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

The logic followed here is:-

• Tezpur is a city located in Assam.
• Similarly, Kochi is a city located in the state of Kerala.

Hence, 'option 4' is the correct answer.

Given

Speed of train = 240 km/h

Time = 5 hours

Formula used

Speed = Distance/Time

1 Km = 1000 m

1 hour = 60 minutes

Calculation

Distance cover by train in 1 hour = 240 km

Distance cover by train in 5 hour = 240 × 5 km

⇒ 1200 km

Time taken by flight to cover 1200 km = 45/60

⇒ 3/4 hour

speed of flight = 1200/(3/4)

⇒ (1200/1) × (4/3)

⇒ 1600 km/h

∴ A flight has to cover the same distance in 45 mins, it must travel at a speed of 1600 km/h

Given

area of a square field = 7200 m2

Formula used

Area of square = (side)²

Diagonal of square = √{(side)² + (side)²}

Time = Distance/speed

Calculation

Distance cover = √{7200 + 7200}

⇒ √14400

⇒ 120 m

Speed of cycle = 4 km/h

⇒ (4 × 1000)/60

⇒ 400/6

⇒ (200/3) m/min

Time taken by cycle to cover 120 m = 120/(200/3)

⇒ (120/1) × (3/200)

⇒ 360/200

⇒ 9/5 minutes

∴ 9/5 minutes will a cycle take to cross the field diagonally at a constant rate of 4 km/h

Given

sum of the interior angles of a polygon = 3240°

Concept used

Sum of the interior angles of a polygon = (n - 2) × 180° 

where n is the number of sides of a polygon

Calculation

3240 = (n - 2) × 180

⇒(n - 2) = 3240/180

⇒n - 2 = 18

⇒n = 18 + 2

⇒n = 20

∴ Polygon have 20 sides.

Given

3x + 4 × 8 ÷ 9 = x ÷ 3 – 1

Concept

BODMAS

Calculation

3x + 4 × 8 × $1\over9$ = x × $1\over3$ - 1

⇒ 3x + 32/9 = x/3 - 1

⇒ 3x - (x/3) = - 1- (32/9)

⇒ (9x - x)/3 = (-9 - 32)/9

⇒ 8x/3 = -41/9

⇒ x = (-41/9) × (3/8)

⇒ x = -41/24

∴ The value of x is - 41/24

The correct answer is G Madhavan Nair.

• G Madhavan Nair was the chairman of ISRO when ISRO launched India's first lunar probe mission in October 2008.

Key Points

• On 22 October 2008, in its fourteenth flight from Satish Dhawan Space Center (SDSC) SHAR, Sriharikota, the Indian Space Research Organization (ISRO) Polar Satellite Launch Vehicle, PSLV-C11 successfully launched the 1380 kg Chandrayaan-1.
• The spacecraft is placed in a transfer orbit with a perigee (closest point to Earth) of 255 km and an apogee (farthest point from Earth) of 22,860 km, inclined at an angle of 17.9° to the equator.

Additional Information

Given

180 ÷ 20 {(15 – 6) + (24 – 18)} 

Concept

BODMAS

Calculation

180 ÷ 20 {(15 – 6) + (24 – 18)} is

180 ÷ 20 {(9 + 6)}

⇒ 180 ÷ 20 (15)

⇒ 180 ÷ 300

⇒ 180 × (1/300)

⇒ 18/30

⇒ 9/15

∴ The value of 180 ÷ 20 {(15 – 6) + (24 – 18)} is 9/15.

The least possible Venn Diagram is as follows:-

Conclusions:

1. Some boys are smart and intelligent.→ True (Using the Venn diagram, we can see that all boys are smart and intelligent then some boys are smart and intelligent is definite true.)

Note: All A are B means Some A are B.

2. All intelligent are smart.→ False ( it is possible but not definite)

Hence, 'option 4' is the correct answer.

Given

x² + 1 = 2x

Calculation

x² + 1 = 2x

⇒ x²  - 2x + 1 = 0

⇒ x² - x - x + 1 = 0

⇒ x(x - 1) - 1(x - 1) = 0

⇒ (x - 1) (x - 1) = 0

⇒ x = 1 and x = 1

Value of x - ($1\over x$)

⇒ 1 - (1/1)

⇒ 1 - 1

⇒ 0

∴ x - (1/x) is 0.

Given

[3 ÷ 5 – 8 of 4 + 3 × {8 ÷ 2 – (4 + 3)}]

Concept

BODMAS

Calculation

[3 ÷ 5 – 8 of 4 + 3 × {8 ÷ 2 – (4 + 3)}]

⇒ [3 × (1/5) - 8 × 4 + 3 × {8 × (1/2) - (7)}

⇒ [(3/5) - 32 + 3 × {4 - 7}

⇒ [(3/5) - 32 + 3 × (-3)

⇒ [(3/5) - 32 - 9]

⇒ (3 - 160 - 45)/5

 ⇒ - 202/5

∴ The value of [3 ÷ 5 – 8 of 4 + 3 × {8 ÷ 2 – (4 + 3)}] is -202/5

Concept

First taken the L.C.M of the given numbers and then subtract 25 from the L.C.M.

Calculation

Factors of 25 = 5 × 5

Factors of 36 = 2 × 2 × 3 × 3

Factors of 40 = 2 × 2 × 2 × 5

L.C.M of 25, 36 and 40 = 2 × 2 × 2 × 3 × 3 × 5 × 5

⇒ 1800

Subtract 25 from the L.C.M, then we will get the smallest number on which we add 25, then the number will be exactly divisible by 25, 36 and 40.

⇒ 1800 - 25

⇒ 1775

∴ 1775 will be smallest number, which on adding 25 to it, is exactly divisible by 25, 36 and 40

The correct answer is Vladimir Putin.

• Vladimir Putin got elected as the Head of the State four times.

Key Points

Additional Information

• Viktor Alekseevich Zubkov is a Russian civil servant, politician and businessman who served as the 36^th Prime Minister of Russia from September 2007 to May 2008.
• He was Vladimir Putin's first deputy prime minister during the presidency of Dmitry Medvedev.
• Boris Nikolayevich Yeltsin was a Russian and Soviet politician who served as the first President of the Russian Federation from 1991 to 1999.
• He was a member of the Communist Party of the Soviet Union from 1961 to 1990.
• Dmitry Anatolyevich Medvedev is a Russian politician serving as Deputy Chairman of the Security Council of Russia since 2020.
• Medvedev served as President from 2008 to 2012 and as Prime Minister from 2012 to 2020.
• Medvedev was elected president in the 2008 election.

The correct answer is push.

• People migrate for a better economic and social life. There are two sets of factors that influence migration.
• The Push factors make the place of origin seem less attractive for reasons like unemployment, poor living conditions, political turmoil, unpleasant climate, natural disasters, epidemics and socio-economic backwardness.
• The Pull factors make the place of destination seem more attractive than the place of origin for reasons like better job opportunities and living conditions, peace and stability, security of life and property, and a pleasant climate.

Additional Information

• When people move from one place to another, the place they move from is called the Place of Origin, and the place they move to is called the Place of Destination. The place of origin shows a decrease in population while the population increases in the place of destination.  Migration may be interpreted as a spontaneous effort to achieve a better balance between population and resources. 
• Emigration: Migrants who move out of a place are called Emigrants
• Immigration: Migrants who move into a new place are called Immigrants.
• It may take place from rural to rural areas, rural to urban areas, urban to urban areas and urban to rural areas.
• Migration may be permanent, temporary or seasonal.

According to the given information-

Name of persons- A, E, C, H and L

• A likes to work with → C and H
• E likes to work with → C
• C likes to work with → E

♦ Also, H and L does not like to work with anyone.

Clearly, L is left isolated as he does not like to work with anyone and no one likes to work with L..

Hence, 'option 1' is the correct answer.

The correct answer is Human Body.

• The human body is NOT an example of an insulator.

Key Points

• Electric charges do not flow freely through insulators.
• This is an ideal quality in many cases—strong insulators are often used to coat or provide a barrier between conductors to keep electric currents under control.
• This can be seen in rubber-coated wires and cables.

Important Points

• The most effective electrical insulators are:
• Rubber
• Glass
• Pure water
• Oil
• Air
• Diamond
• Dry wood
• Dry cotton
• Plastic
• Asphalt

Given

Distance = 500 m

Time = 10 minutes

Formula used

Speed = Distance/time

1 Hour = 60 minutes

1 km= 1000 m

Calculation

Distance = (500/1000)km

⇒ 1/2 km

Time = (10/60)hours

Speed = (1/2)/(10/60)

⇒ (1/2) × (60/10)

⇒ 3 km/h

∴ The person's speed be in kilometres per hour is 3 km/h

The statement highlights the problem that a lot of people drive on the wrong side of the road.

• From the statement, we cannot conclude that drivers do not know which side they are supposed to drive because the statement has used the words 'wrong' and "these days". It means that the drivers know they are driving on the wrong side but still, they are practicing it and they have started doing it these days.
• If people drive on the wrong side of the road, it is obvious that the possibility of accidents will be high. Thus, conclusion II follows.

Hence the correct answer is option 1.

Given

√(1 + cos 2A)/(1 - cos 2A)

Formula used

cos 2A = cos² A - sin² A

sin 2A = 2 sin A cos A

cos² A + sin² A = 1

Calculation

${√\frac{1 + cos\ 2A}{1 - cos\ 2A}}$

⇒ √ (1 + cos 2A) × (1 + cos 2A)/(1 - cos 2A) (1 + cos 2A)

⇒ √ (1 + cos 2A)²/[(1)² - (cos²2A)

⇒ (1 + cos 2A)/ sin 2A

⇒ (cos² A + sin² A + cos² A - sin² A)/sin 2A

⇒ 2 cos² A /2 sin A cos A

⇒ cos A/sin A

⇒ cot A

∴ The value of ${\sqrt\frac{1 + cos\ 2A}{1 - cos\ 2A}}$ is cot A.

Shortcut Trick Use $cos2A= cos^2A - sin^2A$

${√\frac{1 + cos\ 2A}{1 - cos\ 2A}}$ = ${√\frac{1 + cos^2A-sin^2A}{1 - (cos^2A-sin^2A)}}$

${√\frac{cos^2A + cos^2A}{sin^2A+sin^2A}}$ ⇒ ${√\frac{2cos^2A}{2sin^2A}}$

⇒ cot A

The correct answer is Transmission Control Protocol/Internet Protocol.

• TCP/IP stands for Transmission Control Protocol/Internet Protocol.
• TCP/IP is a set of standardized rules that allow computers to communicate on a network such as an internet.

Key Points

• The Internet Protocol Suite, commonly known as TCP/IP, is the set of communication protocols used in the Internet and similar computer networks.
• The current basic protocols in the suite are Transmission Control Protocol (TCP) and Internet Protocol (IP).
• Web browser or Internet browser, the browser is a software program for rendering and exploring content on the World Wide Web.
• These pieces of content, including images, videos, and web pages, are linked using hyperlinks and classified with URIs (Uniform Resource Identifiers).
• This page is an example of a web page that can be viewed using a browser.
• List of some Internet browsers:
• Google Chrome
• Microsoft Edge
• Microsoft Internet Explorer
• Mozilla Firefox
• Opera
• Apple Safari
• Amazon Silk

Given

Cost price of 120 pens = selling price of x pens

Concept

Profit and loss

Formula used

selling price = cost price + Profit

Calculation

 let the cost price of 120 pens = Rs.100

cost price of 1 pen = (100/120)

cost price of x pens = 100x/120

selling price of x pens = Rs. 100

Selling price = cost price + 25% of profit

100 = 100x/120 + 25% of (100x/120)

⇒ 100 = (100x/120 ) + (25x/120)

⇒ 100 = (100x + 25x)/120

⇒ 100 = 125x/120

⇒ x = (100 × 120)/125

⇒ x = 96

∴ The value of x is 96.

Given

x cos 45º sin 120° + sin 60º = –x sin 90° + 1

identities

cos 45° = 1/√2

sin 120° = √3/2

sin 60° = √3/2

sin 90°  = 1

Calculation

x cos 45º sin 120° + sin 60º = –x sin 90° + 1

x ×(1/√2) × (√3/2) + (√3/2) = -x × 1 + 1

⇒ (√3x/2√2)+ √3/2 = - x + 1

⇒ (√3x/2√ 2) + x = 1 - (√3/2)

⇒ (√3x + 2√2x)/2√ 2 = (2 -√ 3)/2

⇒ x(√3 + 2√2)/√2 = (2 - √ 3)

⇒ x = √2 ( 2 - √3)/(√3 + 2√2)

⇒ x = (2√2 - √6)/(2√2 + √ 3)

∴ x is (2√2 - √6)/(2√2 + √ 3)

The correct answer is Hemodialysis.

• Hemodialysis is a procedure where a dialysis machine and a special filter called an artificial kidney, or a dialyzer, are used to clean your blood.
• Dialysis is a procedure to remove waste products and excess fluid from the blood when the kidneys stop working properly.
• It often involves diverting blood to a machine to be cleaned.

Key Points

• Kidneys are two reddish-brown bean-shaped organs found in vertebrates.
• They receive blood from paired renal arteries; Blood exits in paired renal veins.
• Each kidney is connected to a ureter, a tube that carries excreted urine to the bladder.
• Function of Kidneys:
• Formation of urine
• Hormone secretion
• Blood pressure regulation
• Acid–base balance
• Regulation of osmolality
• Measuring function
• Clinical significance

Additional Information

• Excretion is a general term referring to the separation and throwing off of waste materials or toxic substances from the cells and tissues of a plant or animal.
• Metabolism is the process by which your body converts the food you eat into energy.
• During this complex process, the calories in food and beverages are combined with oxygen to release the energy your body needs to function.
• The circulatory system is a system of organs that includes the heart, blood vessels, and blood that circulates throughout the body of a human or other vertebrate.
• This includes the cardiovascular system, or vascular system, which consists of the heart and blood vessels.

The correct answer is 193.

• As of 31^st October 2020, the United Nation comprises 193 member states.

Key Points

• The United Nations is the largest intergovernmental organization in the world.
• The United Nations Organization (UNO) or just United Nations (UN) is an intergovernmental organization whose purpose is to maintain international peace and security, develop friendly relations among nations, achieve international cooperation, and be a centre for harmonizing the actions of nations.
• It is the largest and most familiar international organization in the world.
• The United Nations is headquartered on the international arena in New York City, and has other main offices in Geneva, Nairobi, Vienna and The Hague (home of the International Court of Justice).

Additional Information

• Region which is common to writers, singers and dancers = e + j

• Region that includes writers, singers, and dancers, but not actors is :-

Thus, region 'j' represents writers, singers and dancers but does not include actors.

Hence, 'option 3' is the correct answer.

The logic followed here is:

Hence, 'option 3' is the correct answer.

Given

Spends = 10% of total income

Saving = Rs. 5400

Concept

Income = Expenditure + saving

Calculation

Let the total income is Rs. x

x = 10% of x + 5400

⇒ x - 10% of x = 5400

⇒ 90x/100 = 5400

⇒ x = (5400 × 100)/90

⇒ x = 6000

∴ Ashoka monthly income is Rs. 6000

The correct answer is 1993.

• The National Human Rights Commission (NHRC) of India was established on 12 October, 1993.

Key Points

• The statute under which it is established is the Protection of Human Rights Act (PHRA), 1993 as amended by the Protection of Human Rights (Amendment) Act, 2006.
• It is in conformity with the Paris Principles, adopted at the first international workshop on national institutions for the promotion and protection of human rights held in Paris in October 1991, and endorsed by the General Assembly of the United Nations by its Regulations 48/134 of 20 December, 1993.
• The NHRC is an embodiment of India’s concern for the promotion and protection of human rights.
• Section 2(1)(d) of the PHRA defines Human Rights as the rights relating to life, liberty, equality and dignity of the individual guaranteed by the Constitution or embodied in the International Covenants and enforceable by courts in India.

Additional Information

The correct answer is Luna 9.

• Luna 9 was the first spacecraft to achieve a lunar soft landing and to transmit photographic data from the Moon's surface to Earth, preceding the U.S. Surveyor 1 soft lander by about 4 months.

Additional Information

• Apollo 17 was the final mission of NASA's Apollo program, the most recent time humans have set foot on the Moon or traveled beyond low Earth orbit.
• Sputnik 25 was originally designated Sputnik 33 in the U.S. Naval Space Command Satellite Situation Summary.
• Ranger 6 was a lunar probe in the NASA Ranger program, a series of robotic spacecraft of the early and mid-1960s to obtain the first close-up images of the Moon's surface.

Important Points

• Yuri Alekseyevich Gagarin was a Soviet pilot and cosmonaut who became the first human to journey into outer space.
• Sputnik 1 was the first artificial Earth satellite.
• It was launched into an elliptical low Earth orbit by the Soviet Union on 4 October 1957 as part of the Soviet space program.

Karma is NOT correct.

• As of 2021, apart from Mother India, only two Indian films have been nominated for the Oscars—Salaam Bombay! (1988) and Lagaan (2001).

Key Points

• At the 30^th Academy Awards, Mehboob Khan's 1957 Hindi-language film Mother India was India's first submission for the Academy Award for the Best International Feature Film category.
• It was nominated along with four other films and lost by one vote to the Italian film Knights of Cabiria (1957).
• In 1982, the National Film Development Corporation of India was instrumental in co-producing the Richard Attenborough biographical film Gandhi.
• Bhanu Athaiya became the first Indian to win an Academy Award for costume design at the 55^th Academy Awards.
• Ravi Shankar was nominated for Best Original Score for the same film. As of 2021, apart from Mother India, only two Indian films have been nominated for an Oscar – Salaam Bombay! (1988) and Lagaan (2001).

Additional Information

• The Academy Awards, popularly known as the Oscars, are awards given for artistic and technical merit in the film industry.
• First awarded May 16, 1929
• Oscars 2021 Winners List
• Best Picture: Nomadland
• Best Actor: Anthony Hopkins – The Father
• Best Actress: Frances McDormand – Nomadland

Given

48 and 65

Concept

Find the factors of 45 and 65

Calculation

Factors of 48 = 2 × 2 × 2 × 2 × 3

Factors of 65 = 5 × 13

L.C.M of 48 and 65 = 2 × 2 × 2 × 2 × 3 × 5 × 13

⇒ 3120

∴ The LCM of 48 and 65 is 3120

The correct answer is Uruk.

• The main sites of the Indus Valley Civilization are Rakhigarhi (first site with genetic testing), Sanauli, Farmana, Kalibangan, Lothal, Dholavira, Mehrgarh, Harappa, Chanhudaro and Mohenjo-Daro.

Key Points

• Uruk, also known as Warka or Warkah, was an ancient city of Sumer (and later of Babylonia) situated east of the present bed of the Euphrates River on the dried-up ancient channel of the Euphrates 30 km east of modern Samawah, Al-Muthannā, Iraq.
• Uruk is the type site for the Uruk period.

Additional Information

Major Sites of Indus Valley Civilization

Given

a cot θ = b

Formula used

cos θ = Side adjacent to θ/Hypotenuse

Calculation

In triangle ABC

(AC)² = AB² + BC²

(AC)² = a² + b²

AC = √a² + b²

cot θ = b/a

cos θ = BC/AC

cos θ = b/(√ a² + b²)

sin θ = AB/AC

sin θ = a/(√a² + b²)

$\frac{a\ cos θ - b\ sin θ}{a\ cos θ + b\ sin θ}$

⇒ [{a × b/(√ a2 + b2)} - {b × a/(√a2 + b2)}] /[{a × b/(√ a2 + b2)} + {b × a/(√a2 + b2)}]

⇒ [{ab/(√a2 + b2)} - {ab/(√a2 + b2)}]/[a × b/(√ a2 + b2) + b × a/(√a2 + b2)]

⇒ 0/[a × b/(√ a2 + b2) + b × a/(√a2 + b2)]

⇒ 0

∴ the value of $\frac{a\ cos \theta - b\ sin \theta}{a\ cos \theta + b\ sin \theta}$  is 0

The correct answer is Fishes have double circulation.

Key Points

• In fish, the system has only one circuit, with the blood being pumped through the capillaries of the gills and onto the capillaries of the body tissues.
• This is known as single cycle circulation. Hence, option 3 is incorrect.
• The heart of fish is therefore only a single pump (consisting of two chambers).
• Fishes have only a two-chambered heart with an atrium and a ventricle, and the chambers of the heart which receive the blood from body tissues are called auricles. Fishes respire through their gills.
• In the heart of fish, blood goes only once in a cycle because their heart is of two chambers.
• They carry oxygen through the gills where the blood is oxygenated and through the heart to the rest of the body.
• Fish have a closed-loop circulatory system.
• The atrium collects blood that has returned from the body and the ventricle pumps the blood to the gills where gas exchange occurs and the blood is re-oxygenated; this is called gill circulation.

Additional Information

• Birds and mammals - Four-chambered heart, having two auricles and two ventricles.
• Reptiles - three-chambered heart (except crocodile which has 4 chambered heart).
• Fishes - Two chambered hearts.
• Dolphin - Mammal has a four-chambered heart.
• Salamander - Amphibian has a three-chambered heart.

The correct answer is Bank of Hindustan.

• The oldest bank in India is The Madras Bank (1683), followed by the Bank of Bombay, founded in 1720, which is then followed by the Bank of Hindustan, founded in 1770.

Key Points

• Bank of Hindustan:
• The Bank of Hindustan (1770-1832), set up by the agency house of Alexander and Company in the year 1770 was the first bank established in India.
• It was no longer exists now.

Additional Information

• Bank of Baroda is an Indian nationalized banking and financial services company.
• Founded - 20 July 1908
• Founder - Sayajirao Gaekwad III
• Headquarters - Vadodara, Gujarat, India
• State Bank of India:
• It is the largest public sector bank in India.
• It began with the establishment of the Bank of Calcutta in Calcutta, on 2 June 1806.
• It was the first-ever joint-stock bank of British India, established under the sponsorship of the Government of Bengal.
• Indian Bank is a major nationalized bank. It is owned by the Ministry of Finance, Government of India.
• It was established in 1907 and is headquartered in Chennai, India.

Given

8 + $(\frac{1}{2} + \frac{1}{4})$ × 16 

Concept:

Calculation

⇒ 8 + ${(2 + 1)\over 4}$ × 16

⇒ 8 + $3\over 4$ × 16

⇒ 8 + 12

⇒ 20

∴ The value of  8 + $(\frac{1}{2} + \frac{1}{4})$ × 16 is 20

The logic followed here is:-

Similarly,

Hence, 'option 3'  is the correct answer.

The correct answer is Satyendra Nath Bose.

• Satyendra Nath Bose was an Indian mathematician and physicist specializing in theoretical physics.
• He is best known for his work on quantum mechanics in the early 1920s, collaborating with Albert Einstein in developing the foundations of Bose-Einstein statistics and the theory of the Bose-Einstein condensate.

Additional Information

The correct answer is Millie Bobby Brown.

• On 20 November 2018, Emmy-nominated actress Millie Bobby Brown has been announced as UNICEF’s newest Goodwill Ambassador.
• The appointment – marked on World Children’s Day at United Nations Headquarters and the Empire State Building in New York – makes the 14-year-old UNICEF’s youngest-ever Goodwill Ambassador.

Key Points

• Millie Bobby Brown is a British actress.
• In 2018, Brown was featured on the Time 100 list of the world's most influential people and was appointed as a UNICEF Goodwill Ambassador, the youngest person ever elected to the position.

Important Points

• List of UNICEF Goodwill Ambassadors
• Serbia Novak Djokovic (August 2015)
• India Priyanka Chopra (December 2016)
• Canada Lilly Singh (July 2017)
• United Kingdom Millie Bobby Brown (November 2018)

Additional Information

• Lily Singh is a Canadian comedian, actress, former talk show host and YouTuber who formerly appeared under the pseudonym Superwoman, her longtime YouTube username. Born and raised in Scarborough, Ontario, Singh began making YouTube videos in 2010.
• Novak Djokovic is a Serbian professional tennis player.
• He is currently ranked world No. 1 by the Association of Tennis Professionals as of 21 March 2022.
• Priyanka Chopra Jonas is an Indian actress, model and singer. The winner of the Miss World 2000 pageant, Chopra is one of the highest-paid actresses of India.
• He has received several awards, including two National Film Awards and five Filmfare Awards.

According to the information given in question,

1. Number of friends = 7
2. Three persons are sitting on the left-hand side of Q, of which V is the last one. 3. R and V are sitting on the corner sides.

So, this can be represented as-

Also,

4. S and V are sitting beside each other. 5. More than two persons are sitting on the right-hand side of T, of which R is the last one.

So, the arrangement becomes-

Thus, two persons are sitting to the left of T and four persons are sitting to the right of T.

Hence, 'option 4'  is the correct answer.

Given 

a ∶ b = √7 ∶ √ 3

Formula used

(a + b)² = a² + b² + 2ab

(a² - b²) = (a + b) (a - b)

calculation

let a = √7x and b = √3x

(3 × √7x + 2 × √3x)/(3 × √ 7x - 2 × √3x)

[{(3 × √7x + 2 × √3x) × (3 × √ 7x + 2 × √3x)}]/ [{(3 × √7x - 2 × √3x) × (3 × √ 7x + 2 × √3x)}]

(3√7x)² + (2√3x)² + 2 (3√7x)(2√ 3x)/{(3√7x)² - (2√3x)²}

(63x² + 12x² + 12√ 21x²)/(63x² - 12x²)

(75 + 12√ 21)/51

(25 + 4√ 21)/17

Check option 2

(2 + √21)/(- 2 + √21)

Rationalize multiply (2 + √21) both numerator and denominator 

⇒ (2 + √21)² /(- 2 + √21)(2 + √21)

⇒ (25 + 4√ 21)/17

∴ The value of (3a + 2b) : (3a – 2b) is equal to $\frac{2 + \sqrt{21}}{(-2 + \sqrt{21})}$

Given

a = $\frac{3}{7}$ b 

Calculation

a/b = 3/7

a ∶ b = 3 ∶ 7

let a = 3x and b = 7x

$\frac{8a - b}{2a + 3b}$

[(8 × 3x) - 7x]/[(2 × 3x) + (3 × 7x)]

⇒ (24x - 7x)/(6x + 21x )

⇒ 17x/27x

⇒ 17/27

∴ The value of $\frac{8a - b}{2a + 3b}$ is 17/27

The logic followed here is:-

♦ Alphabets are written as the positional value of the opposite letter.

♦ And sum of 24 + 19 + 26 + 9 + 20 + 22 + 9 = 129

Similarly,

♦ Sum of 19 + 18 + 13 + 20 + 22 + 8 = 100

Hence, 'option 4'  is the correct answer.

The correct answer is White-collar workers.

• White Collar Worker
• Those group of workers who is highly qualified and skilled and does mental work is called white-collar worker.
• These workers enjoy a high standard of living and better social status.

Key Points

• Blue Collar Worker
• Those group of workers which is not so qualified and skilled and does physical work is called blue-collar worker.
• They get relatively lesser wages.

The correct answer is Kochi.

Key Points

• Kochi is known as the 'Queen of the Arabian Sea'.
• It was the centre of the Indian spice trade for many centuries.
• Kochi was the centre of the Indian spice trade for many centuries and was known to the Yavanas (Greeks and Romans) as well as Jews, Syrians, Arabs, and Chinese since ancient times.

Additional Information 

The correct answer is .gov.

• Domain Name Types:
• .com – commercial business (the most common TLD)
• .org – organizations (typically, nonprofit)
• .gov – government agencies
• .edu – educational institutions
• .net – network organizations
• .mil – military

Additional Information

• A domain name is an identification string that defines the scope of administrative autonomy, authority, or control within the Internet.
• Domain names are used in a variety of networking contexts and for application-specific naming and addressing purposes.
• In general, a domain name identifies a network domain, or it represents an Internet Protocol (IP) resource, such as a personal computer used to access the Internet, hosting a website.
• A server computer, or the Web site itself, or any other service of communication through the Internet.

The correct answer is Bhutan.

• Gross national happiness was first coined in 1972 by the fourth King of Bhutan, King Jigme Singye Wangchuck.
• The concept implies that sustainable development should take a holistic approach to notions of progress and give equal importance to the non-economic aspects of well-being.
• The Gross National Happiness Index, Bhutan sought to create a measurement tool that would be useful for policymaking and to create policy incentives for the government, NGOs and businesses in Bhutan to increase GNH.

Additional Information

• The GNH measure has been designed to include nine core domains that are regarded as components of happiness in Bhutan and are constructed of indicators that are robust and informative with respect to each of the domains.
• The nine domains are:
• Psychological well being.
• Health.
• Time use.
• Education.
• Cultural diversity and resilience.
• Good Governance.
• Community vitality.
• Ecological diversity and resilience.
• Living standard.

Given

Selling price of bike  = Rs 42,000

Cost price of  bike = Rs 30,000 + Rs.5000

Formula used

Profit = Selling Price - Cost Price

Calculation

Cost price = 30,000 + 5,000

⇒ Rs. 35000

Selling price = Rs 42,000

Profit = Rs. (42,000 - 35,000)

⇒ Rs. 7,000

Profit percentage = (7000/35000) × 100

⇒ 20%

∴ Gain percentage is 20%

The correct answer is Carbonic acid.

• Carbon dioxide or CO₂ is filled in beverages like soft drinks to give a fizzy nature to the beverage.
• The process of adding carbon dioxide gas to a beverage is called Carbonation.

Additional Information

The correct answer is Political Geography.

Key Points

• Political Geography is NOT a sub-field of economic geography.
• Political geography is concerned with the study of both the spatially uneven outcomes of political processes and the ways in which political processes are themselves affected by spatial structures.
• Conventionally, for the purposes of analysis, political geography adopts a three-scale structure with the study of the state at the center, the study of international relations (or geopolitics) above it, and the study of localities below it.
• The primary concerns of the subdiscipline can be summarized as the inter-relationships between people, state, and territory.
• Critical political geography is mainly concerned with the criticism of traditional political geographies vis-a-vis modern trends.
• As with much of the move towards 'Critical geographies', the arguments have drawn largely from postmodern, post-structural, and postcolonial theories.

Additional Information

• Economic geography is the subfield of human geography which studies economic activity and factors affecting them.
• It can also be considered a subfield or method in economics.
• There are four branches of economic geography.
• There is the primary sector, Secondary sector, Tertiary sector, & Quaternary sector.
• Economic geography takes a variety of approaches to many different topics, including the location of industries, economies of agglomeration (also known as "linkages"), transportation, international trade, development, real estate, gentrification, ethnic economies, gendered economies, core-periphery theory, the economics of urban form, the relationship between the environment and the economy (tying into a long history of geographers studying culture-environment interaction), and globalization.
• Sub-fields of Economic Geography are Geography of Resources, Geography of Agriculture, Geography of Tourism, Geography of Industries, Geography of Marketing, and Geography of International Trade.

Given

x : y = 2 : 3

Calculation

let x = 2a and y = 3a

[(5 × 2a) + ( 3 × 3a)] ∶ [(5 × 2a) - (3 × 3a)]

⇒ (10a + 9a) ∶ (10a - 9a)

⇒ 19a ∶ a

⇒ 19 ∶ 1

∴ The value of (5x + 3y) : (5x – 3y) is 19 ∶ 1.

The correct answer is Indore.

Key Points

• Swachh Survekshan is an annual survey of cleanliness, hygiene, and sanitation in cities and towns across India.
• Swachh Survekshan 2020 declared Indore as India's cleanest city.
• The government today announced the results of an annual survey of cleanliness, Swachh Survekshan 2020.
• Indore once again bagged the top spot as the cleanest city of India, the fourth time in a row.
• The second and third positions in the category were grabbed by Surat and Navi Mumbai respectively.
• The Swachh Survekshan awards 2020 were announced by Union Housing and Urban Affairs Minister Hardeep Singh Puri at a ceremony.

Additional Information

• Swachh Survekshan is a ranking exercise taken up by the Government of India to assess rural and urban areas for their levels of cleanliness and active implementation of Swachhata mission initiatives in a timely and innovative manner.
• The objective of the survey is to encourage large-scale citizen participation and create awareness amongst all sections of society about the importance of working together towards making towns and cities a better place to live in.
• Additionally, the survey also intends to foster a spirit of healthy competition among towns and cities to improve their service delivery to citizens, towards creating cleaner cities and towns.
• The Ministry of Urban Development, Government of India takes up the Swachh Survekshan in urban areas and the Ministry of Drinking Water and Sanitation in rural areas.
• The Quality Council of India (QCI) has been commissioned the responsibility of carrying out the assessment.
• Swachh Survekshan was introduced by the government with the objective of generating large-scale citizen participation in the Mission, along with inculcating a spirit of healthy competition among cities towards becoming India's cleanest cities.

• Doctors, engineers and lawyers have no characteristics common to each other.
• Therefore, the best Venn diagram representation is as follows:-

Hence, 'option 3'  is the correct answer.

The correct answer is Amritsar.

Key Points

• Sri Guru Ram Dass Jee International Airport is located in Amritsar.
• Sri Guru Ram Das Ji International Airport is an international airport about 11 kilometers northwest of the city of Amritsar, Punjab, India.
• It is named after Guru Ram Das, the fourth Sikh Guru and the founder of Amritsar city.
• Amritsar Airport is the largest and busiest airport in the Indian state of Punjab.
• It is the second-largest airport in Northern India after Delhi Airport.
• The airport was the 3^rd fastest-growing airport in India during the fiscal year 2017–18.
• It is a hub of cargo movements, domestically and internationally.
• The Airport is ranked the 6^th-best regional airport in India and Central Asia in 2019 and 2020 by Skytrax.
• The airport is awarded as the best airport in Asia-Pacific in 2020 (2 to 5 million passengers per annum) by Airports Council International.

Additional Information

• Guru Ram Das  (24 September 1534 – 1 September 1581) was the fourth of the Ten Gurus of Sikhism.
• He was born on 24 September 1534 in a family-based in Lahore.
• His birth name was Jetha, and he was orphaned at age seven; he thereafter grew up with his maternal grandmother in a village.
• At age 12, Bhai Jetha and his grandmother moved to Goindval, where they met Guru Amar Das.
• The boy thereafter accepted Guru Amar Das as his mentor and served him.
• The daughter of Guru Amar Das married Bhai Jetha, and he thus became part of Guru Amar Das's family.
• As with the first two Gurus of Sikhism, Guru Amar Das instead of choosing his own sons chose Bhai Jetha as his successor and renamed him Ram Das or "servant of God."

The logic followed here is:-

♦ Alphabets are assigned the positional value of the opposite letter or in the reverse alphabetical order.

• So, AMAZON can be written as:-

• Code for AMAZON will be 26142611213.

• Hence, 'option 1' is the correct answer.

The correct answer is Atharvaveda.

Key Points

• The Vedas are considered the earliest literary record of Indo-Aryan civilization.
• There are four Vedas: Rigveda, Samaveda, Yajurveda and the fourth one is Atharvaveda.
• The Atharva Veda is the "knowledge storehouse of atharvāṇas, the procedures for everyday life".
• The text is the fourth Veda but has been a late addition to the Vedic scriptures of Hinduism.
• The language of the Atharvaveda is different from Vedic Sanskrit, preserving pre-Vedic Indo-European archaisms.
• It is a collection of 730 hymns with about 6,000 mantras, divided into 20 books.
• About a sixth of the Atharvaveda texts adapts verses from the Rigveda, and except for Books 15 and 16, the text is mainly in verse deploying a diversity of Vedic meters.

Additional Information

• Dhanurveda is a Sanskrit treatise on warfare and archery, traditionally regarded as a upaveda attached to Yajurveda (1100 – 800 BCE) and attributed either to Bhrigu or Vishvamitra, or Bharadwaj.
• It is one among the four upavedas to Vedas (along with Ayurveda, Gandharvaveda, and Sthapatyaveda).
• Ayurveda is a traditional system of medicine with historical roots in the Indian subcontinent.
• It is traditionally considered the Upaveda associated with the Atharvaveda.
• Ayurveda focuses on the balance of body, mind, and spirit, and is widely practiced in India and Nepal.
• Shilpaveda is considered as the Upaveda instead of Arthashastra according to Charanavyuha and Katyayana.
• The Upavedas supplement the Vedas with more specific applications of Vedic teachings into the cultural field.
• Upavedas are considered as a part of Veda and not as a separate entity according to a few scholars, in such case there are Chaturdhasha Vidyasthanas only.

Given

27 and 81

Concept

To find the H.C.F and L.C.M of the numbers, first take factors of the numbers.

Calculation

Factors of 27 = 3 × 3 × 3

Factors of 81 = 3 × 3 × 3 × 3 

L.C.M of 27 and 81 = 3 × 3 × 3 × 3

⇒ 81

H.C.F of 27 and 81 = 3 × 3 × 3

⇒ 27

∴ The LCM and HCF of 27 and 81 is 81 and 27.

Given

Cost price of 10 toffees = Re. 1

Gain = 25%

Concept

Selling price = cost price + profit

Calculation

cost price of 10 toffee = Re. 1

cost price of 1 toffee = Re. 1/10

Selling price x toffee = Re.1

selling price of 1 toffee = 1/x

(1/x) = (1/10) + 25% of (1/10)

⇒ (1/x) = (1/10) + (25/1000)

⇒ (1/x) = (1/10) + (1/40)

⇒ (1/x) = (4 + 1)/40

⇒ (1/x) = (5/40)

⇒ x = 40/5

⇒ x = 8

∴ Vendor should sell 8 toffees for Re1 to gain 25%.

The correct answer is 2010.

Key Points

• In 2010 the new currency symbol of the Indian rupee was officially adopted.
• The symbol of the Indian Rupee typifies India's international identity for money transactions and economic strength.
• The Indian Rupee sign is an allegory of Indian ethos.
• The symbol is an amalgam of Devanagari "Ra" and the Roman Capital "R" with two parallel horizontal stripes running at the top representing the national flag and also the "equal to" sign. The Indian Rupee sign was adopted by the Government of India on 15^th July 2010.
• The symbol, conceptualized and designed by Udaya Kumar, a postgraduate in Design from the Indian Institute of Technology Bombay, has been chosen from thousands of concept entries received by the Ministry of Finance through an open competition among resident Indian nationals.
• The process of establishing and implementing this new identity is underway through various digital technology and computer applications.

Additional Information

• On 5 March 2009, the Indian government announced a contest to create a sign for the Indian rupee.
• During the 2010 Union Budget, then Union Finance Minister Pranab Mukherjee said that the proposed sign should reflect and capture the Indian ethos and culture.
• From around 3,331 responses received, five symbols were shortlisted.
• These were the entries from Nondita Correa-Mehrotra, Hitesh Padmashali, Shibin KK, Shahrukh J. Irani, and D. Udaya Kumar:
• one of them was due to be selected at the Union Council of Ministers of India meeting held on 24 June 2010.
• However, the decision was deferred at the request of the Finance Minister, and the final decision was made when they met again on 15 July 2010, when they chose the symbol created by Udaya Kumar, Associate Professor IIT Guwahati.

The given information can be represented by a Venn diagram as follows:

• Total students in class = 30
• Total friends of L and A = 10 + 5 + 12  = 27
• Number of students who are friends with neither L nor A = 30 - 27 = 3

Hence, 'option 2' is the correct answer.

The correct answer is Champaran Satyagraha.

Key Points

• Champaran Satyagraha was inspired by Mahatma Gandhi against the forced cultivation of indigo.
• The Champaran Satyagraha of 1917 was the first Satyagraha movement led by Mahatma Gandhi in British India and is considered a historically important rebellion in the Indian independence movement.
• It was a farmer's uprising that took place in the Champaran district of Bihar in the Indian subcontinent, during the British colonial period.
• The farmers were protesting against having to grow indigo with barely any payment for it.
• When Gandhi returned to India from South Africa in 1915 and saw peasants in Northern India oppressed by Indigo planters, he tried to use the same methods that he had used in South Africa to organize mass uprisings by people to protest against injustice.
• Champaran Satyagraha was the first popular satyagraha movement.

Additional Information

• Munda Rebellion is one of the prominent 19^th century tribal rebellions in the subcontinent.
• Birsa Munda led this movement in the region south of Ranchi in 1899-1900.
• The Mundas traditionally enjoyed a preferential rent rate as the khuntkattidar or the original clearer of the forest.
• But in course of the 19^th century, they had seen this khuntkatti land system being eroded by the jagirdars and thikadars coming as merchants and moneylenders.
• The non-cooperation movement was a political campaign launched in 1920, by Mahatma Gandhi to have Indians revoke their cooperation from the British government, with the aim of inducing the British to grant self-governance.
• The Salt March, also known as the Salt Satyagraha, Dandi March, and the Dandi Satyagraha, was an act of nonviolent civil disobedience in colonial India led by Mahatma Gandhi.
• The twenty-four-day march lasted from 12 March 1930 to 6 April 1930 as a direct action campaign of tax resistance and nonviolent protest against the British salt monopoly.
• Another reason for this march was that the Civil Disobedience Movement needed a strong inauguration that would inspire more people to follow Gandhi's example.

The correct answer is Shashi Tharoor.

Key Points

• The book, 'Why I am Hindu' was written by Shashi Tharoor.
• Why I Am a Hindu is a 2018 book by Indian politician Shashi Tharoor.
• In the book, he wrote about the history of Hinduism and its core tenets, as well as socio-cultural developments in India that relate to the religion, while elucidating his own religious convictions.
• Shashi Tharoor is an Indian former international diplomat, politician, writer, and public intellectual who has been serving as Member of Parliament, Lok Sabha from Thiruvananthapuram, Kerala, since 2009.
• He was formerly Under-Secretary-General of the United Nations and ran for the post of Secretary-General in 2006.
• He also serves as Chairman of the Parliamentary Standing Committee on Information Technology and All India Professionals Congress.
• He formerly served as Chairman of the Parliamentary Standing Committee on External Affairs (2014 to 2019).
• In 2019, Shashi Tharoor received the Sahitya Academy Award for his book An Era of Darkness in a non-fiction category in the English language.

Additional Information

• Manmohan Singh is an Indian economist, academic, and politician who served as the 13^th Prime Minister of India from 2004 to 2014.
• He is also the longest-serving Prime Minister after Jawaharlal Nehru and Indira Gandhi.
• Books:  Prime Minister Manmohan Singh: June 2005 to May 2006, India's Export Trends & Prospects for Self-Sustained Growth in 1964.
• Atal Bihari Vajpayee was an Indian politician who served three terms as the prime minister of India, first for a term of 13 days in 1996, then for a period of 13 months from 1998 to 1999, followed by a full term from 1999 to 2004.
• Vajpayee was one of the co-founders and a senior leader of the Bharatiya Janata Party.
• Books: National Integration - 1961, India's Foreign Policy: New Dimensions - 1977, Dynamics of an Open Society - 1977, Assam Problem: Repression no Solution - 1981, Atal Bihari Vaj Mem Tina Dasaka - 1992, Kucha Lekha, Kucha Bhashana - 1996
• Narendra Damodardas Modi is an Indian politician serving as the 14^th and current prime minister of India since 2014.
• He was the chief minister of Gujarat from 2001 to 2014 and is a Member of Parliament from Varanasi.
• Sakshi Bhaav's book literally means 'the witness state' which is a collection of poems.
• It was originally a diary written by PM Modi Ji when he was 36.
• These poems are free-flowing his dialogues with the mother goddess.

The correct answer is Womesh Chandra Banerjee.

Key Points

• Womesh Chandra Banerjee was the first president of the Indian National Congress.
• Womesh Chandra Bannerjee (or Umesh Chandra Banerjee by current English orthography of Bengali names) (29 December 1844 – 21 July 1906) was an Indian barrister.
• He was the co-founder and first president of the Indian National Congress.
• Born in 1844 at Calcutta he studied at the Oriental Seminary and the Hindu School.
• His career began in 1862 when he joined the firm of W. P. Gillanders, attorneys of the Calcutta Supreme Court, as a clerk where he acquired a knowledge of the law.
• In 1864 he was sent to England where he joined the Middle Temple and was called to the Bar in June 1867.
• He presided over the first session of the Indian National Congress held at Bombay in 1885 from 28 to 31 December.
• He was the president of the Indian National Congress again in the 1892 session in Allahabad where he denounced the position that India had to prove for the worthiness of political freedom.

Additional Information

• Annie Besant was a British socialist, theosophist, women's rights activist, writer, orator, educationist, and philanthropist.
• Regarded as a champion of human freedom, she was an ardent supporter of both Irish and Indian self-rule.
• She was the first Non-Indian Women President of the Indian National Congress.
• Jivatram Bhagwandas Kripalani, popularly known as Acharya Kripalani, was an Indian politician, noted particularly for holding the presidency of the Indian National Congress during the transfer of power in 1947 and the husband of Sucheta Kripalani.
• Jawaharlal Nehru was an Indian anti-colonial nationalist, secular humanist, social democrat, and author who was a central figure in India during the middle of the 20^th century.
• Nehru was a principal leader of the Indian nationalist movement in the 1930s and 1940s.
• He wrote the famous book "The Discovery of India".

Given

Vikas completes a job = 15 days

Bablu completes a job = 10 days

Concept

first find the total work and then the efficiency of each person.

work = efficiency × time

Calculation

let the total work is 30 units. 

L.C.M of 15 and 10

Vikas complete work in one day = 30/15

⇒ 2 units

Bablu complete work in 1 day = 30/10

⇒ 3 units

Vikas and Bablu complete work in 1 day = 2 + 3 

⇒ 5 units

Total days taken by Vikas abd Bablu to complete a work = 30/5

⇒ 6 days.

∴ They complete the job in 6 days if work together.

The correct answer is 41^st Native Infantry.

Key Points

• 41^st Native Infantry battalion was involved in the killing of all its white officers in the Revolt of 1857.
• On 29 March 1857 at Barrackpore, Sepoy Mangal Pandey of the 34^th Bengal Native Infantry attacked his officers.
• When his comrades were ordered to restrain him they refused, but they stopped short of joining him in open revolt.
• Although only a handful of sepoys had been involved, the entire regiment was disbanded in disgrace.
• Sepoys elsewhere thought this too harsh a punishment.
• The Mutiny proper began at Meerut on 10 May 1857.
• Eighty-five members of the 3^rd Bengal Light Cavalry, who had been jailed for refusing to use cartridges they believed to be at odds with their religion, were broken out of prison by their comrades.
• They ransacked the nearby military station and killed any Europeans they could find.

Additional Information

• The immediate cause of the Sepoy Mutiny of 1857 was the introduction of greased cartridges that were supplied to the soldiers for the New Enfield Rifles.
• A rumour spread that the cartridges of the new enfield rifles were greased with the fat of cows and pigs.
• Before loading these rifles the sepoys had to bite off the paper on the cartridges. Both Hindu and Muslim sepoys refused to use them.
• The political causes of the revolt were the British policy of expansion through the Doctrine of Lapse and direct annexation.
• The abolition of practices like sati and female infanticide, and the legislation legalizing widow remarriage, was believed as threats to the established social structure.
• Introducing western methods of education was directly challenging the orthodoxy for Hindus as well as Muslims.
• After the Industrial Revolution in England, there was an influx of British manufactured goods into India, which ruined industries, particularly the textile industry of India.

Given

15 – (6 + 6 × 6) ÷ (2 + 5)

Concept

BODMAS

Calculation

15 – (6 + 6 × 6) ÷ (2 + 5)

⇒ 15 - (6 + 36) × (1/7)

⇒ 15 - 42 × (1/7)

⇒ 15 - 6

⇒ 9

∴ The value of 15 – (6 + 6 × 6) ÷ (2 + 5) is 9

Given

x + y = 5 and xy = 6

Formula used

(x + y)³ = x³ + y³ + 3xy(x + y)

Calculation

x + y = 5 

cube on both sides

(x + y)³ = (5)³

⇒ x³ + y³ + 3xy(x + y) = 125

⇒ x³ + y³ + 3 × 6 × 5 = 125

⇒ x³ + y³ + 90 = 125

⇒ x³ + y³ = 125 - 90

⇒ x³ + y³ = 35

∴ The value of x³ + y³ is 35.

The correct answer is Gulzarilal Nanda.

Key Points

• Gulzarilal Nanda was the first and only acting PM of India.
• Gulzarilal Nanda BR was an Indian politician and economist who specialized in labor issues.
• He was the Interim Prime Minister of India for twice 13-day stints following the deaths of Jawaharlal Nehru in 1964 and Lal Bahadur Shastri in 1966 respectively.
• Both his terms ended after the ruling Indian National Congress's parliamentary party elected a new prime minister.
• He was awarded the Bharat Ratna, India's highest civilian award, in 1997.

Additional Information

• Haradanahalli Doddegowda Deve Gowda is an Indian politician from the state of Karnataka.
• He served as the 11^th prime minister of India from 1 June 1996 to 21 April 1997.
• He was previously the 14^th Chief Minister of Karnataka from 1994 to 1996.
• Vishwanath Pratap Singh, shortened to V. P. Singh, was an Indian politician who was the 7^th Prime Minister of India from 1989 to 1990 and the 41^st Raja Bahadur of Manda.
• He is India's only prime minister to have been former royalty.
• He was educated at Allahabad University and Pune University.
• Inder Kumar Gujral was an Indian diplomat, politician, and freedom activist who served as the 12^th prime minister of India from April 1997 to March 1998.
• Born in Punjab, he was influenced by nationalistic ideas as a student and joined the All India Students Federation and the Communist Party of India.

Given

Height of lighthouse = 81 m

Angle of elevation = 45° and 60°

Formula used

tan A = side opposite to A/side adjacent to A

tan 45° = 1

tan 60° = √3

Calculation

let AD is the lighthouse which is 81 m high. ∠B = 45°  and ∠C = 60°

distance between two ships are (x + y)

In triangle ABD

tan 45° = AD/BD

⇒ 1 = 81/x

⇒ x = 81

tan 60° = 81/y

⇒ √3 = 81/y

⇒ y = 81/√ 3

x + y = 81 + (81/√3)

⇒ x + y = (81√ 3 + 81)/(√ 3)

⇒ x + y = 81(√3 + 1)/√ 3

∴ Distance between two ships are 81[(√3 +1)]/√3.

Given

Height of observer = 2 m

Distance between observer and tower = 150√3 m

Angle of elevation from the eye of an observer = 60° 

Concept

tan A = Side  opposite of A/Side adjacent to A

tan 60° = √ 3

Calculation

Let the DC  is the height of the observer which is 2 m. AB is the height of the tower. ∠D is the angle of elevation from the eye of the observer towards the top of the tower. BC is the distance between the tower and observer which is 150√3.

In triangle AED

tan 60° = AE/DE

⇒ √3 = x/(150√ 3)

⇒ √3 × 150√3 = x

⇒ 150 × 3 = x

⇒ 450 = x

AB = AE + EB

⇒ AB = 450 + 2

⇒ AB = 452

∴ The height of the tower is 452 m

The correct answer is Haemoglobin.

Key Points

• Hemoglobin is a pigment present in human blood that carries oxygen from our lungs to all parts of the body.
• RBCs contain hemoglobin a protein that carries oxygen.
• Blood gets its bright red color when hemoglobin picks up oxygen in the lungs.
• As the blood travels through the body, the hemoglobin releases oxygen to the different body parts.
• Each RBC lives for about 4 months.
• Hemoglobin in the blood carries oxygen from the respiratory organs (e.g. lungs or gills) to the rest of the body (i.e. tissues).
• There it releases the oxygen to permit aerobic respiration to provide energy to power functions of an organism in the process called metabolism.
• A healthy individual human has 12 to 20 grams of hemoglobin in every 100 mL of blood.
• In mammals, the chromoprotein makes up about 96% of the red blood cell's dry content (by weight), and around 35% of the total content (including water).
• Hemoglobin has an oxygen-binding capacity of 1.34 mL O2 per gram, which increases the total blood oxygen capacity seventy-fold compared to dissolved oxygen in the blood.

Additional Information

• White blood cells are part of the body's immune system.
• They help the body fight infection and other diseases.
• Types of white blood cells are granulocytes (neutrophils, eosinophils, and basophils), monocytes, and lymphocytes (T cells and B cells).
• A platelet count is a lab test to measure how many platelets you have in your blood.
• Platelets are parts of the blood that help the blood clot.
• They are smaller than red or white blood cells.
• A platelet count is a lab test to measure how many platelets you have in your blood.
• Platelets are parts of the blood that help the blood clot.
• They are smaller than red or white blood cells.
• Lymph is the fluid that flows through the lymphatic system, a system composed of lymph vessels and intervening lymph nodes whose function, as the venous system, is to return fluid from the tissues to the central circulation.

The correct answer is 1853.

Key Points

• In 1853 the Railway was introduced by the British in India for passengers.
• The history of Indian Railways dates back to over 160 years ago.
• On 16^th April 1853, the first passenger train ran between Bori Bunder (Bombay) and Thane, a distance of 34 km.
• It was operated by three locomotives, named Sahib, Sultan, and Sindh, and had thirteen carriages.

Additional Information

• On 8 May 1845, the Madras Railway was incorporated, followed that year by the East India Railway.
• On 1 August 1849, the Great Indian Peninsular Railway was incorporated by an act of parliament.
• The "guarantee system", providing free land and a guaranteed five-percent rate of return to private British companies willing to build railways was finalized on 17 August 1849. In 1851, the Solani Aqueduct Railway was built in Roorkee.
• It was hauled by the Thomason steam locomotive, named after a British officer-in-charge of that name.
• The railway transported construction materials for an aqueduct over the Solani River.
• In 1852, the Madras Guaranteed Railway Company was incorporated.

The correct answer is Wikipedia.

Key Points

• Wikipedia is NOT a web browser.
• Wikipedia is a free online encyclopedia, created and edited by volunteers around the world and hosted by the Wikimedia Foundation.
• A web browser (also referred to as an Internet browser or simply a browser) is application software for accessing the World Wide Web or a local website.
• When a user requests a web page from a particular website, the web browser retrieves the necessary content from a web server and then displays the page on the user's device.
• A web browser is not the same thing as a search engine, though the two are often confused.
• A search engine is a website that provides links to other websites. However, to connect to a website's server and display its web pages, a user must have a web browser installed.
• Web browsers are used on a range of devices, including desktops, laptops, tablets, and smartphones.
• In 2020, an estimated 4.9 billion people used a browser.
• The most used browser is Google Chrome, with a 63% global market share on all devices, followed by Safari with 20%.

Additional Information

• Opera is a multi-platform web browser developed by its namesake company Opera. Opera is a Chromium-based browser.
• It distinguishes itself from other browsers through its user interface and other features.
• Google Chrome is a cross-platform web browser developed by Google.
• It was first released in 2008 for Microsoft Windows, built with free software components from Apple WebKit and Mozilla Firefox.
• It was later ported to Linux, macOS, iOS, and Android, where it is the default browser.
• Mozilla Firefox, or simply Firefox, is a free and open-source web browser developed by the Mozilla Foundation and its subsidiary, the Mozilla Corporation.
• Firefox uses the Gecko rendering engine to display web pages, which implements current and anticipated web standards.

The correct answer is 1765.

Key Points

• In 1765 did the East India Company acquire 'Diwani' rights over Bengal and Bihar.
• The Mughal Emperor Shah Alam II granted the Diwani of Bengal, Bihar, and Orissa to the East India Company in 1765.
• The Treaty of Allahabad was signed on 16 August 1765, between the Mughal Emperor Shah Alam II, son of the late Emperor Alamgir II, and Robert Clive, of the East India Company, in the aftermath of the Battle of Buxar of 23 October 1764.
• The treaty was handwritten by I'tisam-ud-Din, a Bengali Muslim scribe and diplomat to the Mughal Empire.
• The Treaty marked the political and constitutional involvement and the beginning of British rule in India.
• Based on the terms of the agreement, Alam granted the East India Company Diwani rights, or the right to collect taxes on behalf of the Emperor from the eastern province of Bengal-Bihar-Orissa.
• These rights allowed the company to collect revenue directly from the people of Bengal, Bihar, and Orissa.
• In return, the Company paid an annual tribute of twenty-six lakhs of rupees (equal to 260,000 pounds sterling) while securing for Shah Alam II the districts of Kada and Allahabad.
• The tribute money paid to the emperor was for the maintenance of the Emperor's court in Allahabad.

Given

Perimeter of rhombus = 68 cm

One of the diagonal of rhombus = 16 cm

Formula used

Perimeter of rhombus = 2√(diagonal₁)² + (diagonal₂)²

Calculation

68 = 2√(16)² + (diagonal₂)²

⇒ 34 = √256 + (diagonal₂)²

squaring on both sides

⇒ 1156 = 256 + (diagonal₂)²

⇒ 1156 - 256 = (diagonal₂)²

⇒ 900 = (diagonal2)²

⇒ 30 = Diagonal₂

Area of rhombus = (1/2) × diagonal 1 × diagonal 2

⇒ (1/2) × 16 × 30

⇒ 16 × 15

⇒ 240 sq cm

∴ Area of rhombus is 240 sq cm.

The correct answer is South Africa.

Key Points

• The famous 'Zulu' tribe belongs to South Africa.
• Zulu people are a Nguni ethnic group in Southern Africa.
• The Zulu people are the largest ethnic group and nation in South Africa with an estimated 10–12 million people living mainly in the province of KwaZulu-Natal.
• They originated from Nguni communities that took part in the Bantu migrations over millennia.
• As the clans integrated together, the rulership of Shaka brought success to the Zulu nation due to his improved military tactics and organization.
• Zulus take pride in their ceremonies such as the Umhlanga, or Reed Dance, and their various forms of beadwork.
• The art and skill of beadwork take part in the identification of Zulu people and act as a form of communication.
• Today the Zulu people predominantly believe in Christianity but have created a syncretic religion that is combined with the Zulu's prior belief systems.

Additional Information

Given

4 × 5 ÷ 2 – 8 × 7 + 9 – (3 + 2)

Concept

BODMAS

Calculation

4 × 5 ÷ 2 – 8 × 7 + 9 – (3 + 2)

⇒ 4 × 5 × (1/2) - 56 + 9 - 5

⇒ 10 - 56 + 4

⇒ - 46 + 4

⇒ - 42

∴ The value of 4 × 5 ÷ 2 – 8 × 7 + 9 – (3 + 2) is - 42.