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The correct answer is option 3 i.e. Large grassland.

Grasslands are known by different names in different regions.

Given:

Distance between Raja and Gopal = 48 km

Speed of Raja and Gopal = 7 km/hr and 5 km/hr respectively

Formula used:

When the two objects travel in the same direction their relative speed = (a – b) km/hr

When the two objects travel in the opposite direction their relative speed = (a + b) km/hr

Were a and b are speeds of two objects in km/hr and (a > b)

Time = distance/speed

Calculation:

As they meet after some time, means they are traveling towards each other and their speed will be added

∴ Time after they meet = 48/(7 + 5) = 48/12 = 4 hours

Calculation:

If the denominators are the same, then the fraction with the greater numerator is the greater fraction. The fraction with the lesser numerator is the lesser fraction.

Reverse the above fraction:

219/2 = 109.5       ---- (1)

343/3 = 114.3       ---- (2)

437/4 = 109.25     ---- (3)

687/6 = 114.5       ---- (4)

Since we have reversed the fraction, the lowest value will be the highest fraction:

437/4 = 109.25 has the lowest value after reversing and hence will have higher fraction:

∴ 4/437 is the greatest fraction.

\(x = \frac{2n^2+3n}{5n^2},\)

⇒ x = n(2n + 3)/5n²

⇒ x = (2n + 3)/5n

We can see that in the denominator, n is increasing by 5 times whereas, in the numerator, n is increasing by 2 times only.

∴ x will decrease, since denominator is greater than numerator

The correct answer is option 3 i.e. The Bengal Gazette.

• The Bengal Gazette also known as Calcutta General Advertiser started its publication in Calcutta, the centre of colonial India during that time was India’s first newspaper in 1780.
• It was an English language weekly that was started by James Augustus Hicky, an Irishman who acted as the paper’s writer, editor and publisher.

The correct answer is option 3 i.e. Bibhutibhushan Bandyopadhyay.

Calculation:

Total questions = 48

Let the correct question be x,

⇒ Positive marks = x × 1

According to question:

x + wrong answered question = 48

Wrong answered question = 48 - x,

⇒ Marks deducted = 0.5(48 - x)

According to the question

Marks obtained = 21,

⇒ 21 = x × 1 - 0.5(48 - x)

⇒ 21 = x - 24 + 0.5x

x + 0.5x = 45

⇒ 1.5x = 45

⇒ x = 30

∴ Number of questions answered wrongly = 48 - 30 = 18

Short Trick:

By hit and trial method

Let 30 question were correct, So marks obtained in correct answer = 30 × 1 = 30

So left 18 question must be wrong and marks deducted = 18 × 0.5 = 9

∴ Marks obtained = 30 - 9 = 21. which satisfies the question.

∴ 18 questions are wrongly answered

Given:

Ratio of 2 numbers is 3 : 4 

Each number is increased by 2

New ratio of numbers = 7 : 9 

Calculation:

Let the numbers be 3x and 4x

According to the question,

(3x + 2)/(4x + 2) = 7/9

⇒ 9(3x + 2) = 7(4x + 2)

⇒ 27x + 18 = 28x + 14

⇒ x = 4

∴ The numbers are 3 × 4 = 12 and 4 × 4 = 16

Concept:

a³ + b³ + c³ – 3abc = (a + b + c)(a² + b² + c² – ab – bc − ca)

Calculation: 

Using the above formula:

a³ + b³ + c³ = (a + b + c)(a² + b² + c² – ab – bc − ca) + 3abc

put x - y = a, y - z = b, z - x = c

⇒ (x - y)³ + (y - z)³ + (z - x)³ = (x - y + y - z + z - x)[(x – y)2 + ( y   - z)2 + (z - x)2 – (x – y) - (y – z)  - (z – x)]  + 3(x - y)(y - z)(z - x)

∴ 3(x - y)(y - z)(z - x) (∵ (x - y + y - z + z - x) = 0 and it cancels out the product )

The correct answer is option 4 i.e. Nuclear fusion reaction.

Explanation:

• Nuclear fusion reactions are the source of energy in the Sun and other stars.
• It takes considerable energy to force the nuclei to fuse. The conditions needed for this process are extreme – millions of degrees of temperature and millions of pascals of pressure.
• Nuclear fusion
• Fusion means joining lighter nuclei to make a heavier nucleus, most commonly hydrogen or hydrogen isotopes to create helium, such as

2H¹ + 2H¹ → ₂He⁴ (+ ₀n¹)

• It releases a tremendous amount of energy, according to the Einstein equation, as the mass of the product is a little less than the sum of the masses of the original individual nuclei.

Hence, solar energy is due to Nuclear fusion reaction.

Additional Information 

• Chemical reactions
• The transformation of chemical substances (known as reactants) into a new chemical substance (known as products) by making and breaking of chemical bonds between different atoms of reactants sometimes in presence of a catalyst (which changes the rate of reaction) is known as Chemical Reaction.
• Combustion Reaction 
• A chemical reaction between substances, usually including oxygen and usually accompanied by the generation of heat and light in the form of flame. Combustion reactions must involve O₂ as one reactant.
• Many combustion reactions occur with a hydrocarbon, a compound made up solely of carbon and hydrogen. The products of the combustion of hydrocarbons are carbon dioxide and water.
• Nuclear fission
• In a process called nuclear fission, the nucleus of a heavy atom (such as uranium, plutonium or thorium), when bombarded with low-energy neutrons, can be split apart into lighter nuclei.
• When this is done, a tremendous amount of energy is released if the mass of the original nucleus is just a little more than the sum of the masses of the individual products.
• The fission of an atom of uranium, for example, produces 10 million times the energy produced by the combustion of an atom of carbon from coal.
• In a nuclear reactor designed for electric power generation, such nuclear ‘fuel’ can be part of a self-sustaining fission chain reaction that releases energy at a controlled rate.
• The released energy can be used to produce steam and further generate electricity.