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The logic followed here is:

Logic: In the triangle, First number = (Second number + Third number)/ 2

Let's check each triangle,

In triangle 1,

→ 6 = (7 + 5)/ 2

→ 6 = 12/ 2

In triangle 3,

→ 7 = (10 + 4)/ 2

→ 7 = 14/2

Similarly, In triangle 2,

→ ? = (8 + 6)/ 2

→ ? = 14/ 2 = 7

Hence, the correct answer is "7".

The correct answer is Lamarck.

Key Points

• Lamarck was a pioneering biologist and is best known for his theory of inheritance of acquired characteristics.
• The law of use and disuse suggests that parts of the body that are used extensively become larger and stronger, while those that are not used deteriorate.
• Lamarck's ideas were an important early attempt to explain evolution, although they have been largely superseded by Darwin's theory of natural selection.

Additional Information

• Jean-Baptiste Lamarck was a French naturalist who lived from 1744 to 1829.
• Although his theories were eventually overshadowed by Darwinian evolution, Lamarck's work laid important groundwork for the field of evolutionary biology.
• His ideas were some of the first to suggest that complex organisms evolved from simpler ones over time.

Given:

Average age of 10 students = 10.3 years

Average age of 3 students = 12 years

Average age of 5 students = 9 years

Formula Used:

Average age = Total age of students / Number of students

Calculation:

Total age of 10 students = 10 × 10.3

Total age of 10 students = 103 years

Total age of 3 students = 3 × 12

Total age of 3 students = 36 years

Total age of 5 students = 5 × 9

Total age of 5 students = 45 years

Total age of remaining 2 students = Total age of 10 students - Total age of 3 students - Total age of 5 students

Total age of remaining 2 students = 103 - 36 - 45

Total age of remaining 2 students = 22 years

Average age of remaining 2 students = Total age of remaining 2 students / Number of remaining students

Average age of remaining 2 students = 22 / 2

The average age of the remaining 2 students is 11 years.

The correct answer is France.

Key Points

• Emmanuel Macron is the current President of France.
• He has been serving as the President since May 14, 2017.
• Macron is a former civil servant and investment banker.
• He founded the political party La République En Marche! in 2016.

Additional Information

• Before becoming President, Emmanuel Macron served as the Minister of the Economy, Industry, and Digital Affairs from 2014 to 2016.
• He is one of the youngest Presidents in French history, assuming office at the age of 39.
• Macron's policies focus on economic reform, labor laws, and European Union integration.

Given:

Numbers: 21, 36, and 66

Formula used:

To find the least perfect square divisible by given numbers, we first find the Least Common Multiple (LCM) of these numbers and then ensure the LCM is a perfect square.

Calculation:

Prime factorization:

21 = 3 × 7

36 = 2² × 3²

66 = 2 × 3 × 11

LCM is found by taking the highest power of all prime factors present in any of the numbers:

LCM = 2² × 3² × 7 × 11

⇒ LCM = 4 × 9 × 7 × 11

⇒ LCM = 2772

To make 2772 a perfect square, all prime factors must be raised to an even power:

2772 = 2² × 3² × 7 × 11

Missing factors for a perfect square:

We need another 7 and another 11:

Therefore, the least perfect square = 2772 × 7 × 11

⇒ Least perfect square = 2772 × 77

⇒ Least perfect square = 213,444

∴ The least perfect square divisible by 21, 36, and 66 is 213,444.

The correct answer is Wellington.

Key Points

• Wellington is not a cricket field in South Africa.
• Wellington is actually the capital city of New Zealand.
• It is known for its cricket ground, the Basin Reserve.
• The cricket fields in South Africa include:
• Johannesburg (Wanderers Stadium)
• Durban (Kingsmead)
• Centurion (SuperSport Park)
• South Africa is known for its rich cricketing history and has several prominent cricket grounds where international matches are held.

Additional Information

• Cricket is a popular sport in South Africa, with a strong domestic and international presence.
• Other notable cricket grounds in South Africa include:
• Newlands in Cape Town
• St George's Park in Port Elizabeth
• Boland Park in Paarl

According to the given information,

Here, we can see that I's position is 9. It has the same position in English alphabet.

Hence, the correct answer is "I".

The correct answer is Coromondol Coast.

Key Points

• The Coromandel Coast receives significant winter rainfall.
• This is primarily due to the northeast monsoon winds.
• These winds pick up moisture from the Bay of Bengal and bring rainfall to the region.
• Other coastal areas like Gujarat Coast, Konkan Coast, and Malabar Coast do not experience significant winter rainfall.
• The northeast monsoon is also known as the retreating monsoon.

Additional Information

• The northeast monsoon typically occurs from October to December.
• During this period, the Coromandel Coast receives the bulk of its annual rainfall.
• The southwest monsoon, which occurs from June to September, brings rainfall to other parts of India.
• The Coromandel Coast does not receive much rainfall from the southwest monsoon.

According to the given information,

→ A watch gets slow by 6 minutes in every hour.

Number of minutes the watch gets delayed in 9 hours i.e from 7 am to 4 pm:

→ 6 minutes × 9 = 54 minutes.

Number of minutes it gets delayed in 20 minutes = 6/3 = 2 minutes.

Now, total number of minutes the watch gets delayed between 7 am and 4 pm:

→ (54 + 2) = 56 minutes.

So, the time faulty watch will show when the original time is 4 past 20 minutes is:

→ (4 past 20 minutes - 56 minutes) = 3 past 24 mins

Hence, the correct answer is "3 past 24 mins".

The correct answer is Fa Hiyen.

Key Points

• Fa Hiyen was a Chinese Buddhist monk and a renowned traveller.
• He came to India during the reign of Chandragupta II to study Buddhism and collect Buddhist scriptures.
• His journey to India is well documented and provides valuable insights into the history and culture of the time.
• He traveled through Central Asia and reached India around the early 5^th century AD.

Additional Information

• Al Beruni was a Persian scholar who visited India during the reign of Mahmud of Ghazni in the 11^th century.
• Ibn Battuta was a Moroccan traveller who visited India during the reign of Muhammad bin Tughlaq in the 14^th century.
• Hiuen Tsang was another Chinese Buddhist monk who visited India during the reign of Harsha in the 7^th century AD.