}{12}$

∴ Square root of $\frac{(3\frac{1}{4})^4 -(4\frac{1}{3})^4 }{(3\frac{1}{4})^2 - (4\frac{1}{3})^2}$ is 5$\frac{5}{12}$.

The correct answer is 7.

Key Points

• UN's 'World Cities Report 2016' provides a comprehensive overview of urbanization trends across the world.
• According to the report, India is expected to have 7 megacities by 2030.
• A megacity is defined as a city with a population of more than 10 million people.
• This trend indicates significant urban growth and development in India.
• Current megacities in India include Mumbai, Delhi, and Kolkata, among others.

Additional Information

The UN's 'World Cities Report 2016' is a detailed examination of the state of urbanization globally, offering insights into demographic, social, economic, and environmental trends. It highlights the challenges and opportunities associated with rapid urban growth, particularly in developing countries.

The correct answer is Damodar.

Key Points

• Damodar Valley Corporation (DVC) was the first major multipurpose river valley project undertaken by the Government of India after independence.
• The project was initiated in 1948 and aimed at flood control, irrigation, and power generation.
• The Damodar River, often referred to as the "Sorrow of Bengal" due to its frequent floods, was chosen for this significant project.
• The first dam constructed under this project was the Tilaiya Dam, which became operational in 1953.

Additional Information

Given:

$\frac{225^{0.2} \times 225^{0.3}}{225^{0.6} \times 225^{0.4}}$

Formula Used:

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$(a^m \times a^n = a^{m+n})$

Calculation:

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⇒ $(\frac{225^{0.2} \times 225^{0.3}}{225^{0.6} \times 225^{0.4}})$

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⇒  $(\frac{225^{0.2+0.3}}{225^{0.6+0.4}})$

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⇒  $(\frac{225^{0.5}}{225^{1}})$

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⇒  $(\frac{1}{225^{0.5}})$

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⇒ 1/15

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Therefore, the correct answer is option 4.

Shortcut Trick

Directly substitute the standard trigonometric values:

sin 30° = 1/2, cos 60° = 1/2, and sin 180° = 0.

Expression: 2(1/2) + 5(1/2) + 3(0)

⇒ 1 + 2.5 + 0 = 3.5 = 7/2.

∴ The correct answer is 7/2.

Alternate Method

Given: 2sin30° + 5cos60° + 3sin180°

Using the trigonometric ratios for standard angles:

⇒ Value of sin 30° = 1/2

⇒ Value of cos 60° = 1/2

⇒ Value of sin 180° = 0

Now, substitute these values into the given expression:

⇒ 2 × (1/2) + 5 × (1/2) + 3 × 0

⇒ 1 + 5/2 + 0

⇒ (2 + 5) / 2

⇒ 7/2

Thus, the final evaluated result is 7/2, which matches Option 4.

∴ The correct answer is 7/2.

Additional Information

Complementary Angles Property

For any angle θ, sin θ = cos(90° − θ). This is why sin 30° = cos 60° = 1/2.

Values of sin(nπ)

The sine of any integer multiple of 180° (π radians) is always zero. ∴ sin 0° = sin 180° = sin 360° = 0.

Standard Trigonometric Table

Always remember the basic values: sin 45° = 1/√2, cos 30° = √3/2, and tan 45° = 1 for quick calculations.

The correct answer is Secondary storage.

Key Points

• Hard disks are classified as secondary storage devices because they are not directly accessed by the CPU.
• They provide non-volatile storage, meaning data is retained even when the computer is turned off.
• Hard disks are used to store large amounts of data, programs, and files that are not currently in use by the system.
• They offer a higher storage capacity compared to primary storage like RAM.
• Data on a hard disk is accessed via an interface like SATA or SSD.

Additional Information

Secondary storage refers to devices that store data persistently and are not directly accessed by the CPU. Examples include hard disks, SSDs, and external storage devices.

Given:

6 h : 3 days

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Formula Used:

1 day = 24 h

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Calculation:

⇒ 6 h : 3 days

⇒ 6 h : 3 × 24 h

⇒ 6 h : 72 h

⇒ 6 : 72

⇒ 1 : 12

∴ Option 1 is the correct answer.

The correct answer is Sri Lanka.

Key Points

• "Sri Lanka" faced coordinated bombings on Easter Sunday, April 21, 2019. - The attacks targeted three "churches", four "hotels", and a "housing complex". - Over "250 people" were killed and more than "500 injured" in the bombings. - The attacks were carried out by "Islamist extremist" groups, including the local group "National Thowheeth Jama'ath (NTJ)". - The incident raised global concerns about "terrorism" and "security" in "South Asia".

Additional Information

The logic followed here is:

The next term in the given series will be:

Hence, 'QU' is the correct answer.

The correct answer is Eight times.

Key Points

• India has been elected to the UN Security Council as a non-permanent member eight times as of 1st January 2021.
• The most recent term started in 2021 and will end in 2022.
• India's previous terms were in 1950-51, 1967-68, 1972-73, 1977-78, 1984-85, 1991-92, and 2011-12.
• The UN Security Council consists of 15 members, including 5 permanent members and 10 non-permanent members.

Additional Information

The correct answer is Pakistan.

Key Points

• Chashma-III is one of the nuclear power plants located in Pakistan.
• It is situated near the town of Chashma, in the Punjab province.
• The plant is operated by the Pakistan Atomic Energy Commission (PAEC).
• Chashma-III started its commercial operation in 2016.

Additional Information

Given:

Central angle for Mathematics = 180°

Score in Statistics = 80

Score in Economics = 70

Formula Used:

Total angle of pie chart = 360°

Percentage of total score = (Central angle of subject / Total angle) × 100

Calculation:

Total score = Score in Mathematics + 80 (Statistics) + 70 (Economics)

Percentage of Mathematics = (180° / 360°) × 100% = 50%

Percentage of remaining subjects = 100% - 50% = 50%

Score in Statistics and Economics together = 80 + 70 = 150

Since the remaining 50% (Statistics + Economics) represents 150 marks

⇒ 100% represents = 150 × 2 = 300 marks

Score in Mathematics:

Total marks = 300

Marks in Statistics and Economics = 150

⇒ Marks in Mathematics = 300 - 150 = 150

Therefore, his score in Mathematics is 150.

Given:

The surface area of a cube = 1014 m²

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Formula Used:

Surface area of a cube = 6 × (side)²

Calculation:

Surface area of a cube = 6 × (side)²

⇒ 1014 = 6 × (side)²

⇒ side² = 1014/6

⇒ side = √(1014/6)

⇒ side = 13 m

Volume of a cube = (side)³

⇒ Volume = (13 m)³

⇒ Volume = 2197 m³

∴ Option 4 is the correct answer.

The correct answer is administrative divisions in the Gupta period.

Key Points

• Bhukti, Bhoga, Visaya, Vithi, and Mandal were administrative divisions in the Gupta period.
• These divisions helped in the efficient administration of the vast Gupta Empire.
• Bhukti was equivalent to a province, while Visaya referred to a district.
• Vithi and Mandal were smaller subdivisions within a district.
• The Gupta rulers implemented a well-structured administrative system to maintain control over their territories.

Additional Information

The correct answer is Rectifier.

Key Points

• A rectifier is an electrical device that converts alternating current (AC) to direct current (DC).
• It works by allowing current to flow only in one direction.
• Rectifiers are used in power supplies for electronic devices.
• They are essential in converting the AC power from the mains supply to the DC power required by most electronic circuits.

Additional Information

Given:

Ratio of incomes of Barun and Anil = 12 : 13

Ratio of expenditures of Barun and Anil = 10 : 13

Savings of Barun = Rs. 2,100

Savings of Anil = Rs. 1,300

Formula Used:

Income = Expenditure + Savings

Calculation:

Let Barun's income = 12x and Anil's income = 13x.

Let Barun's expenditure = 10y and Anil's expenditure = 13y.

Since savings = income - expenditure,

Barun's savings = 12x - 10y = 2,100 ... (1)

Anil's savings = 13x - 13y = 1,300 ... (2)

From equation (1), ⇒ 12x - 10y = 2,100

From equation (2), ⇒ 13x - 13y = 1,300

Multiplying equation (2) by 10 and equation (1) by 13 to make the coefficients of y equal:

⇒ 130x - 130y = 13,000

⇒ 156x - 130y = 27,300

⇒ 26x = 14,300 ⇒ x = 14,300 / 26 ⇒ x = 550

Now, substituting the value of x in equation (1) or (2), ⇒ 12x = 12 × 550 = 6,600 ⇒ 13x = 13 × 550 = 7,150

Therefore, Barun's income is Rs. 6,600 and Anil's income is Rs. 7,150.

The least possible Venn diagram is as follows:

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Conclusions:

1. Some students know English language. → True (as most students know English language)
2. Some students do not know English language. → True (as most students know English language, it means all students do not know English language and there are some students who do not know English language)

Thus, both conclusion follows.

Hence, the correct answer is "Both conclusions 1 and 2 follows.".

The correct answer is Loktak Lake, Manipur.

Key Points

• Loktak Lake is the largest freshwater lake in northeastern India, located in Manipur.
• The lake is known for its unique circular floating swamps, called phumdis.
• The floating elementary school was inaugurated to provide education to children living in the lake's vicinity.
• It aims to address the educational needs of children from the local fishing community.
• The school is part of an initiative to promote sustainable living and education in remote areas.

Additional Information

Given:

$(\frac{3}{\sqrt{0.0009}} + \frac{4}{\sqrt{0.0016}})$

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Formula Used:

$(\sqrt{a^2} = a)$

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Calculation:

⇒ $(\frac{3}{\sqrt{0.0009}} + \frac{4}{\sqrt{0.0016}})$

⇒ $(\frac{3}{0.03} + \frac{4}{0.04})$

⇒ 100 + 100

⇒ 200

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Hence, the correct answer is 200.

Given:

Principal (P) = Rs. 12,000

Down payment = Rs. 2,000

Time (t) = 1 year

Rate (r) = 10% per year

Formula Used:

Simple Interest (SI) = (P × r × t) / 100

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Calculation:

Interest will be incurred on the amount = 12000 - 2000 = 10000

⇒ SI = (10,000 × 10 × 1) / 100

⇒ SI = 1,000

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Total amount paid = Principal + SI

⇒ Total amount = 12,000 + 1,000

⇒ Total amount = Rs. 13,000.

∴ Option 2 is the correct answer.

Given:

A's efficiency = 0.4 × B's efficiency

C's efficiency = 0.5 × (A's efficiency + B's efficiency)

C alone completes the task in 30 days

Formula Used:

Efficiency = Work / Time

Calculation:

Let B's efficiency be 1 unit/day.

⇒ A's efficiency = 0.4 × B's efficiency = 0.4 units/day

Since C's efficiency = 0.5 × (A's efficiency + B's efficiency),

⇒ C's efficiency = 0.5 × (0.4 + 1) = 0.5 × 1.4 = 0.7 units/day

C completes the task in 30 days,

⇒ Work = C's efficiency × Time = 0.7 units/day × 30 days = 21 units

Combined efficiency of A, B, and C together = 0.4 units/day + 1 unit/day + 0.7 units/day = 2.1 units/day

Time taken by A, B, and C together to complete the task: = 21 units / 2.1 units/day = 10 days.

∴ Option 2 is the correct answer.

Given:

A does half of the work done by B in 3/4th of time 

Time taken by A and B to complete the work = 12 days 

Calculation:

Let the number of days taken by B to complete the work be x.

Then the number of days taken by A to complete half of the work = 3x/4.

Hence, we have the number of days taken by A to complete the work = 2 × (3x/4)= 3x/2.

The number of days taken by both A and B to complete the work =12.

Part of the work done by both in 1 day = 1/12

Part of the work done by A alone in 1 day =1/(3x/2) = 2/3x.

Part of work done by B alone in 1 day = 1/x.

⇒1/x + 2/3x = 1/12

⇒ (3+2)/3x = 1/12

⇒ 5/3x = 1/12

⇒ 3x = 5×12

⇒ x = 20

∴ B will take 20 days to do the work.

The correct answer is decreases.

Key Points

• Speed of sound is affected by the medium through which it travels.
• In a solid medium, particles are closely packed, allowing sound waves to travel faster.
• In a gaseous medium, particles are spread out, causing sound waves to travel slower.
• Thus, as sound passes from a solid to a gaseous medium, its speed decreases.

Additional Information

The correct answer is Burma.

Key Points

• Bahadur Shah Jafar was the last Mughal Emperor of India.
• He was a symbolic leader during the 1857 Revolt, which is also known as India's first war of independence.
• After the failure of the revolt, he was captured by the British forces.
• In 1858, he was exiled to Burma (present-day Myanmar), where he lived the remainder of his life.
• He died in exile in Rangoon (now Yangon) in 1862.

Additional Information

Additional Information

• 1857 Revolt: Also known as the Sepoy Mutiny, it was a major, but ultimately unsuccessful, uprising in India against the British East India Company's rule.
• Bahadur Shah Zafar: He was more of a symbolic figurehead during the revolt, as the actual fighting was led by Indian soldiers (sepoys) and local leaders.
• British Repression: The British brutally suppressed the revolt, leading to significant changes in their approach to ruling India.
• End of Mughal Rule: The exile of Bahadur Shah Zafar marked the official end of the Mughal Empire in India.

The logic followed here is :

In each figure 2 is placed in first square and the product of both the numbers in square is placed in circle.

In figure 1:

2 × 6 = 12;

In figure 2:

2 × 8 = 16

Similarly, in figure 3:

2 × 10 = 20

Hence, both the question marks will be replaced by 2 and 10 respectively from left to right.

The correct answer is Microsoft Office.

Key Points

• Microsoft Office is a software suite, not hardware.
• Hardware components are physical parts of a computer.
• Examples of hardware include the monitor, keyboard, and CPU.
• Software like Microsoft Office is used to perform tasks on a computer.

Additional Information

The correct answer is Setu-Bharatam Project.

Key Points

• Setu-Bharatam Project was launched in March 2016 by the Government of India.
• The aim of the project is to make all national highways free from railway level crossings.
• The project includes the construction of new bridges and the renovation of old ones on national highways.
• The initiative is expected to enhance road safety and reduce travel time across the country.

Additional Information

Given:

Adjacent sides of the parallelogram = 4a and 3a

Angle between two adjacent sides = 60°

Formula used:

Two adjacent sides and the respective diagonal makes a triangle and here, we have the length of two sides and the angle between them

Cosine Law:

a2 = b2 + c2 – 2bc cos α

Calculation:

By using cosine law, we get

⇒ d² = (4a)² + (3a)² - 2 × 4a × 3a × cos 60°

⇒ d² = 16a² + 9a² - 24a² × 1/2

⇒ d² = 25a² - 12a²

⇒ d² = 13a²

⇒ d = √(13a²)

⇒ d = a√13

∴ Option 3 is the correct answer.

The correct answer is real exchange rate.

Key Points

• The real exchange rate measures the value of a currency against another, adjusted for price levels.
• It reflects the purchasing power of one currency in terms of another.
• The real exchange rate can indicate whether a currency is overvalued or undervalued compared to another.
• This rate is crucial for evaluating the competitiveness of a country's goods and services.

Additional Information

The correct answer is Plasma.

Key Points

• Plasma is the liquid component of blood that holds the blood cells in suspension.
• It makes up about 55% of the body's total blood volume.
• Plasma is composed mostly of water (about 90%), along with proteins, glucose, electrolytes, hormones, and waste products.
• It serves as a medium for transporting nutrients, hormones, and proteins to the parts of the body that need them.

Additional Information

The correct answer is Rajasthan.

Key Points

• Ghoomar is a traditional folk dance of Rajasthan, known for its graceful movements and colorful attire.
• The dance is typically performed by women who wear flowing dresses called ghagras.
• Ghoomar is often performed during special occasions, such as weddings and festivals like Teej and Holi.
• The dance involves pirouetting and moving in a circular motion, symbolizing happiness and celebration.

Additional Information

Given

$\frac{289 \times 289 \times 289 + 111 \times 111 \times111}{289 \times 289 -289 \times 111 + 111 \times111}$

Formula Used

<br>

a³ + b³ = (a + b)(a² - ab + b²)

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Calculation

<br>

⇒ $\frac{289 \times 289 \times 289 + 111 \times 111 \times111}{289 \times 289 -289 \times 111 + 111 \times111}$

Using formula,

⇒ $\frac{(289 + 111)(289 \times 289 -289 \times 111 + 111 \times111)}{289 \times 289 -289 \times 111 + 111 \times111}$

⇒ 400

∴ Option 4 is the correct answer.

Given

A can complete a task in 8 days working 5 h a day

B can complete the same task in 10 days working 6 h a day

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Formula Used

Work done = Rate of work × Time taken

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Calculation:

Total hours A works to complete the task = 5 × 8 = 40 hours Total hours B works to complete the task = 6 × 10 = 60 hours

⇒ LCM of 40 and 60 = 120 hours 

Work done by A in 1 hour = 120 / 40 = 3 units/hour

Work done by B in 1 hour = 120 / 60 = 2 units/hour

Combined work done by A and B in 1 hour = 3 + 2 = 5 units/hour

If they work together 8 hours a day,

⇒ Total work done in 1 day = 5 units/hour × 8 hours = 40 units

⇒ Total work / Work done per day = 120 / 40 = 3 days

Therefore, working 8 hours a day, A and B can jointly complete the task in 3 days.

The correct answer is option 4.

The correct answer is Malik Muhammad Jayasi.

Key Points

• Malik Muhammad Jayasi wrote the epic poem "Padmavat" in 1540.
• The poem is a fictionalized account of the siege of Chittor by Alauddin Khilji in 1303.
• "Padmavat" is written in the Awadhi language and is considered a significant work in Indian literature.
• The poem blends elements of history, legend, and folklore, focusing on the beauty and valor of Queen Padmini.

Additional Information

The correct answer is Maharatna.

Key Points

• Bharat Heavy Electricals Limited (BHEL) is a Maharatna company. - The Maharatna status is granted to select public sector enterprises in India. - BHEL is a leading company in the energy-related and infrastructure sector in India. - The Government of India awards the Maharatna status based on certain criteria, including net worth and profitability. - BHEL has a significant presence in the power generation and transmission sectors.

Additional Information

Bharat Heavy Electricals Limited (BHEL) is one of the largest engineering and manufacturing companies in India. Established in 1964, it primarily operates in the power generation and transmission sectors, offering products and services for thermal, hydro, and nuclear power plants. BHEL also caters to industries such as transportation, renewable energy, and defense. The company has a significant presence both in India and globally, with a strong track record of delivering high-quality engineering solutions.

The logic followed here is:

Hence, '1R8' is the correct answer.

The correct answer is Vikram Kumar Doraiswami.

Key Points

• Vikram Kumar Doraiswami was appointed as the Indian Envoy to Bangladesh in October 2020.
• He succeeded Riva Ganguly Das in this position.
• Before this appointment, Doraiswami served as the Additional Secretary in the Ministry of External Affairs.
• He has also served as the Ambassador of India to South Korea.

Additional Information

The correct answer is Odometer.

Key Points

• The odometer is an instrument used in vehicles to measure the distance travelled by the vehicle.
• It is typically located on the vehicle's dashboard.
• Odometers can be mechanical, digital, or a combination of both.
• This device helps in tracking the vehicle's mileage, which is crucial for maintenance and resale purposes.

Additional Information

The correct answer is Bihar.

Key Points

• Bihar is the most thickly populated state in India as per the 2011 census.
• The population density of Bihar is approximately 1102 persons per square kilometer.
• This high density is due to a combination of factors including high birth rates and relatively small land area.
• Other states like Uttar Pradesh have large populations but lower population density compared to Bihar.

Additional Information

Calculation:

Sum of first 'n' natural numbers = n(n + 1)/2

∴ Option 4 is the correct answer.

The correct answer is 21 years.

Key Points

• Article 243V of the Constitution of India prescribes the minimum age requirement for becoming a member of a Municipality.
• The minimum age requirement is 21 years.
• This provision ensures that members have attained a certain level of maturity and responsibility.
• It aligns with the age requirement for other local bodies in India.
• The age criterion is part of broader eligibility criteria that may include residency and non-disqualification clauses.

Additional Information

The logic followed here is:

Let the initial number be x

Calculations of Atul:

x² - 15

Calculations of Pratul:

(x - 15)²  = x² - 30x + 225

As per the given problem:

x2 - 15 = x2 - 30x + 225

30x = 225 + 15

30 x = 240

x = 8

Hence, 8 was the initial answer.

The correct answer is grasslands.

Key Points

• Pampas are extensive lowlands in South America, primarily in Argentina, known for their fertile soil and grassland vegetation.
• Steppes are large areas of flat, unforested grassland, particularly in southeastern Europe and Siberia.
• Savannas are mixed grasslands and woodlands, commonly found in Africa, characterized by seasonal rainfall.
• Prairies are extensive flat areas of grassland in North America, particularly in the central United States and Canada.

Additional Information

Given:

tan θ = 5/12

Calculation:

tan θ = 5/12 = p/b

p = 5, b = 12

h = √{p² + b²} = √{5² + 12²} = √{25 + 144} = √169 = 13

So,

(cos θ + 5cot θ)/(cosec θ - cos θ)

⇒ (12/13 + 5 × 12/5) / (13/5 - 12/13)

⇒ (12/13 + 60/5) / (13/5 - 12/13)

⇒ [(60 + 780)/ 65] / [(169 - 60)/65]

⇒ 840 / 109

Therefore, the correct answer is option (4).

Given data:

The fraction after increasing the numerator and decreasing of the denominator is 5/6.

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The numerator is increased by 20%.

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The denominator is increased by 50%.

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Concept:

The percentages of increase applied to the numerator and denominator would be applied as follows: original value × 1 + (percentage/100)

Calculation:

Let the numerator be x and the denominator be y.

According to question,

⇒ (x × 120/100)/(y × 50/100) = 5/6

⇒ (x × 120)/(y × 50) = 5/6

⇒ x/y = 5/6 × 5/12

⇒ x/y = 25/72

∴ The correct answer is 25/72.

The correct answer is electricity to all households in India.

Key Points

• Saubhagya Yojana was launched by the Government of India in 2017.
• The main objective of the scheme is to provide electricity connections to all households in rural and urban areas.
• The scheme aims to achieve universal household electrification by ensuring last-mile connectivity and electricity connections to all remaining households.
• Under this scheme, free electricity connections are provided to Below Poverty Line (BPL) households.
• The scheme is also known as the Pradhan Mantri Sahaj Bijli Har Ghar Yojana.

Additional Information

Given:

Two natural numbers are in the ratio of 6 : 8 and their product is 768.

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Formula Used:

Let the numbers be 6x and 8x.

Then, (6x) × (8x) = 768

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Calculation:

⇒ 48x² = 768

⇒ x² = 768/48

⇒ x² = 16

⇒ x = √16

⇒ x = 4

⇒  6x = 6 × 4 = 24.

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Therefore, the smaller of the numbers is 24.

The logic followed here is:

The arrangement as per dictionary order will be as follows:

The letter D, I, and S are common in the all these words, so we will start from fourth letter.

i) Discrepancy

ii) Discriminate

iii) Discuss

iv) Disdain

v) Disease

Thus, 'Disdain' will come second last if they are arranged as per their order in an English dictionary.

Hence, the correct answer is "Disdain".

Shortcut Trick

Apply Alligation on speeds to find the Time Ratio.

Average speed = 40 km ÷ 7 hours = 40/7 km/h.

Alligation: (Cycling: 12.5) − (Avg: 40/7) vs (Avg: 40/7) − (Walking: 3).

Ratio of Time = (40/7 − 3) : (12.5 − 40/7) ⇒ (19/7) : (47.5/7) ⇒ 19 : 47.5 ⇒ 2 : 5.

Total time parts = 2 + 5 = 7 units. Since total time is 7 hours, 1 unit = 1 hour.

∴ The correct answer is 2 hours.

Alternate Method

Given: Cycling speed = 12.5 km/h, Walking speed = 3 km/h, Total distance = 40 km, Total time = 7 hours.

Formula Used: Distance = Speed × Time

Let the time spent cycling be t hours.

Then, time spent walking = (7 − t) hours.

⇒ Distance by Cycle + Distance by Walk = Total Distance

⇒ (12.5 × t) + [3 × (7 − t)] = 40

⇒ 12.5t + 21 − 3t = 40

⇒ 9.5t = 40 − 21

⇒ 9.5t = 19

⇒ t = 19 ÷ 9.5

⇒ t = 2 hours.

∴ The correct answer is 2 hours.

Additional Information

Alligation on Speed

When alligation is applied to speeds, the resulting ratio is always the ratio of the Time taken for each part of the journey.

Average Speed

Average Speed = Total Distance ÷ Total Time. In this case, 40 ÷ 7 ≈ 5.71 km/h.

Relative Speed

Used when two objects move. In same direction, subtract speeds (S₁ − S₂); in opposite directions, add speeds (S₁ + S₂).

Given:

Total candidates = 250

Candidates passed = 225

<br>

Formula Used:

Percentage = (Candidates passed × 100) / Total candidates

Calculation:

⇒ Percentage = (225 × 100) / 250

⇒ Percentage = 90%

∴ Option 4 is the correct answer.

The correct answer is 1000 km.

Key Points

• The Nirbhay missile is an Indian long-range, all-weather, subsonic cruise missile.
• It has a strike range of approximately 1000 km, making it capable of hitting targets at a considerable distance.
• Developed by the Defence Research and Development Organisation (DRDO) of India, it is designed to carry both conventional and nuclear warheads.
• The missile can be launched from multiple platforms, including land, sea, and air.
• It features a terrain-hugging capability to avoid detection and improve survivability.

Additional Information

The logic followed here is:

Hence, TG is the correct answer.

The correct answer is Zero.

Key Points

• The Simon Commission was a group of seven British Members of Parliament.
• It was established in 1927 to report on the political situation in India.
• The commission did not include any Indian members, which led to widespread protests.
• Indian leaders boycotted the commission because it did not represent Indian interests.

Additional Information

The logic followed here is:

In a column:

First number × second number × third number = fourth number.

Column 1:

2 × 3 × 4 = 6 × 4 = 24;

Column 2:

9 × 8 × 7 = 72 × 7 = 504;

Similarly,

Column 3:

5 × 1 × 6 = 30

Hence**,  '1'** can replace the question mark.

The correct answer is Kalamandalam Hemlatha.

Key Points

• Bandana Nepal set a Guinness World Record for the 'Longest Dancing Marathon by an Individual' in 2019.
• She danced continuously for 126 hours.
• She broke the previous record held by Kalamandalam Hemlatha.
• Kalamandalam Hemlatha had set the previous record by dancing for 123 hours and 15 minutes in 2011.

Additional Information

Bandana Nepal is a Nepalese dancer who gained international recognition for her endurance and passion for dance. Her record-breaking performance was a testament to her dedication and physical stamina. The event was widely covered by the media and brought significant attention to Nepalese culture and talent.

The correct answer is Mitochondria.

Key Points

• Mitochondria are known as the powerhouse of the cell because they generate most of the cell's supply of adenosine triphosphate (ATP), which is used as a source of chemical energy.
• They are involved in other tasks such as signaling, cellular differentiation, and cell death, as well as maintaining control of the cell cycle and cell growth.
• Mitochondria have their own DNA and are thought to have originated from ancient symbiotic bacteria.
• They are double-membrane-bound organelles, with the inner membrane being highly folded into structures known as cristae.

Additional Information

Given,

A person selling 50 mangoes for Rs. 30, incurs loss by = 10%

Formula:

CP = SP × 100/(100 – Loss%)

Calculation:

Selling price of 50 mangoes = 30

Selling price of 1 mango = 30/50

Cost price of 1 mango = 30/50 × 100/90 = RS. 2/3

Selling price of 1 mango, if he wants 20% profit = Rs. 2/3 × (120/100) = Rs. 4/5

The person sells in Rs. 4/5 = 1 mango

The person sells in Rs. 28 = 1 × 5/4 × 28 = 35 mango

∴ The person sells 35 mango.

The correct answer is Sardar Sarovar Project.

Key Points

• The Sardar Sarovar Project is one of the largest dam projects on the river Narmada.
• It aims to provide water for irrigation, drinking water supply, and hydroelectric power generation.
• The project is located in the state of Gujarat.
• It is a part of the larger Narmada Valley Development Project, which includes multiple dams and canals.

Additional Information

The correct answer is phone line.

Key Points

• Modem stands for Modulator-Demodulator.
• A modem converts digital data from a computer into analog signals that can be sent over a phone line.
• It also converts incoming analog signals back into digital data.20
• This is essential for internet connectivity over traditional phone lines.

Additional Information

Given:

(14 ÷ 7) × [8 + {3 + 8 - 2}] - (5 - 2)

Concept Used:

Calculation:

⇒ (14 ÷ 7) × [8 + {3 + 8 - 2}] - (5 - 2)

⇒ (2) × [8 + {11 - 2}] - (3)

⇒ (2) × [8 + 9] - (3)

⇒ (2) × 17 - (3)

⇒ 34 - (3)

⇒ 31

∴ Option 2 is the correct answer.

The correct answer is Uber.

Key Points

• Uber launched a helicopter service in New York in October 2019.
• The service is known as Uber Copter.
• Uber Copter offers flights between Manhattan and JFK Airport.
• The service aims to reduce travel time significantly compared to traditional road transport.

Additional Information

The logic followed here is:

• Goldsmith is a person who makes items out of gold.

Similarly, 

• Blacksmith is a person who makes items out of Iron.

Hence, Iron is the correct answer.

The relationship between Words, Letters and Sentence is as follows:

• All sentence have words.
• All words have letters.

The least possible Venn Diagram will be as follows:

Hence, figure 'A' is the correct answer.

Given:

a = 9, b = -5 and c = -4

FORMULA USED:

If a + b + c = 0, then

a3 + b3 + c³ = 3abc

CALCULATIONS:

a = 9, b = -5 and c = -4

⇒ a + b + c = 9 + (-5) + (-4) = 0

⇒ a3 + b3 + c3 = 3abc

⇒ 3 × 9 × (-5) × (-4)

⇒ 540

∴ Option 3 is the correct answer.

Given:

When x4 – px3 + 2x2 – 5x + 8 is divided by (x - 1), the remainder is (2p).

Formula Used:

Remainder Theorem: If a polynomial (f(x)) is divided by ((x-a)), then the remainder is (f(a)).

Calculation:

Using the Remainder Theorem with (x - 1), ⇒ (f(1) = 2p)

Substituting (x = 1) into the original polynomial:

⇒ (f(1) = 14 - p(1)3 + 2(1)2 - 5(1) + 8)

⇒ (1 - p + 2 - 5 + 8 = 2p)

⇒ (1 - p + 2 - 5 + 8 = 6 - p = 2p)

⇒ (6 = 3p)

⇒ (p = 2)

∴ Option 4 is the correct answer.

The correct answer is 1266-1287.

Key Points

• Ghiyas-ud-din Balban was one of the most powerful rulers of the Delhi Sultanate.
• He ruled from 1266 to 1287, following the death of Sultan Nasir-ud-din Mahmud.
• Balban is known for his strong centralized administration and military reforms.
• He implemented a policy of iron-fisted governance to consolidate his rule and suppress rebellions.

Additional Information

Given

Present age ratio of Sheo Kumar and Dileep Kumar = 9:10.

After 11 years, their age ratio will be = 10:11.

Formula Used

Present age = Ratio × Common multiple.

Future age = Present age + Years added.

Future age ratio = Future Age of Person 1 / Future Age of Person 2.

Calculation

Let the common multiple be x.

Thus, the present ages of Sheo Kumar and Dileep Kumar would be 9x and 10x respectively.

After 11 years:

Sheo Kumar's age = 9x + 11.

Dileep Kumar's age = 10x + 11.

The future ratio of their ages is 10:11, so:

⇒ $[ \frac{9x + 11}{10x + 11} = \frac{10}{11} ]$

⇒ [ 11(9x + 11) = 10(10x + 11) ]

⇒ [ 99x + 121 = 100x + 110 ]

⇒ [ 121 - 110 = 100x - 99x ]

⇒ [ 11 = x ]

Sheo Kumar's age = 9x = 9 × 11 = 99 years.

Dileep Kumar's age = 10x = 10 × 11 = 110 years.

Therefore, the present ages of Sheo Kumar and Dileep Kumar are 99 years and 110 years, respectively.

The correct answer is President.

Key Points

• The President of India is the constitutional head of the Executive of the Union of India.
• The President exercises his/her executive powers through officers subordinate to him as per the Constitution.
• The President is also the Supreme Commander of the Indian Armed Forces.
• The President is elected by an electoral college consisting of elected members of both houses of Parliament and the legislative assemblies of states and union territories.

Additional Information

The relationship between man, smokers, and cricketers is as follows:

i) Some man are smokers.

ii) Some man are cricketers.

iii) Some smokers are cricketers.

The least possible Venn Diagram is as follows:

Hence, figure 'C' is the correct answer.

Given:

$\frac{121}{0.121}$ = $\frac{12.1}{x}$

Calculation:

⇒ $\frac{121}{0.121}$ = $\frac{12.1}{x}$

⇒ $\frac{121 \times 1000}{121}$ = $\frac{121}{x \times 10}$

⇒ $x = \frac{121 \times 121}{121 \times 1000\times 10}$

⇒ $x = \frac{121 }{10000}$

⇒ x = 0.0121

∴ Option 2 is the correct answer.

Given

The roots of the equation (3x^2 + 5x - a = 0) are reciprocals of each other.

Formula Used

For the quadratic equation (ax^2 + bx + c = 0), sum of roots = (-\frac{b}{a}) and product of roots = (\frac{c}{a}).

If roots are reciprocals of each other, the product of roots = 1.

Calculation

Given equation: (3x² + 5x - a = 0)

Product of roots = ($\frac{-a}{3} = 1$)

⇒ (-a = 3)

⇒ (a = -3)

Therefore, the value of (a) is -3.

The correct answer is Tuberculosis.

Key Points

• Tuberculosis is caused by a bacterium called Mycobacterium tuberculosis.
• Unlike the other diseases listed, it is not caused by a virus.
• Tuberculosis primarily affects the lungs but can also affect other parts of the body.
• The other options (Influenza, Chicken Pox, Measles) are all viral diseases.

Additional Information