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The correct answer is Refraction

Key Points

• When a fish is underwater and you observe it from above the water surface, the apparent position of the fish appears closer to the surface than its actual position.
• When light travels from one medium (such as water) to another (such as air), it changes direction due to refraction.
• This phenomenon occurs because light travels at different speeds in different materials.
• The refractive index (or index of refraction) describes how fast light travels through a material.

Additional Information

 Diffraction:

• Diffraction involves the interference or bending of light around the corners of an obstacle or through an aperture into the region of geometrical shadow created by the obstacle or aperture.
• In classical physics, diffraction is described by the Huygens–Fresnel principle, which treats each point in a propagating wavefront as a collection of individual spherical wavelets.

Total Internal Reflection:

• Total internal reflection occurs when light rays travel from a more optically dense medium (like water) to a less optically dense medium (like air) and are reflected back at the surface of the denser medium.
• The angle of incidence must be greater than the critical angle .

Reflection:

• Reflection involves the change in direction of a light ray at an interface between two different media so that the ray returns to the medium from which it originated.
• The laws of reflection determine how incident light rays behave on reflecting surfaces, such as mirrors, smooth metal surfaces, and clear water:
• The incident ray, the reflected ray, and the normal all lie in the same plane.
• The angle of incidence (the angle between the incident ray and the normal) equals the angle of reflection (the angle between the reflected ray and the normal).

The correct answer is Eichhornia crassipes.

Key Points

• Breathing roots are the modified roots which are also called pneumatophores.
• Eichhornia crassipes medical function -Water hyacinth is reported to have anti-inflammatory, antifungal, and antibacterial functions.

Additional Information

• Examples of plants with breathing roots are banyan, money plants, rubber plants, ficus, peepal tree, pakad tree, and many more.

The logic followed here is:

2, 7, 13, 23, 34, 47 →Except 34 all other numbers are prime numbers.

Hence the correct answer is 34.

Additional Information Prime number - The number that is divisible by only 1 and itself.

**Given:**

Question: How many faces does a triangular prism have?

Options: 1) 6, 2) 4, 3) 3, 4) 5

Correct Option: 4

**Concept:**

A triangular prism is a 3-dimensional solid shape with two parallel and congruent triangular bases and three rectangular faces joining them.

**Calculation:**

We need to find the total number of faces of a triangular prism.

⇒ A triangular prism has:

⇒ 2 triangular faces (one at the base and one on top)

⇒ 3 rectangular faces joining the sides of the triangles

⇒ Total faces = 2 (triangular) + 3 (rectangular)

⇒ Total faces = 5

**Hence, the triangular prism has 5 faces.**

``` Explanation: - **Given**: Summarizes the key data from the question. - **Concept**: Describes the main concept needed to solve the problem. - **Calculation**: Provides a step-by-step solution to the problem, using arrows (⇒) to start each step. - **Conclusion**: Summarizes the result with "Hence" and states the final answer.

Given:

The product of two digits of a two-digit number is 12. Adding 36 to the number the digits interchange their place.

Concept:

Let the two-digit number be 10a + b, where 'a' and 'b' are the digits.

Given, ab = 12 and 10a + b + 36 = 10b + a

Calculation:

We have,

⇒ ab = 12

⇒ 10a + b + 36 = 10b + a

⇒ 9a - 9b = -36

⇒ a - b = -4

Now, solve the equations:

From ab = 12, we get possible pairs (a, b) as (2, 6) or (6, 2).

Check each pair:

For (a, b) = (2, 6):

⇒ a - b = 2 - 6 = -4 (valid)

For (a, b) = (4, 3):

⇒ a - b = 6 - 2 = 4 (not valid)

Hence, the number is 23 (since 10a + b = 10×2 + 6 = 26).

∴ The correct answer is option 4 (26).

Formula used:

a³ + b³ = (a + b)(a² + b² - ab)

Calculation: 

\(\frac{{8 \cdot 73 × 8 \cdot 73 × 8 \cdot 73 + 4 \cdot 27 × 4 \cdot 27 × 4 \cdot 27}}{{8 \cdot 73 × 8 \cdot 73 - 8 \cdot 73 × 4 \cdot 27 + 4 \cdot 27 × 4 \cdot 27}}\)

⇒ (8.73)³ + (4.27)³ / [(8.73)2 + (4.27)2 - 8.73 × 4.27]

⇒ (8.73 + 4.27)[(8.73)2 + (4.27)2 - 8.73 × 4.27] / [(8.73)2 + (4.27)2 - 8.73 × 4.27]

⇒ (8.73 + 4.27) = 13

∴ The correct answer is 13.

Given:

P and Q invest Rs 2560 and Rs 2000 respectively in the business. The profit at the end of the year is Rs 1105, and P receives a profit of Rs 320.

Concept Used:

The profit distribution is based on the ratio of their investments.

Formula Used:

Profit Ratio = Investment Ratio

Calculation:

⇒ Let R's investment be Rs x.

⇒ Total investment = 2560 + 2000 + x = 4560 + x

⇒ P's share of profit = (P's investment / Total investment) × Total profit

⇒ 320 = (2560 / (4560 + x)) × 1105

⇒ 320 × (4560 + x) = 2560 × 1105

⇒ 320 × 4560 + 320x = 2560 × 1105

⇒ 1459200 + 320x = 2828800

⇒ 320x = 2828800 - 1459200

⇒ 320x = 1369600

⇒ x = 1369600 / 320

⇒ x = 4280

∴ R invested Rs 4280 in the business.

Calculation:

\(\frac{{b + c}}{{(a - b)(c - a)}}\) + \(\frac{{c + a}}{{(a - b)(b - c)}}\) + \(\frac{{a + b}}{{(c - a)(b - c)}}\)

⇒ \(\frac{(b+c)(b-c)\ +\ (c+a)(c-a)\ + \ (a+b)(a-b)}{(a-b)(b-c)(c-a)}\)

⇒ \(\frac{(b^2-c^2)\ +\ (c^2-a^2)\ + (a^2-b^2)}{(a-b)(b-c)(c-a)}\)

⇒ \(\frac{0}{(a-b)(b-c)(c-a)}\)

⇒ 0

∴ The correct answer is 0.

According to the given information,

1) Shyam left his house and after going west for 40 m, turned right for another 60 m.

2. From there turned left for another 50 m.

3. And again, turned left twice in succession for 80 m and 30 m respectively.

4) Then again started moving to the left. 

Here, we can see that Shyam is now facing North direction.

Hence, the correct answer is "North".

The correct answer is Thyroid,

Key Points

• The Thyroid gland is responsible for secreting thyroxine, also known as T4.
• This hormone plays a crucial role in regulating your body's metabolism, heart and muscle function, brain development, and bone health.

Additional Information

• Hypothalamus: The hypothalamus produces a hormone called thyrotropin-releasing hormone (TRH), which stimulates the pituitary gland to release thyroid-stimulating hormone (TSH). TSH, in turn, tells the thyroid gland to produce thyroxine. So, while the hypothalamus indirectly influences thyroxine production, it doesn't directly secrete it.
• Pituitary: The pituitary gland releases TSH, which signals the thyroid gland to produce thyroxine. Again, not the direct source of thyroxine secretion.
• Thalamus: The thalamus is a part of the brain responsible for relaying sensory and motor information. It has no role in hormone production.