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Given:

Initial ratio of the two numbers = 3 ∶ 5

When 10 is added to both numbers, the ratio becomes 5 ∶ 7.

Formula Used:

Ratio equation: \(\frac{a+10}{b+10} = \frac{5}{7}\)

Calculation:

Let the numbers be 3x and 5x.

According to the problem:

\(\frac{3x + 10}{5x + 10} = \frac{5}{7}\)

Cross-multiplying gives:

⇒ 7(3x + 10) = 5(5x + 10)

⇒ 21x + 70 = 25x + 50

⇒ 21x - 25x = 50 - 70

⇒ -4x = -20

⇒ x = 5

The two numbers are:

First number = 3x = 3 × 5 = 15

Second number = 5x = 5 × 5 = 25

Sum of the two numbers = 15 + 25 = 40

The sum of the two numbers is 40.

The correct answer is Glucagon.

Key Points

• Glucagon is a hormone secreted by the alpha cells of the pancreas.
• It plays a crucial role in glucose metabolism and homeostasis.
• Glucagon increases blood glucose levels by promoting gluconeogenesis and glycogenolysis in the liver.
• It acts in opposition to insulin, which lowers blood glucose levels.
• Glucagon is essential for maintaining normal blood sugar levels, especially during fasting or between meals.

Additional Information

• Insulin, another pancreatic hormone, is secreted by the beta cells and helps lower blood sugar levels by facilitating cellular glucose uptake.
• The pancreas also secretes other hormones:
• Somatostatin from delta cells, which regulates the secretion of both insulin and glucagon.
• Pancreatic polypeptide from PP cells, which helps regulate pancreatic secretions and gastrointestinal motility.

Given:

Initial milk in the container = 20 litres

Milk withdrawn in each step = 4 litres

Water added in each step = 4 litres

Process repeated = 2 times

Formula Used:

Remaining milk after each step = \(Initial milk × (1 - \frac{milk\ withdrawn}{total\ liquid}) \)

Calculation:

Initial milk = 20 litres

Milk withdrawn = 4 litres

Remaining milk = \(20 × (1 - \frac{4}{20})\)

⇒ Remaining milk = \(20 × \frac{16}{20}\)

⇒ Remaining milk = 16 litres

Initial milk = 16 litres

Milk withdrawn = 4 litres

Total liquid after adding water = 20 litres

Remaining milk = \(16 × (1 - \frac{4}{20})\)

⇒ Remaining milk = \(16 × \frac{16}{20}\)

⇒ Remaining milk = 12.8 litres

There will be 12.8 litres of milk left after the process is repeated twice.

Given:

The sum of marks obtained by Arun in English and Mathematics is 170.

The difference in marks obtained by Arun in English and Mathematics is 10.

Formula Used:

Let the marks in English be E and in Mathematics be M .

From the given conditions:

E + M = 170      ......(1)

E - M = 10     ......(2)

Calculation:

Adding equation (1) and (2):

⇒ (E + M) + (E - M) = 170 + 10

⇒ 2E = 180

⇒ E = 90

Substituting the value of E in equation (1):

⇒ 90 + M = 170

⇒ M = 80

Now, the ratio of marks in English to Mathematics is:

⇒ E : M = 90 : 80

⇒ 9 : 8

The ratio of marks obtained by Arun in English and Mathematics is 9 ∶ 8.

The correct answer is Cerebellum.

Key Points

• The Cerebellum is a crucial part of the brain that plays a significant role in maintaining body balance and coordination.
• It is located at the back of the brain, underneath the occipital lobes of the cerebral cortex.
• The cerebellum is responsible for fine-tuning motor activities and ensuring smooth, balanced muscular activity.
• It also helps in maintaining posture and equilibrium, making it essential for everyday activities such as walking, running, and other physical movements.

Additional Information

• The Medulla Oblongata is responsible for regulating vital functions such as heartbeat and breathing.
• The Thalamus acts as a relay station for transmitting sensory and motor signals to the cerebral cortex.
• The Mid Brain is involved in functions such as vision, hearing, eye movement, and body movement.

The logic followed here is :

Hence the correct answer is Option 4.

The correct answer is Common Salt.

Key Points

• Common salt (sodium chloride) is a crystalline solid.
• Amorphous solids are solids that do not have a long-range order of atoms.
• Examples of amorphous solids include substances like chalk, coal tar, and wood.
• Common salt has a well-defined crystalline structure, unlike amorphous solids.

Additional Information

• Amorphous solids have a disordered arrangement of atoms or molecules.
• Crystalline solids have a highly ordered arrangement of atoms or molecules, which contributes to their unique physical properties.
• Common salt is an example of a crystalline solid, characterized by its regular and repeating pattern of sodium and chloride ions.

According to the given information,

Let's check each option,

1) 3 × 4 > 2 - 9 + 3 < 3 

→ 3 + 4 × 2 = 9 ÷ 3 - 3 

→ 3 + 4 × 2 = 3 - 3

→ 3 + 8 = 3 - 3

→ 11 = 3 - 3

→ 11 = 0 ⇒ This is not true.

2) 5 × 3 < 3 ÷ 8 + 4 × 4

→ 5 + 3 - 3 > 8 ÷ 4 + 4

→ 5 + 3 - 3 > 2 + 4

→ 8 - 3 > 6

→ 5 > 6 ⇒ This is not true.

3) 3 × 2 < 4 ÷ 16 > 2 + 4 

→ 3 + 2 - 4 > 16 × 2 ÷ 4 

→ 3 + 2 - 4 > 16 × 1/2 

→ 3 + 2 - 4 > 8

→ 5 - 4 > 8

→ 1 > 8 ⇒ This is not true.

4) 5 > 8 + 4 = 10 < 4 × 8 

→ 5 × 8 ÷ 4 < 10 - 4 + 8 

→ 5 × 2 < 10 - 4 + 8 

→ 10 < 10 - 4 + 8 

→ 10 < 18 - 4

→ 10 < 14 ⇒ This is true.

Hence, the correct answer is "5 > 8 + 4 = 10 < 4 × 8".

Given:

Speed of A = 8 metres/second

Speed of B = 5 metres/second

Initial distance between A and B = 180 metres

Time = 70 seconds

Formula Used:

Relative Speed = Speed of A - Speed of B

Distance covered = Relative Speed × Time

New Distance between A and B = Initial Distance - Distance covered

Calculation:

Relative Speed = 8 - 5

Relative Speed = 3 metres/second

Distance covered in 70 seconds = 3 × 70

⇒ Distance covered = 210 metres

New Distance between A and B = 210 - 180

⇒ New Distance = 30 metres

The distance between A and B after 70 seconds is 30 metres.

The correct answer is Africa.

Key Points

• Madagascar is located in the Indian Ocean, off the southeastern coast of Africa.
• It is the fourth largest island in the world and is part of the African continent.
• The capital city of Madagascar is Antananarivo.
• Madagascar is known for its unique biodiversity and is home to many species that are not found anywhere else in the world.

Additional Information

• Madagascar separated from the Indian subcontinent around 88 million years ago, allowing its flora and fauna to evolve in relative isolation.
• The island is famous for its lemurs, baobab trees, and unique ecosystems.
• Due to its isolation, Madagascar has a high rate of endemism, with many species that are found nowhere else on Earth.