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Given data:

The fraction after increasing the numerator and denominator is 4/11.

The numerator is increased by 200%.

The denominator is increased by 120%.

Concept:

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

Solution:

x × (1+200/100), which equals 3x.

Similarly, the denominator increased by 120% can be represented as y ×

(1+120/100), which equals 2.2y.

Given that we now have the ratio 3x / 2.2y = 4/11.

⇒ We cross-multiply to find the values. 3x × 11 = 4 × 2.2y.

⇒ Simplifying this gives 33x = 8.8y.

⇒ From this, we can conclude that the ratio x/y = 8.8 / 33.

Simplifying this fraction, we get x/y = 4/15.

Therefore, the original fraction is 4/15.

The correct answer is Bangalore.

• Bangalore is popularly referred to as the 'Electronic City of India'.

Key Points

• Electronic City is an information technology hub in Bangalore, India.
• R. K. Baliga was the first Chairman and regarded as the father of the electronics city in Bangalore.
• It is the country's largest IT exporter and is home to many national and international tech companies, startups, and research institutions.
• Bengaluru other Sobriquets:
• Silicon Valley of India
• Space City
• Science city of India
• Garden city of India
• Pensioners Paradise

Additional Information

• Other Sobriquetes:

The Logic followed here is:

2 × 8 + 1 = 17

17 × 8 + 1 = 137

Similarly,

137 × 8 + 1 = 1097

Hence the correct answer is Option 3: 1097

The correct answer is Torricelli.

Key Points 

• Evangelista Torricelli (1608-1647) was an Italian physicist and mathematician who is best known for his invention of the barometer in 1643.
• Torricelli was both a student and a secretary of Galileo, and he made several significant contributions to the field of physics.
• His experiments with mercury and vacuums led to the development of the first mercury barometer.
• 'Barometer' is a scientific instrument that is used to measure air pressure in a certain environment. Pressure tendency can forecast short term changes in the weather.
• Many measurements of air pressure are used within surface weather analysis to help find surface troughs, pressure systems and frontal boundaries.

 Additional Information

• Amedeo Avogadro: He was an Italian scientist, most noted for his contributions to molecular theory, including Avogadro's law on gases' behavior.
• Alexander Graham Bell: Bell is a well-known scientist and inventor. He patented the first practical telephone in 1876.

The correct answer is Plato.

Key Points

• The Republic book was authored by Plato in around 375 B.C.
• Plato was the founder of the Platonist school of thought and the Academy.
• The famous philosopher Aristotle was the student of Plato and the famous philosopher Socrates was the teacher of Plato.
• Historically and intellectually, the Republic book is considered as the world’s most influential work on Political Theory and Philosophy.
• In the book, there is a dialogue between Socrates and various Foreigners and Athenians who tries to understand Justice.
• Other Notable works of Plato are:
• Apology.
• Crito.
• Euthyphro.
• Meno.
• Parmenides.
• Phaedo.
• Phaedrus.
• Symposium.
• Timaeus.

Additional Information

• Homer:
• Homer is a legendary ancient Greek epic poet, traditionally said to be the author of two of the greatest epic poems of ancient Greece, the Iliad and the Odyssey.
• Aristotle:
• Aristotle was a student of Plato and later tutored Alexander the Great.
• He is considered one of the greatest philosophers in history, contributing to many areas, including physical sciences, biology, drama, music, politics, ethics, and government.
• Socrates:
• Socrates was a classical Greek philosopher credited as one of the founders of Western philosophy.
• Socrates did not leave any written works; our knowledge of his teachings comes primarily from the accounts of his students, particularly Plato and Xenophon.
• The Socratic method, lateral thinking, questioning to stimulate critical thinking, and illuminating ideas are named after him.

Here all the land animals and land animals are animals.

The least possible Venn diagram is:

Hence the correct answer is Option 3

The correct answer is Venezuela.

Key Points

• Caracas is the capital of Venezuela.
• Venezuela, officially known as the Bolivarian Republic of Venezuela, is a country located on the northern coast of South America.
• Caracas, located in the center-north of the country close to the Caribbean Sea, is Venezuela's largest city and serves as its administrative and political center.

Additional Information

• Ecuador: The capital of Ecuador is Quito. Also known as San Francisco de Quito, it's one of the highest official capitals in the world, located in the Andean foothills at an altitude of 2,850 meters.
• Philippines: The capital of the Philippines is Manila. It is situated on the eastern shore of Manila Bay and is one of the oldest cities in the country.
• Peru: The capital of Peru is Lima. Lima is located on Peru's arid Pacific coast and it is both the largest city in Peru and the second-largest city in the Americas by population.

The least possible Venn diagram is:

Conclusions: 

I. All cars are windows → True (As all cars are bottles and all bottles are windows)

II. Some cars are dolls → False (As there is no definite relation between cars and dolls. It can be possible but is not definite.

III. Some windows are cars → True (Since all cars are bottles and all bottles are windows. Therefore some windows are cars)

Hence the correct answer is Option 4: Only I and III follow.

The logic follows here:

• Upper side three shapes flip and the lower side two shapes rotate only not flip. According to the given pattern in the solution figure.

​

Hence, the correct answer is "option (2)".

The correct answer is Desert region.

Key Points

• A bajada is a landform found in desert regions.
• Bajadas are common in arid regions like deserts, where they are formed by the confluence of multiple alluvial fans.
• Alluvial fans are cone-shaped deposits of gravel, sand, and smaller sediments that accumulate over time where a narrow mountain stream enters a broader valley or plain.
• When multiple alluvial fans overlap side-by-side, they create the characteristic wedge shape draping down from mountains towards the basin floor, a landform known as a bajada.

Additional Information

• Mountain Peak areas: Mountain peaks typically involve features like ridges, cliffs, and valleys, not bajadas.
• Plainland:  A plain is a broad, typically flat stretch of land. It's not normally characterized by the piled-up sediments which form bajadas, though there are depositional plains where alluvial deposits can accumulate over time.
• Plateau region: Plateaus are elevated regions which are relatively flat on top.