RRB NTPC CBT-I Official Paper (Held On: 9 Feb 2021 Shift 2) (Previous Year Paper)

Given: 

cot(A + B).cot(A - B) = 1

Concept Used: 

tan (A + B) = $\frac{ tan(A) + tan(B)}{1 - tan(A) tan(B)}$

tan (A – B) = $\frac{ tan(A) - tan(B)}{1 + tan(A) tan(B)}$

Calculation: 

⇒ We have,

⇒ cot(A + B).cot(A – B) = 1

⇒ tan(A + B) . tan(A – B) = 1

⇒ Expanding the terms with the help of formula, we get

⇒ $\frac{ tan(A) + tan(B)}{1 - tan(A) tan(B)}$ × $\frac{ tan(A) - tan(B)}{1 + tan(A) tan(B)}$ = 1

⇒ $\frac{ tan^2(A) - tan^2(B)}{1 - tan^2(A) tan^2(B)}$ = 1

⇒  tan²(A) – tan²(B) = 1 – tan2(A) tan2(B)

⇒ tan2(A) + tan2(A) tan2(B) – tan2(B) – 1 = 0 

⇒ tan2(A) (1 + tan2(B)) – 1(1 + tan2(B)) = 0

⇒ (tan2(A) – 1) (1 + tan2(B)) = 0

⇒ tan2(A) = 1 or tan2(B) = –1

⇒ tan²(x) can not be negative.

⇒ So, we will consider, tan2(A) = 1

⇒ A = $\frac {\pi}{4}$

⇒ Now, cot ($\frac {2 A}{3}$)

⇒ cot ($\frac {2}{3}$ x $\frac {\pi}{4}$)

⇒ cot ($\frac {1}{3}$ x $\frac {\pi}{2}$)

⇒ cot ($\frac {\pi}{6}$) = $\sqrt3$

Therefore, the value of cot ($\frac {2 A}{3}$) is $\sqrt {3}$

The positional values of the English alphabet is as follows:

The pattern followed here is:

SPIDER is written as RNHBDP

QUESTION will be written as:

Hence, 'option 1' is the correct answer.

Given: 

a + b + c = 8

b > 0, c > 0

Calculation:

To obtain the maximum value of 'a' considering b and c are positive integers greater than zero,

Let b = c = 1

⇒ a + 1 + 1 = 8

⇒ a = 8 - 2 

⇒ a = 6

Given:

Numbers = 3 to 18

Concept used:

Sum of squares of n natural numbers = $\frac{n (n+1)(2n+1)}{6}$

Calculation:

⇒ Sum of squares of numbers from 1 to 18 = $\frac{18 (18+1)(2(18)+1)}{6}$

⇒  $\frac{18\times 19\times 37}{6}=\frac{12654}{6}=2109$

⇒ Sum of squares of numbers from 1 to 18 = 2109

⇒ Now, Sum of squares of numbers from 3 to 18 = Sum of squares of numbers from 1 to 18 – (1² + 2²)

⇒ 2109 – 5 = 2104

Therefore, the sum of squares of numbers from 3 to 18 is 2104

Given:

$\sqrt{2}$ sin (5x – 5)° = tan 45°

Calculation:

⇒ As, tan 45º = 1

⇒ $\sqrt{2}$ sin (5x – 5)° = 1

⇒  sin (5x – 5)° = $\frac{1}{\sqrt{2}}$

⇒ As, sin 45º = $\frac{1}{\sqrt{2}}$,

⇒ sin (5x – 5)° = sin 45º

⇒ Equating both, we get

⇒ 5x – 5 = 45

⇒ 5x = 50

⇒ x = 10º

Therefore, the value of x is 10º

Correct answer is 1920.

Key Points

• Noncooperation was accepted to by the Indian National Congress at Calcutta in September 1920 and started that December.
• The movement was actually a peaceful and non-violent protest against the British government in India.
• Indians were asked to give up their titles and leave from nominated seats in the local bodies as a mark of protest.
• Middle class people mainly take part in non cooperation movement in towns.

Additional Information

• Civil disobedience, also known as passive resistance, the refusal to obey the demands or commands of a government or occupying power, without resorting to violence or active measures of opposition​.
• Gandhi organised Kheda movement to support farmers of the Kheda district.
• The Champaran Satyagraha is considered to be a important event in the history of India's freedom struggle.

From the given information, we can draw a table:

Hardeep, Jagjeet and Rohan are honest. Kamal, Jagjeet, and Gaurav are ambitious. Rohan, Jagjeet and Kamal hard-working. Gaurav, Hardeep, and Kamal are intelligent.

From the table, we can see that Hardeep is neither ambitious nor hard-working.

Hence the correct answer is option 1)

Given: 

Product of LCM and HCF of two positive numbers = 36

Difference between two numbers = 5

Concept Used:

LCM (a, b) × HCF (a, b) = a × b

Calculation: 

⇒ Let the two positive numbers be a and b.

⇒ LCM × HCF = 36 and b – a = 5

⇒ According to the formula,

⇒ 36 = a × b                → (1)

⇒ Also b – a = 5, can be written as b = 5 + a.

⇒ Substituting b = 5 + a in (1), we get

⇒ 36 = a × (5 + a)

⇒ 36 = 5a + a²

⇒ a² + 5a – 36 = 0

⇒ a² + 9a – 4a – 36 = 0

⇒ a(a + 9) – 4(a + 9) = 0

⇒ (a + 9)(a – 4) = 0

⇒ a + 9 = 0 and a – 4 = 0

⇒ a = –9 (Not possible because a is positive number)

⇒ So, a = 4

⇒ Substitute, a = 4 in (1) we get

⇒ 36 = 4 × b

⇒ b = $\frac{36}{4}=9$

Therefore, the two positive numbers are 4 and 9

Given:

LCM of two numbers = 26 times the HCF of two numbers

HCF + LCM = 729

One number = 81

Concept Used:

LCM (a, b) × HCF (a, b) = a × b

Calculation:

⇒ Let the two numbers be a and b 

⇒ LCM (a, b) = 26 HCF (a, b) 

⇒ HCF (a, b) + LCM (a, b) = 729           → (1)

⇒ Now substitute LCM (a, b) with 26 HCF (a, b) in (1), we get 

⇒ HCF (a, b) + 26 HCF (a, b) = 729      → (2)

⇒ 27 × HCF (a, b) = 729

⇒ HCF (a, b) = $\frac{729}{27}$

⇒ HCF (a, b) = 27

⇒ Now substitute this value in (2), we get

⇒ 27 + LCM (a, b) = 729

⇒ LCM (a, b) = 729 – 27

⇒ LCM (a, b) = 702

⇒ Substitute LCM(a, b), HCF(a, b) and one number in LCM (a, b) × HCF (a, b) = a × b, we get 

⇒ 702 × 27 = 81 × b

⇒ 18954 = 81 × b

⇒ b = $\frac{18954}{81}=234$

Therefore, the other number is 234

Given: 

Total number of students in a school = 500

Boys : Girls = 7 : 3

New girls enrolled in the school = 120

Concept Used:

Total number of students in a school = Total number of boys + Total number of Girls

Calculation:

⇒ Let the total number of boys =  $7x$

⇒ So, the total number of girls = $3x$

⇒ Total number of students in a school = 500

⇒ Boys + Girls = 500

⇒ $7x+3x=500$

⇒ $10x = 500$

⇒ $x = \frac{500}{10}$

⇒ $x=50$

⇒ Substitute $x=50$ to get total number of boys and girls,

⇒ Total number of Boys = $7 \times 50 = 350$ 

⇒ Total number of Girls = $3 \times 50=150$

⇒ If 120 new girls enrolled then the total number of girls becomes, $150+120 = 270$

⇒ The ratio of boys to that of girls is, $350 : 270$ 

⇒ $350:270= \frac{350}{270}$

⇒ $\frac{350}{270}=\frac{35}{27}$

⇒\() \(\frac{35}{27}=35:27\)

Therefore, the ratio of boys to that of girls is 35 : 27

Correct answer is The Preamble of the Constitution.

Key Points

• The Preamble of the constitution establishes India as a Secular State.
• The meaning of a secular state is that it does not prioritize any one religion for the country and its people.
• The word 'Secular' was attached by the Constitution Act, 1976.
• India is known as a secular state because it does not have any state religion and people are free to practice any religion of their choice.

Additional Information

• Directive Principles of State Policy motive to create social and economic conditions under which the citizens can guide a good life.
• Article 44 of the constitution looks for the Indian state to apply directive principles and common law for all Indian citizens while formulating national policies.
• Article 475, delivery to commanding officers of persons liable to be tried by Court-martial.​

The logic followed here is,

Paisa : Rupee

⇒ 1 Rupee = 100 Paise

Similarly,

Kilogram : Quintal

⇒ 1 Quintal = 100 Kilogram

Hence, 'option 1' is the correct answer.

Correct answer is Electronic Voting Machine.

Key Points

• Electronic voting machines (EVM) help to record votes.
• The Indian electronic voting machine (EVM) was developed in 1989 by the Election Commission of India.
• EVM supports provide the basis to assess work progress against a baseline plan, relate technical, time and cost performance.
• The chief cause is EVM requires a bottom-up approach to defining the full scope of work by using a "deliverable-oriented" WBS focused on end products.

Additional Information

• The election commission has the right to permit marks to the political parties.
• It gives identification to the national parties, state parties, and regional parties.
• It sets limitations on poll expenses. ​
• The commission produces electoral rolls and updates the voter's list from time to time.

Correct answer is WTO.

Key Points

• The World Trade Organization (WTO) is an international organization of 164 members that manage the rules of trade between nations.
• The WTO has over 160 members representing 98 per cent of world trade.
• WTO cheif work is to ensure that trade flows as smoothly, predictably and freely as possible.
• The World Trade Organisation was started on January 1, 1995, with the Marrakesh Agreement, which put back the General Agreement on Tariffs and Trade.

Additional Information

• ​The International Monetary Fund (IMF) works to achieve sustainable growth and prosperity for all of its 190 member countries.
• The World Health Organization is an international organization that is a member of the United Nations and helps developing countries by giving them information and medicine.
• India is a originater member of the International Labour Organization, which came alive in 1919.

The positional values of the English alphabet are as follows:

The pattern followed here is:

LOVE is written as NQXG

Similarly, SWEET will be written as:

Hence, 'option 3' is the correct answer.

Correct answer is Airports Authority of India.

Key Points

• The Directorate General of Civil Aviation (DGCA) is the regulatory body in the field of Civil Aviation, primarily dealing with safety issues.
• It is in charge of regulation of air transport services of India.
• The first Indian airline, Tata Sons Ltd., began a regular airmail service between Karachi and Madras without any patronage from the government in 1915.
• 'Air India'  came into being when Tata Airlines changed its name to Air India in 1946.

Additional Information

• The Airports Authority of India, or AAI, is a statutory body, under the ownership of the **Ministry of Civil Aviation, Government of India.**​
• It is responsible for creating, upgrading, maintaining, and managing civil aviation infrastructure in India.
• AAI manages a total of 137 airports which include 24 International airports (3 Civil Enclaves), 10 Customs Airports (4 Civil Enclaves), and 103 Domestic airports (23 Civil Enclaves).

Correct answer is Kapil Dev.

Key Points

• As reffered ahead, India played under the captaincy of Kapil Dev in the 1983 Cricket World Cup.
• Dev was be one of best all-rounders of that era, and he played 225 ODI matches in his career.
• He picked up 253 wickets and scored 3,783 runs.
• Kapil Dev-led India win maiden World Cup trophy in 1983.

Additional Information

• Mohinder Amarnath Bhardwaj is an Indian former cricketer,current cricket analyst and actor.​
• Sunil Manohar Gavaskar is an Indian cricket commentator and former cricketer who represented India and Bombay from 1971 to 1987.
• Ravishankar Jayadritha Shastri is the former cheif coach of the India national cricket team, a cricket commentator and former captain of Indian Cricket Team.

Given:

Time taken to cover certain distance = 13 hours

For the first half the speed = 7 km/hr

For the second half the speed = 6 km/hr

Concept Used:

 $Time = \frac{Distance}{Speed }$

Calculation:

⇒ Let the total distance be $2x$ km.

⇒ For the first half, time taken = $\frac{x}{7}$ hr

⇒ For the second half, time taken = $\frac{x}{6}$ hr

⇒ Total time taken = 13 hr

⇒ $\frac{x}{7}+\frac{x}{6}=13$

⇒ $\frac{6x+7x}{42}=13$

⇒ $\frac{13x}{42}=13$ 

⇒ $x=\frac{13 \times 42}{13}$

⇒ $x=42 km$

⇒ The total distance = $2x=2\times42\ km$

⇒ Total distance = $84 \ km$

Therefore, the total distance is 84 km.

Correct answer is Indefinite detention without trial and censorship of the press.

Key Points

• Rowlatt Acts, (February 1919), legislation proceeded by the Imperial Legislative Council, the legislature of British India.
• The acts allowed definite political cases to be tried without juries and permitted internment of suspects without trial.
• The Rowlatt Act was proceeded by the British government to grow their grasp on power over the common folk.
• This act allow the British government to arrest anybody suspected of terrorist activities.

Additional Information

• Employing 'lathi charge' to crush protests and demonstrations has been inherited from the legal structure used by the colonial police.
• All kinds of goods which are prohibited from import under the Foreign Trade (Development and Regulation) Act, 1992 are banned for imported into India.​

Given:

A woman borrowed some money on simple interest for 4 years.

Returned amount = $\frac{6}{5} \times$ Money borrowed

Concept Used:

Amount = Principal + Interest

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

Calculation:

⇒ Let the principal be Rs.100

⇒ Interest = Amount – Principal 

⇒ Interest =  $\frac{6}{5}\times100-100$

⇒ Interest = $120-100=20$

⇒ Now substituting the values in SI formula, we get

⇒ $20=\frac{100\times4\times r}{100}$

⇒ $20=4\times r$

⇒ $r=\frac{20}{4}=5$

Therefore, rate of interest for the money borrowed by a women is 5% p.a.

Correct answer is MOM.

Key Points

• The Mars Orbiter Mission (MOM) or Mangalyaan, is a space investigation started by the Indian Space Research Organization on November 5, 2013.
• Mangalyaan was India's first interplanetary mission.
• The primitively-built space investigation has been in the Martian orbit since September 24, 2014.
• It was profitably started by the Polar Satellite Launch Vehicle (PSLV) C-25 from the Satish Dhawan Space Center in Sriharikota, Andhra Pradesh.

Additional Information

• Chandrayaan-1, India's first mission to Moon, was started profitably on October 22, 2008, from SDSC SHAR, Sriharikota.​
• GSAT-31 is a high-production telecommunication satellite started by the Indian Space Research Organisation (ISRO).
• ASTROSAT is India's first devoted multi-wavelength space observatory.

Family chart:

According to the statement, the family tree is drawn below,

Vishal is father-in-law of Radhika.

Hence, 'option 1' is the correct answer.

Given:

Speed of Ravi = 80 km/h

Speed of Mohan = 40 km/h

Time = 15 min

Formula Used:

Speed = $\frac{Distance}{ Time}$

Calculation:

⇒ Firstly, convert the time from 15 min to hours by dividing by 60,

⇒ 15 min = $\frac{15}{60}=0.25$ hour

⇒ Distance covered by Ravi = 80 × 0.25 = 20 km

⇒ Distance covered by Mohan = 40 × 0.25 = 10 km

⇒ Distance between Ravi and Mohan after 15 min = 20 + 10 = 30 km

Therefore, the distance between Ravi and Mohan after 15 min is 30 km.

Correct answer is Kinetic energy.

Key Points

• Wind turbines change the kinetic energy in the wind into mechanical power.
• Kinetic energy is a form of energy that an object or a particle has by reason of its motion.
• Any object in motion is using kinetic energy.
• The units of kinetic energy are mass times the square of the speed, or kg · m 2 /s 2 kg · m 2 /s 2 .

Additional Information

• Thermal energy mentions to the movement of molecules inside an object or substance.
• Heat is the form of energy that is transferred between systems or objects with unlike temperatures.
• Hydroelectric energy is a form of sustainable energy that uses the power of moving water to generate electricity.​

Correct answer is Odisha.

Key Points

• The 5,569-square kilometre Similipal Biosphere Reserve is Odisha's first such reserve and was notified on May 20, 1996.
• Simlipal bio-reserve is located in the district of Mayurbhanj in Odisha state.
• Similipal Biosphere Reserve deliberates to encourage the conservation of biodiversity and as well to promote alternate livelihood for man and preserve cultural values.

Additional Information

• The total count of Conservation reserves in Rajasthan is 14.
• The Ranthambore National Park is one of the largest and principal national parks in the country.
• Hastinapur Wildlife Sanctuary is a secured area in the Gangetic plains of Uttar Pradesh, India.
• Noradehi is the largest of all the wildlife sanctuaries in Madhya Pradesh.​

Let's check each option and identify which one is different from the rest:

1) Snakes : Hiss

⇒ Hiss is a sound made by snake.

2) Birds : Chirp

⇒ Chirp is a sound made by birds.

3) Dogs : Coop

⇒ Coop is a shelter name of hens. It is not the sound made by dog.

4) Lion : Roar

⇒ Roar is the sound made by lion.

Hence, 'option 3' is the correct answer.

Correct answer is Uttar Pradesh.

Key Points

• Uttar Pradesh is the state which reports a maximum or more than one-third of sugarcane production.
• Uttar Pradesh is India's largest sugarcane-producing state, producing above 177 million tonnes in 2021.
• Some other states as well produce sugarcane in large quantities.
• Uttar Pradesh, the chief producer of sugarcane in India, is known as the 'Sugar Bowl' of India.

Additional Information

• Haryana is mainly an agricultural economy with the prevalence of wheat, rice, bajra, mustard, sugarcane, and cotton.
• Punjab state continues to be one of the largest producers of food grains and cash crops in the country.​
• Bihar is the largest producer of Litchi, Makhana, Guava, and Lady's finger in India.

Given:

Speed of first woman = 6 km/h

Speed of second woman = 8 km/h \()

Time taken by first woman = 40 min + Time taken by the second woman

Concept Used:

Time = $\frac{Distance }{ Speed}$

Calculation:

⇒ Let the distance be x km/hr.

⇒ Time taken for the first woman = $\frac{x}{6}\ hr$

⇒ Time taken for the second woman = $\frac{x}{8}\ hr$

⇒ Time taken by first woman = 40 min + Time taken by second woman 

⇒ So, firstly change minutes into hours,

⇒ $40\ min=\frac{40}{60} \ hr$

⇒ $\frac{x}{6}=\frac{40}{60}+\frac{x}{8}$

⇒ $\frac{x}{6} - \frac{x}{8}=\frac{40}{60}$

⇒ $\frac{8x-6x}{48}=\frac{2}{3}$

 ⇒ $\frac{2x}{48}=\frac{2}{3}$

⇒ $x= \frac{2\times48}{3 \times2}$

⇒ $x=\frac{96}{6}$

⇒ x = 16 km

Therefore, the distance covered by the two women is 16 km.

BODMAS Rule:

Let us decode the symbols:

1) 20 × 12 + 4 ÷ 3 - 2 = 12

After replacing the mathematical symbols, we get:

⇒ 20 - 12 ÷ 4 + 3 × 2

⇒ 20 - 3 + 3 × 2

⇒ 20 - 3 + 6

⇒ 26 - 3 = 23 ≠ 12

2) 20 × 12 + 6 ÷ 5 - 2 = 12

After replacing the mathematical symbols, we get:

⇒ 20 - 12 ÷ 6 + 5 × 2 

⇒ 20 - 2 + 5 × 2 

⇒ 20 - 2 + 10

⇒ 30 - 2 = 28 ≠ 12

3) 18 × 12 + 6 ÷ 3 - 2 = 12

After replacing the mathematical symbols, we get:

⇒ 18 - 12 ÷ 6 + 3 × 2 

⇒ 18 - 2 + 3 × 2 

⇒ 18 - 2 + 6

⇒ 24 - 2 = 22 ≠ 12

4) 20 ÷ 12 + 6 × 5 - 2 = 12 

After replacing the mathematical symbols, we get:

⇒ 20 + 12 ÷ 6 - 5 × 2 

⇒ 20 + 2 - 5 × 2 

⇒ 20 + 2 - 10

⇒ 22 - 10 = 12 = 12

L.H.S = R.H.S

Hence, 'option 4' is the correct answer.

Correct answer is Xylem tissue.

Key Points

• Water and solutes are moved by the xylem from the roots to the leaves.
• The xylem distributes water and dissolved minerals upward through the plant, from the roots to the leaves.
• Xylem cells form the crucial part of a mature woody stem or root.
• The xylem is located towards the adaxial surface of the leaf.

Additional Information

• The phloem is in charge of the transport and distribution of sugars produced by photosynthesis.​
• Collenchyma helps to provide strength to the plant's stems, branches, leaves, and other structures.
• The chief work of parenchyma is to store and assimilate food.

Given:

Running speed of horse = 40 km/hr

Time taken to cover its distance = 3 hr

And time taken to cover obtained distance = $2\frac{1}{2}hr$

Concept Used:

Distance = Speed × Time

Calculation:

⇒ First to find the distance, 

⇒ Distance = 40 × 3 = 120 km

⇒ Now to find the speed the horse should run to cover a distance of 120 km in $2\frac{1}{2}hrs$,

⇒ Speed = $\frac{Distance }{ Time}$

⇒ Speed =  $\frac{120}{\frac{5}{2}}=\frac{120\times 2}{5}$

⇒ Speed = 24 × 2 = 48 km/h

Therefore, the horse should run at 48 km/hr speed to cover a distance of 120 km in $2\frac{1}{2}\ hrs$.

Given:

Four angles of a pentagon = 70°, 110°, 135°, and 95°

Concept Used:

Sum of the Measure of Interior Angles of a Polygon = (n - 2) × 180° 

Where, n = number of sides of the polygon

∴ Sum of all five angles of the pentagon = 540º

Calculation:

⇒ Sum of four angles of a pentagon = 70 + 110 + 135 + 95 = 410º

⇒ According to the formula,

⇒ Fifth angle of a pentagon = 540 – 410 = 130º

Therefore, the measure of the fifth angle of the pentagon is 130º.

Given:

Reduction in the price of an article = 15%

Increase in the sale = 25%

Calculation:

⇒ Let the price of an article be Rs x and sales be y.

⇒ Total Revenue = xy

⇒ Price of an article after reduction = $x-\frac{15}{100}\times x$

⇒ Price of an article after reduction = $\frac{20x-3x}{20}=\frac{17x}{20}$

⇒ Sales after increase = $y+\frac{25}{100}\times y=y+\frac{y}{4}$

⇒ Sales after increase = $\frac{4y+y}{4}=\frac{5y}{4}$

⇒ Total Revenue after changes = $\frac{17x}{20}\times \frac{5y}{4}=\frac{17xy}{16}$

⇒ Increase in revenue = $\frac{17xy}{16}-xy=\frac{17xy-16xy}{16}=\frac{xy}{16}$

⇒ Net increase in sales = $\frac{\frac{xy}{16}}{xy}\times 100=\frac{100}{16}=6.25\%$

Therefore, the net percentage effect on the daily sale is increase of 6.25%.

Correct answer is Protein.

Key Points

• The main reason for kwashiorkor is not eating sufficient protein or other crucial vitamins and minerals.
• Kwashiorkor is a form of acute malnutrition that happens due to protein deficiency.
• Severe protein deficiency can lead to fluid retention, which can make the stomach look bloated.
• The best treatment to stop malnutrition is to eat a healthy, balanced diet.

Additional Information

• Marasmus is caused by the deficiency of all the nutrients or minerals.
• If a person doesn't get sufficient dietary fat, it could affect the health of his skin and lead to dermatitis.
• Marasmus happens due to a deficiency of carbohydrates, fats, and proteins in the diet, and mainly affects infants below the age of one year.

Correct answer is Morley-Minto Reforms.

Key Points

• Indian Council Act of 1909 is also called as Morley- Minto Reform.
• It was instituted to pacify the Moderates (Congress) and introduce separate electorates on the basis of religion.
• So, Lord Minto came to be famous as the Father of Communal Electorate in India.

Additional Information

• The Wavell Plan was first presented at the Shimla Conference in 1945.​
• Rowlatt's acts authorized definite political cases to be tried without juries and permitted the internment of suspects without trial.
• The Cripps Mission was a failed attempt in late March 1942 by the British government to save full Indian cooperation and support for their efforts in World War II.

Given:

91 × 92 × 93 × ..... × 99

Concept Used:

Logic of 5 and 2 is applied in this problem.

Calculation:

⇒ In this problem logic has been used,

⇒ Since, the number 95 has 5 or 10 as multiples.

⇒ And also here is the number 92 

⇒ So, the number 2 × 5 gives 10

Therefore, the unit digit in the product 91 × 92 × 93 × ..... × 99 is 0

Correct answer is 10.

Key Points

• According to 2011 census, there were 46 million-plus cities in India, with Delhi, Mumbai, and Kolkata having populations above 10 million.
• There are 53 urban agglomerations in India with a population of 1 million or more according to the 2011 census.
• As per the Census of India 2011, the number of Urban Agglomerations in India is 475**.**
• According to the 2011 census, Mumbai is the biggest urban agglomeration in India with a population of 1.84 Crore.

Additional Information

• The population of India according to the 2011 census was 1,210,854,977.
• The population of the nation according to the provisional figures of Census 2011 is 1210.19 million of which 623.7 million (51.54%) are males and 586.46 million (48.46%) are females.
• So, Henry Walter is famous as the father of the Indian Census. ​

Correct answer is Abu Dhabi, UAE.

Key Points

• Special Olympics World Games 2019 was held in Abu Dhabi, Uthe nited Arab Emirates from March 14–21, 2019. ESPN offered international coverage of the games.
• The 2019 Special Olympics World Summer Games was the first Special Olympics games to take place in the Middle East.
• India comes back with a huge tally of 368 medals as the Special Olympics World Games 2019 in Abu Dhabi.
• India produce history in UAE by scooping 85 gold, 154 silver, and 129 bronze.

Additional Information

• The Olympic Games are an international sports festival, held every four years.
• Canada has dispatched athletes to every Winter Olympic Games and nearly every Summer Olympic Games.
• Athens 1896 Olympic Games, athletic festival clasped in Athens that took place April 6–15, 1896.
• When the Olympics came to Tahoe: A look at the 1960 Winter Games. ​

Correct answer is Rio Summit, 1992.

Key Points

• It is a result of the Earth Summit (UN Conference on Environment and Development) held in Rio de Janeiro, Brazil, in 1992.
• Agenda 21 is an action plan regarding sustainable development, but it is non-binding.
• The slogan for Agenda 21 was “think globally and act locally”.
• Agenda 21 sets out a plan of action to guarantee that life in the next millennium will change substantially for the better.

Additional Information

• The United Nations Conference on the Human Environment in Stockholm 1982 Earth Summit in Nairobi (Kenya).​
• The World Summit on Sustainable Development 2002, occurred in South Africa, from 26 August to 4 September 2002.
• The UNCHS, Stockholm,1972  United Nations Conference on the Environment in Stockholm was the first world conference to make the environment an important issue.

Correct answer is They contained sacred relics.

Key Points

• Buddhist stupas were initially built to house the earthly remains of the historical Buddha and his associates and are almost always established at sites sacred to Buddhism.
• The idea of a relic was later increased to include sacred texts.
• The stupa is an main form of Buddhist architecture, though it predates Buddhism.
• It is usually examine to be a sepulchral monument—a place of burial or a receptacle for religious objects.

Additional Information

• Great Stupa, the most notable of the structures at the historic site of Sanchi in Madhya Pradesh state, India.​
• The Great Stupa was initially built in the 3rd-century bce by the Mauryan emperor Ashoka.
• The simple structure was damaged at some point through the 2nd-century bce.

Correct answer is Bengal.

Key Points

• The Brahmo Samaj was a monotheistic sect of Hinduism.
• The movement began between meetings of Bengalis in Calcutta in 1828.
• The imortant motive of the Brahmo Samaj was the worship of the eternal God.
• It was opposed to priesthood, rituals and sacrifices.

Additional Information

• Arya Samaj, robust improve movement of modern Hinduism, started in 1875 by **Dayananda Sarasvati.**​
• Arya Samaj's motive was to renew the Vedas, the earliest Hindu scriptures, as revealed truth.
• The Arya Samaj had a very notable results on the emergence of the community as a cohesive one with a self-confident identity.

Correct answer is Kailash Satyarthi.

Key Points

• Children's rights activist Kailash Satyarthi was granted the Nobel Peace Prize for “focusing attention on the grave exploitation of children for financial gain”.
• One more main cause was that he followed the non-violent tradition of Indian independence leader Mahatma Gandhi.
• In 1998, Satyarthi think up and led the Global March against Child Labour traveling over 103 countries covering 80,000 km to request an International Law on Worst Forms of Child Labour.

Additional Information

• Rajendra Kumar Pachauri was the chairman of the Intergovernmental Panel on Climate Change (IPCC) from 2002 to 2015.​
• Har Gobind Khorana was the first scientist to chemically synthesize oligonucleotides.
• Amartya Sen is an economist presently working as a Professor of Economics and Philosophy at Harvard University.

Friends : P, Q, R, S, T, U, V, and W

1. They are sitting around a circular table facing opposite the center.

2. Q is third to the right of T and second to the left of P.

3. V is not the neighbour of P or T and only two friends are sitting between U and V.

4. W is second to the right of R.

Possible sitting arrangement:

Let's check each option and identify which statement is correct:

1. V is to the immediate right of S → Correct

2. P is to the immediate left of R → Incorrect (Since Q is to the immediate left of R)

3. W is to the immediate right of Q → Incorrect (Since R is to the immediate right of Q)

4. S is to the immediate left of T → Incorrect (Since U is to the immediate left of T)

Hence, 'option 1' is the correct answer.

Given:

Side of triangle = 15 cm

Height of triangle = 6 cm

Concept Used:

Area of triangle = $\frac{1}{2}$ × Base × Height

Calculation:

⇒ Putting the values in the formula, we get

⇒ Area of triangle = $\frac{1}{2}$ × 15 × 6

⇒ Area of triangle = 15 × 3 = 45 cm²

Therefore, the area of a triangle is 45 cm².

Given:

Sum of angles = 155°

Difference of angles = ${\pi } \over 2$ = 90º

Concept used:

Elimination method in a system of 2 variables

Calculation:

⇒ Let x and y be the two angles.

⇒ According to the question,

⇒ x + y = 155                → (1)

⇒ x – y = 90                  → (2)

⇒ By subtracting (2) from (1) , we get 

⇒ 2y = 65

⇒ y = $\frac{65}{2}=32.5$º

⇒ Putting the value of y in equation (2), we get

⇒ x = 122.5º

⇒ To change this angle into radians, we will multiply with $\frac{\pi}{180}$.

⇒ Greater angle = $\frac{122.5\pi}{180}=\frac{1225\pi}{1800}=\frac{49\pi}{72}$

Therefore, the value of greater angle (in radians) is $\frac{49\pi}{72}$.

Correct answer is Venus.

Key Points

• After the successful Mars Orbiter Mission, ISRO is eyeing inter-planetary missions to Jupiter and Venus and is studying them practically.
• The project announce for 'Shukrayaan-I' – the name given to ISRO's Venus mission, is ready and the budget has also been recognized for it.
• Here are 10 fascinating things to know about the Venus Orbiter Mission of ISRO, likely to be started by December 2024.
• It takes Venus longer to rotate once on its axis than to complete one orbit of the Sun.

Additional Information

• ​Saturn was first overtaken by Pioneer 11 in September 1979.
• NASA's Parker Solar Probe is the foremost mission to "touch" the Sun.
• The first spacecraft to visit Mercury was NASA's Mariner 10, which imaged about 45% of the surface.

Correct answer is World Commission on Environment and Development.

Key Points

• The goal of the Brundtland Commission was to support and direct the nations of the world toward the goal of sustainable development.
• The commission is also called the World Commission on Environment and Development (WCED).
• It worked from 1984 to 1987.
• The commission issued its outcomes in the Brundtland report in 1987.

Additional Information

• The UN's World Commission for Environment and Development, chaired by previous Norwegian Prime Minister Gro Harlem Brundtland and so mentioned to as the Brundtland Commission, published the report “Our Common Future,” also called the “Brundtland Report,” in 1987.​
• The Brundtland Commission was chaired by previous Norwegian prime minister Gro Harlem Brundtland. Politicians, civil servants, and environmental experts made up the majority of the members.

Given: 

Amount of petrol = 475 L

Amount of diesel = 420 L

Amount of oil = 495 L

Concept Used:

HCF(Highest common factor)

For least possible number of bottles the capacity of the bottle should be maximum. The amount should be such that it completely divides the three numbers in order to fill the bottle completely.

Calculation: 

⇒ Factors of 420 = 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420

⇒ Factors of 475 = 1, 5, 19, 25, 95, 475

⇒ Factors of 495 = 1, 3, 5, 9, 11, 15, 33, 45, 55, 99, 165, 495

⇒ HCF (420, 475, 495) = 5

⇒ Hence the capacity of each bottle is going to be 5 L.

⇒ Number of bottles filled with diesel = $\frac{420}{5}=84$

⇒ Number of bottles filled with petrol = $\frac{475}{5}=95$

⇒ Number of bottles filled with oil = $\frac{495}{5}=99$

⇒ Total no of bottles = 84 + 95 + 99 = 278

Therefore, the least possible number of bottles required is 278.

Correct answer is Bokaro Steel Plant and Bhilai Steel Plant.

Key Points

• Steel plants that were set up with Russian collaboration are Bokaro Steel Plant in Jharkhand and  Bhilai Steel Plant in Chhattisgarh.
• Bokaro Steel Plant is situated in the Bokaro district of Jharkhand.
• It is the fourth integrated public sector steel plant in India built with Soviet help.
• Bhilai Steel Plant, be one of the largest in India, this industrial city is situated about 25 km far from Raipur.

Additional Information

• Rourkela Steel Plant is located on the northwestern tip of Odisha.
• Durgapur steel plant (DSP) is situated in the Durgapur district of West Bengal.​
• Bhilai Steel Plant has been the head integrated steel plant unit of the Public Sector steel company, the Steel Authority of India Limited, and is its largest and most profitable production facility.

Given:

Consumption of milk per day = 1700 mL

Total time = 5 weeks

Concept Used:

Conversion from  mL to L

Conversion from weeks to days

Unitary method

Calculation:

⇒ Milk consumption per day = 1700 ml = $\frac{1700}{1000}=1.7\ L$

⇒ Milk consumed in 1 week = 1.7 × 7 = 11.9 L   → (1 week = 7 days)

⇒ Milk consumed in 5 weeks = 11.9 × 5 = 59.5 L

Therefore, 59.5 L of milk will be consumed by Terry in 5 weeks.

Given:

Ratio of areas of two squares = 16 : 9

Concept used:

Operation of ratios

Area of a square = (Side)²

Perimeter of a square = 4 × Side

Calculation:

⇒ Let the sides of the two squares be 'a' and 'b' respectively. 

⇒ Their areas are a² and b² respectively.

⇒ According to the question, $a^2 : b^2$ = 16 : 9

⇒ $a^2\over b^2$ = $16 \over9$        → (1)

⇒ Perimeter of the squares will be 4a and 4b respectively.

⇒ Ratio of perimeters = $4a\over 4b$ = $a\over b$      → (2)

⇒ Taking square root on both sides of the equation (1),

⇒ $\frac{a}{b}=\sqrt{\frac{16}{9}}=\frac{4}{3}$              → (3)

⇒ Using (3) in (2): Ratio of perimeters = $4\over 3$

⇒ Ratio of parameter = 4 : 3

Therefore, the ratio of their respective perimeter is 4 : 3

Correct answer is Horticulture.

Key Points

• Horticulture is the branch of plant agriculture using with garden crops, usually fruits, vegetables, and ornamental plants.
• Horticultural crops involve fruits, vegetables, medicinal, aromatic, and ornamental plants.
• Examples of horticulture involve the following: landscaping. gardening.
• Marigowda is also famous as Father of Horticulture in India.

Additional Information

• The artificial reproduction, rearing, and transplantation of fish is known as pisciculture.
• ​Apiculture is the operation of keeping bees and also the manufacturing of honey and beeswax.
• Sericulture is the growing of silkworms to produce silk.

The pattern followed here is as follows:

So the value of '?' is 8.

Hence, 'option 1' is the correct answer.

Preparing the family tree using the following symbols:

From the information given:

Step 1: She is the daughter-in-law 

Step 2: my grandfather's daughter-in-law = my mother 

So the final diagram will be: She is the daughter-in-law of my grandfather's daughter-in-law

According to the given statement, there is a possibility that the lady could be the wife of Raman also but as per the given options, the lady is Raman's brother's wife.

Hence the correct answer is option 4)

From the given information:

Step 1:  D sits third to the right of A and second to the left of C. Only three soldiers sit between D and E.

We place D and then A & C according to the conditions, now we place E with three spots from the left of D.

Step 2: Only two soldiers sit between E and F. F sits second to the left of B.

Now we place F two spots from E and then place B second to the right of F.

Step 3:  A is the neighbor of G. H sits to the right of D.

Here we place G next to A and place H at the only spot left i.e. right end.

From the arrangement, we can see that there are 4 soldiers sitting between H and G.

Hence the correct answer is option 1)

From the given statements:

1. Some kites are birds.
2. All birds are black.

Now we consider the conclusions:

Ⅰ. All black birds are kites: From the diagram and the statements given we can clearly say that not all kites are birds and therefore it will be wrong to say that all black birds are kites. Thus the conclusion does not follow.

Ⅱ. Some black things are kites: All birds are black and some birds are kites so it can be said that some black birds are kites and which can be rephrased as some black things are kites. So the conclusion follows.

Since only conclusion Ⅱ follows.

Hence the correct answer is option 2).

GIVEN:

Number of digits = 6

Digits to be used = 0,4,6 and each of these digits has to be used at least once.

Concept Used:

Basic number system

Calculation:

⇒ For the smallest 6-digit number consisting of 0,4,6,

⇒ First digit can not be 0 or it will not be a 6-digit number; So the next smallest number is 4.

⇒ Note that, we also have to use the digit 6 in the number, so we use it at the unit place to have the least total value of the number.

⇒ Other digits in between can be 0 which makes the number = 400006         → (1)

⇒ For the largest positive 6 digit number we start the number with the largest that is 6.

⇒ We have to make it the largest possible value and hence we will have to use 6 multiple times.

⇒ We also have to use 4 and 0 at least once, so we use it at the last.

⇒ Two possible combinations arise which are: 666640 or 666604

⇒ In order the have largest possible value we will choose 666640          → (2)

⇒ Now to find the sum, we add the numbers obtained in (1) & (2),

⇒ Sum = 400006 + 666640

⇒ Sum = 1066646

The sum of the smallest and the largest positive numbers of 6 digits which contain only 0, 4, 6 and each of them appear at least once is 1066646

Correct answer is Bihar.

Key Points

• The folk art of Bihar, usually called as Madhubani, mentions to the market town of the same name.
• Madhubani paintings use two-dimensional imagery, and the colors used are derived from plants.
• Ochre, Lampblack, and Red are used for reddish-brown and black, appropriately.
• Madhubani paintings mainly depict people and their association with nature and scenes and deities from the old epics.

Additional Information

• Dokra Metal Craft is one of the most famous forms of art practiced in Bengal.
• Phulkari is the most famous handiwork in India (Punjab).
• The Warli Painting tradition in Maharashtra is among the finest examples of the folk style of paintings.​

Correct answer is Columbia.

Key Points

• Kalpana Chawla died when the space shuttle Columbia broke up on re-entry into Earth's atmosphere, killing all seven astronauts on board.
• Her first expedition to space was on board the Space Shuttle Columbia, as a mission specialist and prime robotic arm operator, in 1997.
• Kalpana Chawla was an Indian-born American astronaut and engineer who went to space twice in her life.
• The tragedy happened over Texas, and only minutes before Columbia was scheduled to land at the Kennedy Space Center.

Additional Information

• Discovery shuttle established satellites and served as an orbiting science laboratory.​
• Challenger space shuttle is a reusable spacecraft designed to transport people and cargo between earth and space.
• Atlantis space shuttle is presently displayed at the Kennedy Space Center Visitor Complex.

Given:

Length of rectangle = 49 m

Breadth of rectangle = 35 m

Side of square = 7 m

Concept used:

Area of square = Side × Side

Area of rectangle = Length × Breadth

Calculation:

⇒ Area of rectangle = 49 × 35 = 1715       → (1)

⇒ Area of square = 7 × 7 = 49                   → (2)

⇒ Number of square beds that can fit inside the rectangle = $\frac{Area \ of\ rectangle }{Area \ of\ square\ bed}$

⇒ Number of square beds from (1) & (2) = $1715\over 49$ = 35

Therefore, 35 square beds can be accommodated in this rectangle.

Correct answer is Fifth.

Key Points

• The Integrated Tribal Development Programme was previously started in 1974 with the Fifth Five Year Plan.
• The Integrated Tribal Development Projects (ITDP) under Tribal Sub-Plan (TSP) is being execute since the Fifth Five Year Plan.
• The Integrated Tribal Development Project (I.T.D.P), Rayagada take in of Rayagada Block came into existence on the 29th of  August 1974.
• The Tribal Development Blocks were launched for the development of tribal areas.

Additional Information

• The Second Plan concentrated on the development of the public sector and "rapid Industrialisation".
• The five-year plan is a method of planning economic extensions over limited periods by the use of quotas.
• The Sixth Five-Year Plan decided the start of economic liberalisation. ​

Given:

Increase in rate of rice = 20%

For Rs 630, the amount of less rice a man gets = 3 kg

Calculation:

⇒ Let the old rate of the variety of rice be Rs x.

⇒ Amount of rice a man gets in Rs 630 at old rate = $\frac{630}{x}$

⇒ New price after increase = x + 20% of x

⇒ New price after increase = $x+\frac{20}{100}\times x = x+\frac{x}{5}=\frac{6x}{5}$

⇒ Amount of rice a man gets in Rs 630 in new rate = $\frac{630}{\frac{6x}{5}}$

⇒ According to the question,

⇒ $\frac{630}{x}-\frac{630}{\frac{6x}{5}}=3$

⇒ $\frac{630\times 6-630\times 5}{6x}=3$

⇒ $3780-3150=18x$

⇒ $x=\frac{630}{18}=35$

Therefore, the old rate for that variety of rice was Rs 35 per kg.

Given:

Ratio = 17 : 21

Required ratio = 7 : 9

Calculation:

⇒ Let the subtracted number from the ratio be x.

⇒ According to the question,

⇒ $\frac{17-x}{21-x}=\frac{7}{9}$

⇒ Cross-multiplying the terms, we get

⇒ $9(17-x)=7(21-x)$

⇒ $153-9x=147-7x$

⇒ $9x-7x=153-147$

⇒ $2x=6$

⇒ $x=\frac{6}{2}=3$

Therefore, the term which should be reduced from the ratio 17 : 21 to make it 7 : 9 is 3

Correct answer is Demography.

Key Points

• Demography is the study of demographics, the social characteristics, and statistics of a human population.
• This study of the size, age forms and economics of dissimilar populations can be used for a diversity of purposes.
• The field of demography can be split into two general areas, basic or academic demography and applied demography.
• A demographic mentions to distinct characteristics of a population.

Additional Information

• Resource geography by its very name is the study of the spatial variation in the physical stuff with regard to their appraisal by humans.
• Geography of Marketing works on the concept that people in that place have alike **needs, wants, and cultural considerations.**​
• Geography is important to the study of tourism because tourism is geographical in nature.

Given:

HCF of two numbers = 29

Two factors of their LCM = 13 and 17

Concept Used:

The HCF of a group of numbers will always be a factor of their LCM.

Because HCF is the product of all common prime factors using the least power of each common prime factor, and LCM is the product of the highest powers of all prime factors. 

Calculation :

⇒ Since HCF is a factor in their LCM 

⇒ So, the factors of LCM are 29, 13, 17

⇒ Two numbers are  $(29 \times 13)$ and $(29\times17)$

⇒ Numbers are 377 and 493

Therefore, the smallest of the two numbers is 377

Given:

Selling Price of Gold Ring = ₹19,125

Loss Percentage = 15%

Concept Used:

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

Calculation:

⇒ Cost Price = $\frac{19125}{100\ -\ 15}\times 100$

⇒ Cost Price = $\frac{1912500}{85}$ = ₹22,500

Therefore, the cost price of the gold ring is ₹22,500

According to the English alphabet and its positional values: 

The logic followed here is:

• Alphabets are increased to 2 positional values.
• Numbers are decreased to -1 of the previous difference.

​The pattern followed by the given series is:

Hence the correct answer is option 2).

Correct answer is Bombay, Thane.

Key Points

• The first passenger train in India ran between Bombay (Bori Bunder) and Thane on 16 April 1853.
• The first train began from Bori Bunder in Bombay at 3:35 pm on April 16, 1853 w,ith a 21-gun salute.
• It was worked by three engines, named Sahib, Sultan, and Sindh, and had thirteen carriages.
• The first railway line in India was built during the rule of Lord Dalhousie.

Additional Information

• ​The Indian railways are the largest public sector undertaking in India.
• Railways are the main mode of shipment for goods and passengers in India.
• A railway is a route between two places along which trains travel on steel rails.
• Indian Railways (IR) is a statutory body under the ownership of The Ministry of Railways, Government of India that operates India's national railway system.

Correct answer is Annelida.

Key Points

• Annelids are recognized members of the Lophotrochozoa, a "super-phylum" of protostomes.
• It also involves mollusks, brachiopods, and nemerteans.
• The basic annelid form consists of multiple segments.
• The phylum includes earthworms, polychaete worms, and leeches.
• Annelids show protostome development in embryonic stages and are frequently known as “segmented worms”

Additional Information

• The Cyclostomata are the modified and degenerate offshoot of the primitive vertebrate stalk.
• Pisces people are called for being emotionally sensitive, gracious, and emotionally aware.​
• Reptiles are air-breathing vertebrates covered in special skin made up of scales, bony plates, or a combination of both.

The correct answer is "King George V".

Key Points

• George V was King of the United Kingdom and the British Dominions, and Emperor of India, from 6 May 1910 until his death in 1936.
• After his father passed away in 1910, George V was crowned as king-emperor.
• During George's reign, the political climate of the British Empire was drastically altered by the rise of socialism, communism, fascism, Irish republicanism, and the Indian independence movement.

Additional Information

• Sir William Jones was a British philologist, a puisne judge on the Supreme Court of Judicature at Fort William in Bengal, and a scholar of ancient India.
• Dalhousie was responsible for introducing a variety of modern reforms such as the railways, telegraph and postal networks, and public works in India.
• The Ganga Canal was completed during his tenure but, he is most remembered for the Doctrine of Lapse policy which many hold directly responsible for the Indian Revolt of 1857.
• Portugal was the major European commercial power in the Far East in the sixteenth century, and its Estado da India trading company operated throughout the Indian Ocean basin.