RRB NTPC CBT-I Official Paper (Held On: 16 Feb 2021 Shift 2) (Previous Year Paper)

Given:

Principal (P) = Rs. 4,500

Rate of intetrest (R) = 12% per annum

Time (T) = 2 years and 8 months

Formula Used:

Amount (A) = P (1 + R/100)^T

Calculation:

for the 1^st 2 years, rate = 12%

For the next 8 months:

12 months ⇒ rate = 12%

So, 8 months ⇒ rate = 12/12 × 8 = 8%

Now,

A = 4500 (1 + 12/100)² (1 + 8/100)

⇒ A = 4500 (1 + 3/25)² (1 + 2/25)

⇒ A = 4500 × (28/.25)² (27/25)

⇒ A = 4500 × 28/25 × 28/25 × 17/25

⇒ A = (180 × 28 × 28 × 27) / 625

⇒ A = 3810240 / 625 = 6096.38

Hence, the correct answer is option (2).

The logic followed here is:

Logic: Third number = Sum of first two numbers, Fourth number = Product of first two numbers

(8, 15, 23, 120) 

→ 23 = 8 + 15

→ 120 = 8 × 15

Let's check each option,

1) (9, 18, 27, 162)

→ 27 = 9 + 18

→ 162 = 9 × 18

2) (7, 14, 98, 21)

→ 98 ≠ 7 + 14

→ 21 ≠ 7 × 14 ⇒ Doesn't follow the logic.

3) (12, 5, 17, 60)

→ 17 = 12 + 5

→ 60 = 12 × 5

4) (11, 12, 23, 132)

→ 23 = 11 + 12

→ 132 = 11 × 12

Hence, the correct answer is "Option 2".

Given:

$\sqrt{12321} \times \sqrt{x} = 13431$

Formula used:

$\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$

Calculations:

First, find the square root of 12321:

⇒ $\sqrt{12321} = 111$

Now substitute:

⇒ $111 \times \sqrt{x} = 13431$

Divide both sides by 111:

⇒ $\sqrt{x} = \dfrac{13431}{111}$

⇒ $\sqrt{x} = 121$

Square both sides to solve for x:

⇒ $x = 121^2$

⇒ $x = 14641$

∴ The value of x is 14641.

The correct answer is Bauxite

Key Points

• Bauxite is the principal ore of aluminium.
• It is primarily composed of minerals such as gibbsite, boehmite, and diaspore.
• Bauxite is found in various regions around the world, including Australia, China, and Brazil.
• The extraction of aluminium from bauxite involves a process called the Bayer process.
• Bauxite is also used in the production of refractory materials, abrasives, and chemicals.

Additional Information

• Malachite is an ore of copper.
• Magnetite and Haematite are ores of iron.
• Aluminium is the most abundant metal in the Earth's crust and is widely used in various industries due to its properties such as low density, high strength, and resistance to corrosion.
• The discovery of bauxite dates back to 1821, when it was first identified in Les Baux, France.
• Recycling aluminium is energy-efficient and significantly reduces the environmental impact compared to extracting it from bauxite.

According to the given information,

1) A is on H4 and is not blue or brown.

2. B is green and is not running on H3 or H5.

3) C is blue and is not on H1.

4. D is running on H1 and is not orange or brown.

5) E is not running on H5 or H2.

Here, we can see that E is running on H3 highway.

Hence, the correct answer is "Option 1".

Given:

$x + \dfrac{1}{x} = 7$

Formula used:

$(x + \dfrac{1}{x})^2 = x^2 + \dfrac{1}{x^2} + 2$

$(x - \dfrac{1}{x})^2 = x^2 + \dfrac{1}{x^2} - 2$

Calculations:

Square the given equation:

⇒ $(x + \dfrac{1}{x})^2 = 7^2$

⇒ $(x^2 + \dfrac{1}{x^2} + 2) = 49$

⇒ $x^2 + \dfrac{1}{x^2} = 49 - 2 = 47$

Now use this to find $(x - \dfrac{1}{x})^2$:

⇒ $(x - \dfrac{1}{x})^2 = x^2 + \dfrac{1}{x^2} - 2$

⇒ $(x - \dfrac{1}{x})^2 = 47 - 2 = 45$

Take the square root:

⇒ $(x - \dfrac{1}{x}) = √{45}$

⇒ $(x - \dfrac{1}{x}) = 3√{5}$

∴ The value of $(x - \dfrac{1}{x})$ is 3√5.

Given:

Number of clips sold for 1 rupee = 16

Profit percentage = 25%

Formula Used:

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

Calculation:

Selling Price (SP) of 16 clips = 1 rupee

Profit Percentage = 25% = 25/100 = 1/4

Using the formula:

Cost Price (CP) of 16 clips ⇒ 1 rupee / (1 + 1/4)

⇒ CP of 16 clips = 1 / (5/4)

⇒ CP of 16 clips = 4/5 rupee

So, for 1 rupee, the number of clips = 16 × (5/4)

⇒ Number of clips = 20

The number of clips he bought for a rupee is 20.

Given:

Base of the right-angled triangle, b = 15 cm

Altitude of the right-angled triangle, a = 8 cm

Formula Used:

1. Hypotenuse, c = √(a² + b²)
2. Area of the triangle, Area = (1/2) × a × b
3. Altitude from the opposite vertex to the hypotenuse, h = $\frac{2 × \text{Area}}{c}$

Calculation:

First, find the hypotenuse:

⇒ c = √(8² + 15²)

⇒ c = √(64 + 225)

⇒ c = √(289)

⇒ c = 17 cm

Next, calculate the area of the triangle:

⇒ Area = (1/2) × 8 × 15

⇒ Area = (1/2) × 120

⇒ Area = 60 cm²

Finally, find the altitude from the opposite vertex to the hypotenuse:

⇒ h = $\frac{2 × 60}{17}$

⇒ h = $\frac{120}{17}$

⇒ h ≈ 7.06 cm

The altitude from the opposite vertex to its hypotenuse is approximately $7\frac{1}{17}$ cm.

Given:

The traffic lights change after every 35 s, 45 s, and 75 s respectively.

They all change simultaneously at 6:20:15 hours.

Formula Used:

Least Common Multiple (LCM) of the given times.

Calculation:

To find the time when the lights will change simultaneously again, we need to calculate the LCM of 35, 45, and 75.

Prime factorization:

35 = 5 × 7

45 = 3² × 5

75 = 3 × 5²

LCM = Highest power of all prime factors = 3² × 5² × 7

LCM = 9 × 25 × 7

LCM = 1575 seconds

Convert 1575 seconds to hours, minutes, and seconds:

1575 ÷ 3600 = 0 hours (remaining seconds: 1575)

1575 ÷ 60 = 26 minutes (remaining seconds: 15)

So, 1575 seconds = 0 hours 26 minutes 15 seconds

Add this to the initial time 6:20:15:

6:20:15 + 0:26:15

⇒ 6:46:30

The traffic lights will change again simultaneously at 6:46:30 hours.

The logic followed here is:

Logic: The numbers are the product of two prime numbers.

Let's check each option,

1. 143: This number is the product of two prime numbers, 11×13.

2) 105: This number can be factored as 3×5×7, it is not the product of only two prime numbers but three prime numbers, making it different from the others.

3. 21: This number is also the product of two prime numbers, 3×7.

4. 65: This number is the product of two prime numbers, 5×13.

Hence, the correct answer is "Option 2".

The least possible venn diagram is shown below,

Conclusions: 

1. Some horses are monkeys → False (No horse is a monkey implies that some horses can't be monkeys).
2. Some donkeys are not monkeys → True (All monkeys are donkeys, some donkeys are horses and no horse is a monkey implies that some of those donkeys which are horses are not monkeys).

Hence, the correct answer is "Option 1".

The correct answer is United Nations

Important Points

• The previous year's paper contained an error. We have corrected the options to reflect accurate information.

Key Points

• The United Nations is not a Bretton Woods Institution.
• The Bretton Woods Institutions include the International Monetary Fund (IMF) and the World Bank.
• These institutions were established in 1944 during the United Nations Monetary and Financial Conference held in Bretton Woods, New Hampshire, USA.
• The World Trade Organization (WTO) is also not a Bretton Woods Institution. It was established later in 1995.

Additional Information

• The International Monetary Fund (IMF) aims to foster global monetary cooperation, secure financial stability, facilitate international trade, promote high employment and sustainable economic growth, and reduce poverty around the world.
• The World Bank provides financial and technical assistance to developing countries for development programs (e.g., bridges, roads, schools, etc.) that are expected to improve the economic prospects and quality of life for people in those countries.
• The United Nations is an international organization founded in 1945. It is currently made up of 193 Member States and is committed to maintaining international peace and security, developing friendly relations among nations, achieving international cooperation, and being a center for harmonizing the actions of nations.
• The World Trade Organization (WTO) deals with the global rules of trade between nations. Its main function is to ensure that trade flows as smoothly, predictably, and freely as possible.

Given:

$\dfrac{3 + \sqrt{5}}{3 - \sqrt{5}} + \dfrac{3 - \sqrt{5}}{3 + \sqrt{5}} + \dfrac{\sqrt{5} - 1}{\sqrt{5} + 1}$

Formula used:

$\dfrac{a + b}{a - b} + \dfrac{a - b}{a + b} = 2 + \dfrac{4b^2}{a^2 - b^2}$

Rationalize the denominator for the third term:

$\dfrac{\sqrt{5} - 1}{\sqrt{5} + 1} \times \dfrac{\sqrt{5} - 1}{\sqrt{5} - 1} = \dfrac{(\sqrt{5} - 1)^2}{(\sqrt{5})^2 - 1^2}$

Calculations:

Solve the first two terms using the formula:

⇒ $\dfrac{3 + \sqrt{5}}{3 - \sqrt{5}} + \dfrac{3 - \sqrt{5}}{3 + \sqrt{5}} = 2 + \dfrac{4 \times 5}{9 - 5}$

⇒ $2 + \dfrac{20}{4} = 2 + 5 = 7$

Now simplify the third term:

⇒ $\dfrac{(\sqrt{5} - 1)^2}{5 - 1} = \dfrac{5 - 2\sqrt{5} + 1}{4} = \dfrac{6 - 2\sqrt{5}}{4} = \dfrac{3 - \sqrt{5}}{2}$

Combine the results:

⇒ $7 + \dfrac{3 - \sqrt{5}}{2}$

Express 7 as a fraction with a denominator of 2:

⇒ $\dfrac{14}{2} + \dfrac{3 - \sqrt{5}}{2}$

⇒ $\dfrac{14 + 3 - \sqrt{5}}{2} = \dfrac{17 - \sqrt{5}}{2}$

∴ The answer is $\frac{{17 - \sqrt 5 }}{2}$.

Given Statement: "From next month, everyone has to pay income tax no matter what your income is" - Government notice said.

Now, 

Assumptions:

1. Government Treasury fund is getting short - Not Implicit (The statement does not provide any information regarding the state of the Government Treasury fund.) 2. People of the country have become rich - Not Implicit (The statement does not provide any information about the wealth status of the people.)

Here, Neither assumption I nor II is implicit.

Hence, the correct answer is "Option 2".

The correct answer is yellow

Key Points

• The yellow oval spot in the human eye is known as the macula.
• The macula is responsible for the sharp, detailed central vision that we use for activities like reading and driving.
• It is located near the center of the retina and contains a high concentration of photoreceptor cells, specifically cones, which are crucial for color vision.
• The macula allows us to see fine details and perform tasks that require focused vision.

Additional Information

• The human eye functions by converting light into electrical signals that the brain can interpret as visual images.
• The retina, where the macula is located, is a light-sensitive layer at the back of the eye.
• Damage to the macula can lead to central vision loss, a condition known as macular degeneration.
• Regular eye exams are important for detecting early signs of macular degeneration and other eye conditions.

The correct answer is Rajasthan

Key Points

• Rajasthan was the first Indian state to implement the 'National Policy on Biofuels' approved by the government of India in May 2018.
• The policy aims to promote the use of biofuels in the country, reducing dependency on fossil fuels and ensuring a cleaner environment.
• Rajasthan's early adoption of this policy demonstrates its commitment to sustainable and eco-friendly energy sources.
• The state has taken several initiatives to encourage the production and use of biofuels, including incentives for farmers and industries.

Additional Information

• Biofuels are derived from renewable biological sources, such as plant materials and animal waste.
• The promotion of biofuels is part of India's broader strategy to enhance energy security, reduce greenhouse gas emissions, and support the rural economy.
• The National Policy on Biofuels classifies biofuels into three categories: Basic Biofuels (First Generation), Advanced Biofuels (Second Generation), and Bio-CNG (Third Generation).
• The policy also outlines the vision for setting up a National Biofuel Coordination Committee to provide policy guidance and support to stakeholders.
• Rajasthan's implementation of the biofuel policy includes the establishment of biofuel refineries and the promotion of biofuel crops like Jatropha.

Given:

$\frac{3 + 4 \div 2 \times 3}{4 + 3 \times 2 \div 3}$

Formula used:

Apply BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction) rule.

Calculations:

Simplify the numerator:

⇒ $3 + \frac{4}{2} \times 3 = 3 + 2 \times 3 = 3 + 6 = 9$

Simplify the denominator:

⇒ $4 + \frac{3 \times 2}{3} = 4 + \frac{6}{3} = 4 + 2 = 6$

Now, divide the simplified numerator by the denominator:

⇒ $\frac{9}{6} = \frac{3}{2}$

∴ The answer is $\frac{3}{2}$.

Given:

$\left( 1 + \frac{1}{3} \right)\left( 1 + \frac{1}{4} \right)\left( 1 + \frac{1}{5} \right)...\left( 1 + \frac{1}{{n - 1}} \right)$

Formula used:

Simplify each term:

$1 + \frac{1}{k} = \frac{k+1}{k}$

Thus, the expression becomes:

$\frac{4}{3} \times \frac{5}{4} \times \frac{6}{5} \times ... \times \frac{n}{n-1}$

Calculations:

The terms will cancel out sequentially:

⇒ $\frac{n}{3}$

∴ The value of the expression is $\left( {\frac{n}{3}} \right)$.

The correct answer is Hindustan Socialist Republican Association

Key Points

• Hindustan Socialist Republican Association (HSRA) was a revolutionary organization that aimed to overthrow British rule in India.
• Prominent freedom fighters such as Ram Prasad Bismil, Chandrashekhar Azad, and Bhagat Singh were associated with this organization.
• The HSRA was founded in 1928, following the reorganization of the Hindustan Republican Association (HRA).
• The organization was known for its radical approach, including armed struggle and acts of violence against British officials.
• It played a significant role in inspiring young Indians to join the freedom movement and fight for independence.

Additional Information

• The HSRA was initially formed as the Hindustan Republican Association (HRA) in 1924 by revolutionaries like Ram Prasad Bismil, Ashfaqulla Khan, and Sachindra Nath Sanyal.
• In 1928, the HRA was reorganized and renamed HSRA to emphasize its socialist orientation and commitment to achieving independence through revolutionary means.
• One of the most notable actions of HSRA was the Kakori Train Robbery in 1925, which aimed to fund their activities by stealing money from the British government.
• Bhagat Singh, a key member of the HSRA, is remembered for his role in the Lahore Conspiracy Case and his execution in 1931, which galvanized the Indian independence movement.
• The legacy of HSRA continues to inspire contemporary movements and the youth of India in their pursuit of justice and freedom.

The correct answer is Dr. Gagandeep Kang

Key Points

• Dr. Gagandeep Kang became the first Indian woman to be elected to the Fellow of the Royal Society (FRS) in April 2019.
• She is a renowned clinical scientist and a leading researcher in enteric infections, particularly in children.
• Her election to the FRS is a significant milestone for Indian science and highlights her contributions to public health.
• Dr. Kang has been instrumental in the development of the rotavirus vaccine, which is crucial for preventing severe diarrheal disease in children.

Additional Information

• The Fellow of the Royal Society (FRS) is one of the most prestigious scientific honors, recognizing individuals who have made substantial contributions to the improvement of natural knowledge.
• The Royal Society is a fellowship of many of the world's most eminent scientists and is the oldest scientific academy in continuous existence, founded in 1660.
• Dr. Kang's election to the FRS underscores the global impact of her research and her dedication to improving health outcomes in low-income settings.
• She has also played a significant role in mentoring young scientists and promoting scientific research in India.

The logic is here: 

Numerators: start 5 and add 5 each term → 5, 10, 15, 20, 25, 30, 35, 40

Denominators: start 1 and multiply by 2 each term → 1, 2, 4, 8, 16, 32, 64, 128

Hence, The missing number is 15/16.

The correct answer is Voter Verifiable Paper Audit Trail

Key Points

• VVPAT stands for Voter Verifiable Paper Audit Trail.
• It is a method of providing feedback to voters using a ballotless voting system.
• VVPAT is used in Indian elections to ensure that the citizen's vote has been correctly placed.
• The machine generates a paper slip with the name of the candidate for whom the vote was cast, allowing the voter to verify their vote.
• This paper slip is then deposited into a sealed box, which can be used later for cross-verification and auditing purposes.

Additional Information

• VVPAT was first used in a by-election in Nagaland in 2013 and later in the general elections in 2014.
• The introduction of VVPAT has added an extra layer of transparency and trust in the electoral process.
• The system is intended to detect possible election fraud or malfunction and provide a means to audit the stored electronic results.
• VVPAT slips are counted in a randomly selected polling station in each Assembly constituency to cross-check the electronic results.

The correct answer is Kathak

Key Points

• Kathak is one of the eight major forms of Indian classical dance.
• This dance form traces its origins to the nomadic bards of ancient northern India, known as Kathakars or storytellers.
• During the Mughal era, Kathak evolved to include intricate footwork, spins, and expressive gestures influenced by Persian and Mughal cultures.
• The dance is characterized by its intricate footwork and spins, which are performed to the accompaniment of classical Hindustani music.
• Kathak dancers traditionally wear elaborate costumes that are reflective of Mughal influences, including heavy jewelry and embroidered dresses.

Additional Information

• Mohiniyattam is a classical dance form from Kerala, known for its graceful movements and feminine style.
• Kathakali is another classical dance from Kerala, noted for its elaborate costumes and dramatic storytelling.
• Bharatanatyam is a classical dance from Tamil Nadu, characterized by its fixed upper torso, bent legs, and intricate footwork.
• While these other dance forms have their own unique histories and styles, it is Kathak that prominently reflects the influence of Mughal tradition.

Given:

Radius of the circumscribed circle = 7 cm.

Formula Used:

For an equilateral triangle, the radius (R) of the circumscribed circle is related to the side length (a) by the formula:

$R = \frac{a}{\sqrt{3}}$

Calculation:

Given radius R = 7 cm

Using the formula:

7 = $\frac{a}{\sqrt{3}}$

Solving for a:

⇒ a = 7 × $\sqrt{3}$

The length of the side of the equilateral triangle is 7 $\sqrt{3}$ cm.

Given:

Numbers: 6.7, 7.2, 8.7, 9.2, 10.1

Formula used:

Mean = (Sum of all numbers) / (Total number of observations)

Calculation:

Sum = 6.7 + 7.2 + 8.7 + 9.2 + 10.1 = 41.9

Number of observations = 5

Mean = 41.9 / 5 = 8.38

∴ The mean of the given data is 8.38.

The logic followed here is,

Hence, the correct answer is "Option 4".

Given :-

$\frac{1}{{1.4}} + \frac{1}{{4.7}} + \frac{1}{{7.10}} + ... + \frac{1}{{47.50}}.$

Calculation :-

$\frac{1}{{1.4}} + \frac{1}{{4.7}} + \frac{1}{{7.10}} + ... + \frac{1}{{47.50}}.$

we multiply by 3 both numerator and denominator

$\frac{1}{3}[\frac{3}{{1.4}} + \frac{3}{{4.7}} + \frac{3}{{7.10}} + ... + \frac{3}{{47.50}}.]$

Now,

1/3[1 - 1/4 + 1/4 - 1/7 + 1/7 - 1/10 + ....... + 1/47 - 1/50 ]

1/3[ 1 - 1/50 ]

1/3 × 49/50 = 49/150

Given :-

(m + n) : (m - n) = 7 : 3

Concept Use :-

Using componendo and dividendo

if a/b = c/d then

(a+b)/(a-b) = (c+d)/(c-d)

Calculation :-

(m + n) : (m - n) = 7 : 3

⇒ $\frac{m+n+m-n}{m-n-m+n} = \frac{7+3}{7-3}$

⇒ $\frac{m}{n} = \frac{10}{4}$

⇒ m/n = 5/2 

Now , cube of both side

⇒ m³/n³ = 5³/2³

⇒  m3/n³ = 125/8 

Now, 

 (m3 + n3) : (m3 - n3) = (125 + 8) : (125 - 8) = 133/117

(m3 + n3) : (m3 - n3) = 133/117

The correct answer is Acrobat Reader

Key Points

• Acrobat Reader is not a part of Microsoft Office suite.
• Microsoft Office includes applications such as Word, PowerPoint, Excel, and others primarily used for productivity tasks.
• Acrobat Reader is a product of Adobe Systems and is used for viewing, printing, and annotating PDF documents.
• Microsoft Office applications are designed to work seamlessly together, whereas Acrobat Reader is a standalone application for PDF files.

Additional Information

• Microsoft Word is a word processing application used for creating and editing documents.
• Microsoft PowerPoint is a presentation program used for creating slideshows.
• Microsoft Excel is a spreadsheet application used for data analysis and visualization.
• The Microsoft Office suite has been a leading productivity software package for decades.
• Adobe Acrobat Reader is frequently used in conjunction with office software but is not a component of the Microsoft Office suite.

The logic followed here is,

Hence, the correct answer is "Option 3".

The logic followed here is,

COCKROACH is written as CPENVRCDH,

SCOOTER is written as SDQRVFR,

Similarly,

MESMERIZE can be written as,

Hence, the correct answer is "Option 3".

The correct answer is Kalpakkam - Karnataka

Key Points

• Kakrapar is located in Gujarat.
• Kalpakkam is located in Tamil Nadu, not Karnataka.
• Kudankulam is located in Tamil Nadu.
• Kaiga is located in Karnataka.
• Therefore, the incorrect match is Kalpakkam - Karnataka.

Additional Information

• Kakrapar Atomic Power Station (KAPS) is situated in the state of Gujarat.
• Madras Atomic Power Station (MAPS), also known as Kalpakkam, is situated in Tamil Nadu.
• Kudankulam Nuclear Power Plant (KKNPP) is located in the Tirunelveli district of Tamil Nadu.
• Kaiga Generating Station (KGS) is situated near the river Kali in Karnataka.

The correct answer is Mumbai

Key Points

• The National Museum of Indian Cinema was inaugurated in January 2019 in Mumbai.
• The museum aims to showcase the history of Indian cinema and its impact on social and cultural evolution.
• It is located at the Films Division Complex on Peddar Road in South Mumbai.
• The museum features interactive displays, memorabilia, and digital installations that trace the journey of Indian cinema from its inception to the present day.
• The museum is divided into two buildings: the New Museum Building and the Gulshan Mahal, a 19^th-century heritage bungalow.

Additional Information

• The National Museum of Indian Cinema is a tribute to the rich legacy and vibrant history of Indian cinema.
• The museum provides an educational experience for visitors, including students, researchers, and cinema enthusiasts.
• The museum also hosts various film screenings, workshops, and seminars to promote the understanding and appreciation of Indian cinema.
• It serves as a significant cultural landmark and a tourist attraction in Mumbai.
• The museum was inaugurated by the Honorable Prime Minister of India, Narendra Modi, on January 19, 2019.

The correct answer is Goods and Services Tax(GST)

Key Points

• Goods and Services Tax (GST) is NOT an instrument of the monetary policy of the Reserve Bank of India (RBI).
• GST is a comprehensive indirect tax on the manufacture, sale, and consumption of goods and services throughout India.
• The primary objective of GST is to consolidate multiple indirect taxes into a single tax to simplify the taxation process and ensure a uniform tax rate across the country.
• On the other hand, the instruments of the monetary policy of the RBI include the Cash Reserve Ratio (CRR), Statutory Liquidity Ratio (SLR), and Bank Rate, which are used to control the money supply and interest rates in the economy.

Additional Information

• The Reserve Bank of India (RBI) is the central banking institution of India, which controls the monetary policy of the Indian rupee.
• The RBI was established on 1^st April 1935 and was nationalized on 1^st January 1949.
• The primary functions of the RBI include regulating the issue of banknotes, maintaining reserves to secure monetary stability, and operating the credit and currency system of the country to its advantage.
• Monetary policy involves the management of money supply and interest rates by the central bank to control inflation and stabilize the currency.
• Other tools of monetary policy include Open Market Operations (OMO) and the Marginal Standing Facility (MSF).

The correct answer is Igor Stimac

Key Points

• Igor Stimac is the current coach of the Indian men's football team as of December 2020.
• He was appointed as the head coach of the Indian national team in May 2019.
• Igor Stimac is a former Croatian footballer who has played for and managed several clubs and national teams.
• Under his coaching, the Indian football team has seen various improvements and strategic changes.

Additional Information

• Stephen Constantine was the previous coach of the Indian men's football team before Igor Stimac.
• The Indian football team, under Igor Stimac, aims to qualify for major international tournaments and improve its FIFA ranking.
• Igor Stimac has a rich history in football, having been part of the Croatian national team that finished third in the 1998 FIFA World Cup.
• He has also managed various clubs in Europe and Asia, bringing a wealth of experience to the Indian football team.

The correct answer is State Goods & Service Tax

Key Points

• State Goods & Service Tax (SGST) is a component of the Goods and Services Tax (GST) in India.
• SGST is levied by the state government on intra-state transactions of goods and services.
• It is one of the three components of GST, the other two being Central Goods & Service Tax (CGST) and Integrated Goods & Service Tax (IGST).
• The revenue collected from SGST is solely for the respective state government.
• SGST replaces multiple state taxes such as Value Added Tax (VAT), Central Sales Tax (CST), Purchase Tax, and others.

Additional Information

• The GST framework in India was implemented on 1^st July 2017.
• It aims to create a single, unified market by subsuming multiple indirect taxes previously levied by both central and state governments.
• GST is governed by a GST Council, which is chaired by the Union Finance Minister and includes the finance ministers of all the states.
• The introduction of GST is considered one of the most significant tax reforms in India.
• It enhances the ease of doing business and ensures a seamless flow of tax credit.

Given:

Mode = 7.52

Mean = 9.83

This is a moderately asymmetrical distribution.

Formula Used:

For a moderately asymmetrical distribution, the relationship between mean, median, and mode is given by:

$Mean - Mode \approx 3(Mean - Median)$

Calculation:

Substitute the given values into the formula:

$Mean - Mode = 3(Mean - Median)$

9.83 - 7.52 = 3(9.83 - Median)

2.31 = 3(9.83 - Median)

Divide both sides by 3:

2.31 / 3 = 9.83 - Median

0.77 = 9.83 - Median

Rearrange to solve for Median:

⇒ Median = 9.83 - 0.77

⇒ Median = 9.06

The median of the distribution is 9.06.

Given :-

5X1 + 6Y7 + 3Z3 = 1471

Concept use :-

sum of unit place digit is 11 and carry 1

x + y + z + 1 = 7  [ here , 1 is carry ]

x + y + z  = 6 

Now,

a/c to question highest value of x we take y = 0 & z = 0

x = 6

 Highest value of x : 6

Given Statement: If you don't follow traffic rules, you will be fined.

Now, 

Assumptions:

1. People may start following rules to avoid fine - Implicit (People are likely to follow traffic rules to avoid being fined as the statement suggests a consequence for not following the rules) 2. Traffic rules are for people's safety - Not Implicit (The statement does not explicitly mention that the traffic rules are for safety, it only mentions the consequence of not following them)

Here, Only assumption I is implicit.

Hence, the correct answer is "Option 4".

Given:

Speed of the bullet train is 35% more than that of the electric train.

Time taken by the electric train = 3 hours 45 minutes = 3.75 hours.

Formula Used:

Time = Distance / Speed

Calculation:

Let the speed of the electric train be S mph.

Speed of the bullet train = S + 0.35S = 1.35S mph.

Time taken by the electric train to cover the distance = 3.75 hours.

Distance covered by the electric train = S × 3.75 miles.

Time taken by the bullet train to cover the same distance:

Let the time taken by the bullet train be T hours.

Distance = Speed × Time

Distance = 1.35S × T

Since the distances are the same:

S × 3.75 = 1.35S × T

⇒ 3.75 = 1.35T

⇒ T = 3.75 / 1.35

⇒ T = 375 / 135

⇒ T = 25 / 9

⇒ T = 2 ⁷/₉ hours

The time taken by the bullet train to cover the same distance is $2\frac{7}{9}$ hours.

Given:

The interior angles of a pentagon are in the ratio 1 : 3 : 5 : 7 : 11.

Formula Used:

Sum of interior angles of a pentagon = (n - 2) × 180^º, where n is the number of sides.

Calculation:

For a pentagon, n = 5.

Sum of interior angles = (5 - 2) × 180^º

Sum of interior angles = 3 × 180^º

Sum of interior angles = 540^º

Let the angles be x, 3x, 5x, 7x, and 11x.

Sum of these angles = x + 3x + 5x + 7x + 11x

Sum of these angles = 27x

⇒ 27x = 540^º

⇒ x = 540^º / 27

⇒ x = 20^º

The measure of the smallest interior angle is 20^º.

Given :-

tan θ = $- \frac{{12}}{5}$

Formula used :-

tanθ = p/b

sinθ = p/h 

h = √ p²+b²

Calculation :-

tan θ = $- \frac{{12}}{5}$

p = -12

b = 5

h = √ (-12)² + (5)²

h = 13

Now,

sinθ = p/h = -12/13

The correct answer is State Bank of India

Key Points

• State Bank of India (SBI) is the largest commercial bank in India.
• SBI is a government-owned corporation with its headquarters in Mumbai, Maharashtra.
• It offers a wide range of banking products and services to its customers, including personal banking, corporate banking, and international banking.
• SBI has the largest branch network in India, with over 22,000 branches and 58,000 ATMs.
• It also has a significant international presence with branches in numerous countries around the world.

Additional Information

• SBI was established in 1955 after the nationalization of the Imperial Bank of India.
• It is one of the oldest banks in India, tracing its roots back to the Bank of Calcutta, which was established in 1806.
• SBI plays a crucial role in the Indian economy, providing financial services to millions of customers, including individuals, businesses, and government entities.
• The bank is also involved in various social and community development initiatives, contributing to the economic growth and development of the country.
• SBI has consistently been ranked among the top banks in India and has received numerous awards for its performance and customer service.

Given:

The sum of $3.\overline{26} - 2.\overline{14} + 1.\overline{33}$

Formula used:

Convert each repeating decimal to fractional form:

$3.\overline{26} = \frac{323}{99}$

$2.\overline{14} = \frac{212}{99}$

$1.\overline{33} = \frac{132}{99}$

Calculations:

Add the fractions:

⇒ $\frac{323}{99} - \frac{212}{99} + \frac{132}{99} = \frac{323 - 212 + 132}{99}$

⇒ $\frac{243}{99} = 2.\overline{45}$

∴ The sum is {\rm{2}}.\mathop {45}\limits^{___}

.

Preparing the family tree using the following symbols,

The family tree can be drawn as per the given information,

Here, we can see that O is the Son's son of W.

Hence, the correct answer is "Option 4".

The correct answer is All India Forward Bloc

Key Points

• All India Forward Bloc was the political party formed by Subhash Chandra Bose after he left the Indian National Congress.
• The party was established in 1939 with the aim to consolidate the political left and to bring about a radical change in the Indian freedom struggle.
• Subhash Chandra Bose, a prominent leader in the Indian independence movement, sought to unify the various leftist groups under one banner to fight against British colonial rule.
• The All India Forward Bloc played a significant role in the Indian independence movement, advocating for complete and immediate independence from British rule.

Additional Information

• Subhash Chandra Bose was known for his strong advocacy for armed struggle against the British Empire, differing from the non-violent approach of Mahatma Gandhi.
• He later formed the Indian National Army (INA) to fight against British forces during World War II with the support of Japan.
• The All India Forward Bloc continues to exist as a political party in India, advocating for socialist policies and preserving the legacy of Subhash Chandra Bose.

The correct answer is IIT, Kharagpur

Key Points

• IIT, Kharagpur was the first Indian Institute of Technology (IIT) to be established.
• It was established in 1951 and is located in Kharagpur, West Bengal.
• IIT Kharagpur was the first of the IITs to be established and is recognized as an Institute of National Importance.
• The establishment of IIT Kharagpur was based on the recommendations of the Sarkar Committee, which was formed to consider the establishment of higher technical institutions in India.
• Over the years, IIT Kharagpur has grown into one of the premier engineering institutions in India, offering a wide range of undergraduate, postgraduate, and doctoral programs.

Additional Information

• The Indian Institutes of Technology (IITs) are autonomous public technical and research universities located across India.
• They are governed by the Institutes of Technology Act, 1961, which has declared them as institutions of national importance.
• The IIT system has 23 institutes, and it is known for its high academic standards and significant contributions to technology and engineering education in India.
• The IITs are known for their rigorous selection process, which includes the Joint Entrance Examination (JEE) - one of the most challenging engineering entrance exams in the world.
• Graduates from IITs are highly sought after by employers worldwide, and many have gone on to achieve significant success in various fields.

The correct answer is Jawaharlal Nehru

Key Points

• Jawaharlal Nehru was one of the defense attorneys in the famous 'Sehgal-Dhillon-Shah Nawaz' trials.
• The trials involved officers of the Indian National Army (INA) who were charged with treason against the British Empire.
• Nehru, along with other prominent leaders, took a stand to defend the INA officers, showcasing his commitment to India's independence movement.
• The trials garnered significant public attention and were instrumental in galvanizing support for the INA and the broader struggle for independence.

Additional Information

• The Sehgal-Dhillon-Shah Nawaz trials are also known as the Red Fort Trials as they were held at the Red Fort in Delhi.
• The trials took place in 1945-46 and were a pivotal moment in the Indian freedom struggle.
• These trials highlighted the sacrifices of the INA soldiers and brought to light the atrocities committed by the British colonial authorities.
• The defense team also included renowned lawyers like Bhulabhai Desai and Tej Bahadur Sapru.
• The public outcry and nationalist sentiments generated by these trials contributed significantly to the eventual withdrawal of British rule from India.

Given:

The number reduced by 37% becomes 315.

Formula Used:

Original Number = Reduced Number / (1 - Reduction Percentage)

Required Increase Percentage = ((Target Number - Original Number) / Original Number) × 100

Calculation:

Let the original number be x .

Reduction Percentage = 37% = 0.37

Reduced Number = 315

Original Number:

⇒ x = 315 / (1 - 0.37)

⇒ x = 315 / 0.63

⇒ x = 500

Target Number = 800

Required Increase Percentage:

⇒ Increase = 800 - 500 = 300

⇒ Increase Percentage = 300 / 500 × 100

⇒ Increase Percentage = 60%

The number should be increased by 60% to become 800.

The correct answer is 'Statue of Unity' in India

Key Points

• The 'Statue of Unity' in India is the tallest statue in the world, standing at a height of 182 meters (597 feet).
• It is a statue of Indian statesman and independence activist Sardar Vallabhbhai Patel, who was the first Deputy Prime Minister and Home Minister of independent India.
• The statue is located on the Narmada River in the state of Gujarat, India.
• It was inaugurated on 31^st October 2018 by the Prime Minister of India, Narendra Modi, on the occasion of Patel's 143^rd birth anniversary.
• The project was designed by Indian sculptor Ram V. Sutar and the construction was completed by Larsen & Toubro, an Indian multinational conglomerate.

Additional Information

• The Spring Temple Buddha in China, which previously held the record, is the second tallest statue, standing at a height of 128 meters (420 feet).
• The Statue of Liberty in the USA is much shorter, with a height of 93 meters (305 feet) including its pedestal.
• The Great Buddha of Thailand stands at a height of 92 meters (302 feet) and is the tallest statue in Thailand.
• The Statue of Unity has become a major tourist attraction, drawing visitors from all over the world.
• The statue is part of a larger complex that includes a museum and an exhibition hall dedicated to Sardar Patel's life and contributions to India.

The correct answer is Himalaya

Key Points

• Maitri, Bharati, and Dakshin Gangotri are the three Indian research stations in Antarctica.
• Maitri was commissioned in 1989 and is located in Queen Maud Land.
• Bharati was commissioned in 2012 and is located in Larsmann Hill.
• Dakshin Gangotri was the first Indian research station in Antarctica, established in 1983, but now it is used only as a supply base.
• Himalaya is not an Indian research station in Antarctica; it is a mountain range in Asia.

Additional Information

• India's Antarctic program is managed by the National Centre for Polar and Ocean Research (NCPOR), under the Ministry of Earth Sciences.
• The objective of the Indian Antarctic program is to conduct scientific research and surveys in various disciplines such as geology, oceanography, and meteorology.
• India is a signatory to the Antarctic Treaty System, which regulates international relations with respect to Antarctica to ensure that it is used for peaceful purposes and scientific research.

Given:

The ratio of the areas of two triangles = 4 : 3

The ratio of their heights = 3 : 4

Formula Used:

Area of a triangle = 1/2 × base × height

Calculation:

Let the base and height of the first triangle be b1b1b1b1b1b1 and h1h1h1[Math Processing Error]h1h1 respectively, and the base and height of the second triangle be b2b2b2[Math Processing Error]b2b2 and h2h2h2[Math Processing Error]h2h2 respectively.

Given the ratio of the areas:

$\frac{Area_1}{Area_2} = \frac{4}{3}$

Also given the ratio of the heights:

$\frac{h_1}{h_2} = \frac{3}{4}$

Using the area formula for both triangles:

$\frac{1/2 × b_1 × h_1}{1/2 × b_2 × h_2} = \frac{4}{3}$

⇒ $\frac{b_1 × h_1}{b_2 × h_2} = \frac{4}{3}$

Substitute the given height ratio:

$\frac{b_1 × \frac{3}{4} h_2}{b_2 × h_2} = \frac{4}{3}$

⇒ $\frac{b_1 × 3}{4 b_2} = \frac{4}{3}$

⇒ $\frac{b_1}{b_2} = \frac{4 × 4}{3 × 3}$

⇒ $\frac{b_1}{b_2} = \frac{16}{9}$

The ratio of their bases is 16 : 9.

The logic followed here is,

HEART is written as USAFI,

CLEANER is written as SFOAFMD,

Similarly,

SHAMPOO can be written as,

Hence, the correct answer is "Option 1".

The correct answer is Kerala

Key Points

• The Sabarimala Sri Ayyappa temple is one of the most prominent and ancient temples in India.
• It is located in the Pathanamthitta district of Kerala.
• The temple is dedicated to Lord Ayyappa, and it attracts millions of devotees every year, especially during the Mandala season (November to January).
• It is situated on a hilltop at an altitude of about 1260 meters above sea level, surrounded by dense forests and mountains.
• The temple is known for its strict pilgrimage rituals and practices, including the 41-day vratham (penance) that devotees must observe before visiting.
• Women of menstruating age (10-50 years) were traditionally not allowed to enter the temple, a practice that has been subject to legal and social debates in recent years.

Additional Information

• Kerala is known for its rich cultural heritage and is often referred to as "God's Own Country".
• The state is famous for its backwaters, ayurvedic treatments, and vibrant festivals.
• Kerala has the highest literacy rate in India and is known for its progressive social indicators.
• It is bordered by Karnataka to the north, Tamil Nadu to the east and south, and the Arabian Sea to the west.

The correct answer is Beijing

Key Points

• The 2022 Winter Olympics is scheduled to be held in the city of Beijing.
• Beijing will make history as the first city to host both the Summer (2008) and Winter (2022) Olympic Games.
• The decision was made by the International Olympic Committee (IOC) during the 128^th IOC Session in Kuala Lumpur, Malaysia, on July 31, 2015.
• The event will feature 109 events across 15 disciplines in 7 sports.
• Beijing's hosting of the Winter Olympics is expected to further promote winter sports in China and across Asia.

Additional Information

• The Winter Olympics is a major international sporting event held once every four years for sports practiced on snow and ice.
• The first Winter Olympics was held in Chamonix, France, in 1924.
• The 2022 Winter Olympics will run from February 4 to February 20, 2022.
• Beijing's iconic National Stadium, also known as the Bird's Nest, will host the opening and closing ceremonies.
• The main competition zones will be in central Beijing, Yanqing, and Zhangjiakou.

Given:

Pendulum 1: 2 strikes in 3 seconds

Pendulum 2: 5 strikes in 7 seconds

Step 1: Find the time for 1 strike for both pendulums.

Time per strike for Pendulum 1 = 3 / 2 = 1.5 seconds

Time per strike for Pendulum 2 = 7 / 5 = 1.4 seconds

Step 2: Find the Least Common Multiple (LCM) of 1.5 seconds and 1.4 seconds.

LCM of 1.5 and 1.4 is 21 seconds.

Step 3: Calculate the number of simultaneous strikes in 1 minute (60 seconds).

Time for simultaneous strikes = 21 seconds

In 1 minute (60 seconds), the number of simultaneous strikes = 60 / 21 ≈ 2 times

∴ The number of simultaneous strikes in 1 minute is 2.

The correct answer is 44^th amendment

Key Points

• The 44^th amendment to the Constitution of India removed the Right to Property from the list of Fundamental Rights.
• The Right to Property was initially a fundamental right under Article 31 of the Indian Constitution.
• This amendment was enacted in 1978 during the tenure of the Janata Party government.
• After the amendment, the Right to Property was made a legal right under Article 300A of the Indian Constitution.
• This change was significant as it allowed the government to acquire private property for public purposes without it being challenged as a violation of Fundamental Rights.

Additional Information

• The Constitution of India was adopted by the Constituent Assembly on 26^th November 1949 and came into effect on 26^th January 1950.
• It lays down the framework defining fundamental political principles, establishes the structure, procedures, powers, and duties of government institutions, and sets out fundamental rights, directive principles, and the duties of citizens.
• The Constitution of India is the longest written constitution of any country in the world.
• It declares India a sovereign, socialist, secular, and democratic republic, assuring its citizens justice, equality, and liberty, and endeavors to promote fraternity.
• The Seventh Schedule of the Constitution contains three lists which delineate the subjects under the Union, State, and Concurrent lists.
• Amendments to the Constitution can be made through a process outlined in Article 368.
• The Union List has been amended several times to meet the evolving needs of the nation.

The correct answer is Igneous Rocks

Key Points

• Igneous Rocks are formed from the solidification of molten magma.
• They are one of the three main types of rocks, along with sedimentary and metamorphic rocks.
• Examples of igneous rocks include granite, basalt, and pumice.
• These rocks are primarily classified based on their mineral composition and texture.

Additional Information

• Igneous rocks can be further classified into intrusive and extrusive types based on where the molten magma solidifies.
• Intrusive igneous rocks form below the Earth's surface, while extrusive igneous rocks form at the surface.
• The word "igneous" comes from the Latin word "ignis," meaning fire, indicative of their fiery origin.
• Igneous rocks play a crucial role in the rock cycle, contributing to the formation of other rock types through weathering and erosion.
• They are commonly used in construction due to their durability and strength.

The correct answer is Germany

Key Points

• Germany is not a founding member of the United Nations.
• The United Nations was established on 24 October 1945, following the end of World War II, with the aim of preventing future conflicts and fostering international cooperation.
• The original founding members of the United Nations include countries such as the USA, France, the Soviet Union, and China, among others.
• Germany joined the United Nations much later, becoming a member on 18 September 1973.

Additional Information

• The United Nations is an international organization founded in 1945 and currently made up of 193 Member States.
• The mission and work of the United Nations are guided by the purposes and principles contained in its founding Charter.
• The UN has evolved over the years to keep pace with a rapidly changing world.
• Its work touches every corner of the globe and includes maintaining international peace and security, protecting human rights, delivering humanitarian aid, promoting sustainable development, and upholding international law.

Given:

The ratio between the speeds of two trains = 7 : 5

Speed of the second train = 400 km / 4 h = 100 km/h

Formula Used:

If the speed ratio of two trains is a : b and the speed of the second train is given, then the speed of the first train is calculated as:

Speed of first train = (Speed of second train × a) / b

Calculation:

Speed of the second train = 100 km/h

Speed ratio a : b = 7 : 5

Speed of first train = (100 × 7) / 5

⇒ Speed of first train = 700 / 5

⇒ Speed of first train = 140 km/h

The speed of the first train is 140 km/h.

The correct answer is Madhya Pradesh

Key Points

• Madhya Pradesh has the largest tribal population in India as per Census 2011.
• Tribal population in Madhya Pradesh is approximately 21.1% of the state's total population.
• The state is home to several major tribes including the Bhils, Gonds, and Oraons, among others.
• Madhya Pradesh has a rich tribal culture and heritage, which is reflected in its festivals, traditions, and arts.

Additional Information

• Odisha has the second largest tribal population in India.
• The Census of India is conducted every ten years, with the most recent one being in 2011 and the next scheduled for 2021.
• Tribal communities in India are provided with various benefits and reservations under the Indian Constitution to promote their development and welfare.
• Madhya Pradesh also has the highest number of tribal districts in India.

The correct answer is China

Key Points

• China is the largest producer of rice in the world based on production in the year 2019-20, according to the USDA.
• China's rice production is significantly higher than that of other major rice-producing countries such as India, Thailand, and Russia.
• Rice is a staple food in China and plays a crucial role in the country's agriculture and economy.
• The favorable climate and advanced agricultural practices contribute to China's high rice production.

Additional Information

• Rice is a key agricultural commodity and is grown in many countries around the world.
• India is the second-largest producer of rice, followed by other countries like Indonesia, Bangladesh, and Vietnam.
• Rice production is influenced by various factors including climate, soil fertility, water availability, and farming techniques.
• Advancements in agricultural technology and practices have significantly increased rice yields over the years.

The correct answer is George Yule

Key Points

• George Yule was the first European president of the Indian National Congress.
• He was elected as the president in the year 1888.
• The Indian National Congress was founded in 1885 by A.O. Hume, Dadabhai Naoroji, and others.
• George Yule's presidency marked a significant moment as it showed the inclusiveness and broad appeal of the Congress during the British rule in India.
• Yule was a businessman and had served as the President of the Bengal Chamber of Commerce.

Additional Information

• Annie Besant was the first woman president of the Indian National Congress, elected in 1917.
• A.O. Hume was one of the founders of the Indian National Congress but never served as its president.
• Alfred Webb was another European who served as the president of the Indian National Congress, elected in 1894.
• The Indian National Congress played a crucial role in the Indian independence movement against British rule.
• Over the years, the Congress has had many prominent leaders who have significantly contributed to India's political landscape.

The correct answer is 60 days

Key Points

• As per the Constitution of India, if a member of either House of Parliament is absent for a period of 60 days without permission, the House may declare their seat vacant.
• This provision ensures that members are regular in attending the sessions and fulfilling their parliamentary duties.
• The rule is aimed at maintaining the efficiency and effectiveness of parliamentary proceedings.
• The absence is calculated based on the actual sitting days of the House, not calendar days.

Additional Information

• The Constitution of India was adopted by the Constituent Assembly on 26^th November 1949 and came into effect on 26^th January 1950.
• It lays down the framework defining fundamental political principles, establishes the structure, procedures, powers, and duties of government institutions, and sets out fundamental rights, directive principles, and the duties of citizens.
• The Constitution of India is the longest written constitution of any country in the world.
• It declares India a sovereign, socialist, secular, and democratic republic, assuring its citizens justice, equality, and liberty, and endeavors to promote fraternity.
• The Seventh Schedule of the Constitution contains three lists which delineate the subjects under the Union, State, and Concurrent lists.
• Amendments to the Constitution can be made through a process outlined in Article 368.
• The Union List has been amended several times to meet the evolving needs of the nation.

Given:

Cost price (CP) = 40% of Selling Price (SP)

Formula Used:

Selling Price (SP) as a percentage of Cost Price (CP) = (SP / CP) × 100

Calculation:

Let Selling Price (SP) = 100 units.

Cost Price (CP) = 40% of SP = 40 units.

Selling Price as a percentage of Cost Price = (SP / CP) × 100

⇒ Selling Price as a percentage of Cost Price = (100 / 40) × 100

⇒ Selling Price as a percentage of Cost Price = 2.5 × 100

⇒ Selling Price as a percentage of Cost Price = 250%

The selling price is 250% of its cost price.