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Given:

9408 ÷ √? = 336

Calculation:

⇒ ? = (9408 ÷ 336)²

⇒ ? = 28²

⇒ ? = 784

∴ The correct answer is option (3).

Given:

Speed of train = 36 km/hr

Time to cross standing man = 10 seconds

Length of platform = 55 m

Formula used:

Speed = Distance / Time

Time to cross platform = Total Distance / Speed

Calculation:

Speed in m/s = \(\frac{36 \times 5}{18}\) = 10 m/s

Length of train = Speed × Time

⇒ Length of train = 10 × 10 = 100 m

Total distance to cross platform = Length of train + Length of platform

⇒ Total distance = 100 + 55 = 155 m

Time to cross platform = Total distance / Speed

⇒ Time = \(\frac{155}{10}\) = 31/2 = \(15\frac{1}{2}\) seconds

∴ The correct answer is option (2).

The correct answer is scattering of light.

Key Points

• The blue color of the clear sky is primarily caused by the scattering of sunlight by atmospheric particles.
• When sunlight enters Earth's atmosphere, it interacts with air molecules and small particles. This phenomenon is called Rayleigh scattering.
• Rayleigh scattering is more effective at shorter wavelengths of light, such as blue and violet. Since our eyes are more sensitive to blue light, the sky appears blue.
• The intensity of scattering is inversely proportional to the fourth power of the wavelength. Therefore, shorter wavelengths like blue are scattered more than longer wavelengths such as red.
• During sunrise and sunset, the sunlight passes through a thicker layer of the atmosphere, scattering out the shorter wavelengths, leaving the longer wavelengths like red and orange, which is why we see reddish hues at these times.

Additional Information

• Diffraction of light:
• Diffraction refers to the bending of light waves around obstacles or the edges of an aperture.
• It occurs when the size of the obstacle or aperture is comparable to the wavelength of light.
• Diffraction is responsible for patterns like those seen in the interference of light waves, such as the rainbow-like colors in CD surfaces or soap bubbles.
• However, diffraction is not responsible for the blue color of the sky.
• Reflection of light:
• Reflection occurs when light waves bounce off a surface, such as a mirror or water body.
• The angle of incidence is equal to the angle of reflection in such cases.
• While reflection is a significant phenomenon in optics, it is unrelated to the blue color of the sky.
• Refraction of light:
• Refraction is the bending of light as it passes from one medium to another with a different refractive index, such as air to water.
• Refraction is responsible for phenomena like the bending of light in a glass prism and the formation of rainbows.
• Although refraction plays an important role in other optical phenomena, it does not explain why the sky appears blue.

The correct answer is Muhammad bin Tughluq.

Key Points

• Ibn Batutah, a Moroccan traveler and scholar, visited India during the reign of Muhammad bin Tughluq in 1334 CE.
• Muhammad bin Tughluq, the Sultan of Delhi, was known for his eccentric policies and ambitious plans, which often ended in failure.
• Ibn Batutah was appointed as the Qazi (judge) of Delhi by Muhammad bin Tughluq, showcasing the Sultan’s appreciation for scholars and administrators.
• The traveler recorded his observations in his book, "Rihla" (The Travels), which provides invaluable insights into the socio-economic and cultural aspects of India during Tughluq’s reign.
• Muhammad bin Tughluq’s court was known for its cosmopolitan nature, attracting scholars, travelers, and merchants from different parts of the world, including Ibn Batutah.

Additional Information

• Sher Shah Suri:
• Sher Shah Suri was an Afghan ruler who established the Suri dynasty in India (1540–1545).
• He is best known for introducing administrative reforms and the construction of the Grand Trunk Road, which connected various parts of India.
• He did not have any notable interaction with Ibn Batutah as his reign occurred after Batutah’s travels.
• Alauddin Khilji:
• Alauddin Khilji was the second ruler of the Khilji dynasty, known for his military conquests and economic reforms.
• He implemented strict market regulations and expanded the Delhi Sultanate significantly.
• Ibn Batutah did not visit India during Alauddin Khilji’s reign as his travels occurred much later.
• Ghiyasuddin Tughluq:
• Ghiyasuddin Tughluq was the founder of the Tughluq dynasty, ruling from 1320 to 1325 CE.
• His reign was marked by military campaigns and efforts to stabilize the empire after the decline of the Khilji dynasty.
• Although Ghiyasuddin Tughluq preceded Muhammad bin Tughluq, Ibn Batutah visited India after his reign.
• Main Theme:
• Ibn Batutah’s travels provide a significant historical account of the Delhi Sultanate under Muhammad bin Tughluq, offering insights into the culture, administration, and political landscape of medieval India.
• His observations are crucial for understanding the historical context of Tughluq’s reign and the broader cultural exchanges during the 14^th century.

The correct answer is Pyrometer.

Key Points

• A pyrometer is an instrument designed for measuring very high temperatures, typically used in industrial processes.
• It works based on the principle of thermal radiation emitted by hot objects, particularly in the visible and infrared spectrum.
• Pyrometers are non-contact devices, making them ideal for measuring the temperature of objects that are too hot or inaccessible to touch directly.
• It is widely used in applications such as metallurgy, ceramics, and glass industries, where temperatures can exceed thousands of degrees Celsius.
• Modern pyrometers often use laser technology for improved precision and accuracy.

Additional Information

• Thermostat:
• A thermostat is a device used to regulate and maintain temperature within a predefined range, typically in heating or cooling systems.
• It does not measure high temperatures but instead controls temperature at safe levels in appliances such as air conditioners, refrigerators, and home heating systems.
• Thermostats work based on sensors and switches to turn devices on or off when the desired temperature threshold is reached.
• Pyrheliometer:
• A pyrheliometer is an instrument used to measure direct beam solar irradiance and is commonly utilized in solar energy research.
• It operates by detecting solar radiation and converting it into electrical signals for analysis.
• This device is not designed for measuring temperature but for studying solar intensity and its impact on the environment.
• Pyknometer:
• A pyknometer is a laboratory device used to measure the density or specific gravity of liquids and solids.
• It is generally used in chemistry and material science research to determine the physical properties of substances.
• Pyknometers are not related to temperature measurement.

The correct answer is (B) KPSU.

The logic is based on the number of letters skipped between each consecutive letter in the group.

• E (+4) J (+3) N (+0) O → Pattern: +5, +4, +1

• N (+4) S (+3) W (+0) X → Pattern: +5, +4, +1

• H (+4) M (+3) Q (+0) R → Pattern: +5, +4, +1

• K (+4) P (+2) S (+1) U → Pattern: +5, +3, +2, which is different.

The correct answer is (D) Hydrogen.

Key Points

• According to the Arrhenius and Brønsted-Lowry definitions, an acid is a substance that produces hydrogen ions (H⁺) or donates protons when dissolved in a solvent like water.
• Therefore, hydrogen is the essential element common to all acids.

The correct answer is (A) Indonesia.

Key Points

• Indonesia is the world's largest archipelagic country, consisting of over 17,500 islands.
• Due to this vast number of islands, it is often referred to poetically as the 'Land of a Thousand Islands'.

The correct answer is (B) 128.

The pattern in the series is as follows: multiply the current number by a decreasing integer (starting from 4) and then add twice that same integer to get the next number.

(30 × 4) + (2 × 4) = 120 + 8 = 128

(128 × 3) + (2 × 3) = 384 + 6 = 390

(390 × 2) + (2 × 2) = 780 + 4 = 784

(784 × 1) + (2 × 1) = 784 + 2 = 786

The correct answer is (A) Cousin.

Key Points

• Here is the step-by-step breakdown of the relationship:
• "His father's wife" is Vinod's mother.
• "The only brother of his father's wife" is the only brother of Vinod's mother, which makes him Vinod's maternal uncle.
• Vishal is the "son of" this person, meaning Vishal is the son of Vinod's maternal uncle.
• The son of one's uncle is their cousin.