1. Consider the following:
- Dispersion
- Total Internal Reflection
- Refraction
Which of the above phenomena contribute to the natural sparkle of a diamond?
[A] 1, 2 and 3
[B] Only 1 and 2
[C] Only 1
[D] 2 and 3
Show Answer
Correct Answer: A [1, 2 and 3]
Notes:
The brilliant sparkle of a diamond results from the combined effects of dispersion, refraction, and total internal reflection. Dispersion splits light into constituent colors, refraction bends the light sharply inside the stone due to high refractive index, and total internal reflection traps light, causing enhanced brightness and vivid sparkle characteristic of diamonds.
2. Consider the following statements:
- It takes approximately 11 seconds for light to reach Earth from the Moon.
- It takes approximately 8 minutes for light to reach Earth from the Sun.
- It takes 4.22 years for light to reach Earth from the nearest star, Alpha Centauri.
Which of the above statements is/are correct?
[A] Only 1 and 2
[B] Only 2 and 3
[C] Only 1 and 3
[D] Only 2
Show Answer
Correct Answer: D [Only 2]
Notes:
The first statement is incorrect, as light takes about 1.3 seconds to reach Earth from the Moon. The second statement is correct: sunlight takes approximately 8 minutes to reach Earth. The third statement is incorrect as the closest star is Proxima Centauri (not Alpha Centauri) and light from Alpha Centauri takes about 4.4 years to reach us.
3. Consider the following statements regarding the blending of gasoline with ethanol:
- Octane number is raised
- Energy content per volume is increased
- The engine is less likely to suffer damage
Which of the above statements is / are correct?
[A] Only 1 and 3
[B] Only 1
[C] Only 2 and 3
[D] 1, 2 and 3
Show Answer
Correct Answer: A [Only 1 and 3]
Notes:
Blending gasoline with ethanol does raise the octane number (statement 1), helping prevent engine knocking and reducing the likelihood of engine damage (statement 3). However, energy content per volume actually decreases because ethanol has lower energy density compared to gasoline. Therefore, only statements 1 and 3 are correct.
4. Consider the following comparisons of Diesel with Gasoline:
- In comparison to Gasoline, Diesel offers low volumetric energy density
- In comparison to Gasoline, Diesel is cheap all over the world
- In comparison to Gasoline, CO2 emissions from diesel are higher
Choose the correct statements:
[A] Only 1
[B] 1 & 2
[C] 1, 2 & 3
[D] None of them
Show Answer
Correct Answer: D [None of them]
Notes:
Diesel is not cheaper then gasoline or petrol in all European and North American countries. In fact, it is generally more expensive compared to gasoline. Diesel is cheaper in India because it’s believed to be generally used by farmers and truck and bus fleets (local and intercity buses owned by state governments) and is subsidized. When burnt, Diesel offers a net heating value of 43.1 MJ/kg as opposed to 43.2 MJ/kg for gasoline. However, due to the higher density, diesel offers a higher volumetric energy density at 35.86 MJ/L (128 700 BTU/US gal) vs. 32.18 MJ/L (115 500 BTU/US gal) for gasoline, some 11% higher, which should be considered when comparing the fuel efficiency by volume. The CO2 emissions from diesel are 73.25 g/MJ, just slightly lower than for gasoline at 73.38 g/MJ.
5. With reference to the Moon's orbit around the Earth, which of the following statements are correct?
- It is a circular orbit
- It is perpendicular to Earth's equatorial plane
- It is getting larger every year by around 3.8 centimetres
Select the correct option from the codes given below:
[A] Only 1 & 2
[B] Only 3
[C] Only 1 & 3
[D] 1, 2 & 3
Show Answer
Correct Answer: B [Only 3]
Notes:
The Moon's orbit is elliptical, not perfectly circular. It is inclined at about 5 degrees to Earth's equatorial plane, not perpendicular. Scientific measurements confirm the Moon's orbit is moving away from Earth at a rate of 3.8 cm per year, increasing the distance between Earth and Moon yearly.
6. Consider the following statements regarding spring tides and neap tides:
- Neap tides occur when the Moon is at its quarter phase.
- Spring tides occur on both Full Moon and New Moon.
- Spring tide results in higher than normal high tides and lower than normal low tides.
- During neap tides, the high tide is lower and the low tide is higher than usual.
Which of the above statements is/are correct?
[A] Only 1 & 2
[B] Only 1, 2 & 3
[C] 2, 3 & 4
[D] 1, 2, 3 & 4
Show Answer
Correct Answer: D [1, 2, 3 & 4]
Notes:
All four statements are correct. Neap tides occur at the Moon’s quarter phases when the Sun and Moon are at right angles. Spring tides happen during both Full and New Moons, leading to extreme tidal ranges—higher high tides and lower low tides. During neap tides, tidal range decreases, so high tides are lower and low tides are higher than average.
7. Consider the following celestial bodies:
- Ceres
- Makemake
- Eris
- Pluto
Which of the above have been recognized as dwarf planets by the International Astronomical Union (IAU)?
[A] 1, 2 & 3 Only
[B] 1 & 2 Only
[C] 2 & 3 Only
[D] 1, 2, 3 & 4
Show Answer
Correct Answer: D [ 1, 2, 3 & 4]
Notes:
The International Astronomical Union (IAU) currently recognizes five dwarf planets: Ceres, Pluto, Haumea, Makemake, and Eris. A dwarf planet is a planetary-mass object that is neither a planet nor a natural satellite. It is in direct orbit of the Sun, and is massive enough for its gravity to crush it.
8. Consider the following differences between Solar day and Sidereal day:
- While Solar day is measured by the apparent diurnal motion of the sun, sidereal day is measured with respect to the distant stars
- The sidereal day is four minutes shorter than the solar day
Which of the above statements is/are correct?
[A] 1 Only
[B] 2 Only
[C] Both 1 & 2
[D] Neither 1 nor 2
Show Answer
Correct Answer: C [ Both 1 & 2]
Notes:
Both are correct statements
9. An ideal fuel should have:
- High calorific value
- Low moisture content
- High anti-knocking value
Select the correct option from codes given below:
[A] 1 & 2 Only
[B] 2 & 3 Only
[C] 1 & 3 Only
[D] 1, 2 & 3
Show Answer
Correct Answer: D [ 1, 2 & 3]
Notes:
High anti-knocking value is necessary to make higher compression ratios. An ideal fuel should have high calorificvalue and low moisture content.
10. Consider the following statements regarding X-Rays and Gamma Rays:
- They have almost similar wavelengths.
- They have almost similar penetrating capacity.
- They are electromagnetic waves.
- They travel with the speed of light.
- Both are ionizing in nature.
Select the correct option from the codes given below:
[A] Only 2, 3, 4 & 5
[B] Only 3, 4, 5
[C] Only 1, 2 & 3
[D] Only 3 & 4
Show Answer
Correct Answer: D [Only 3 & 4]
Notes:
The wavelength of X-rays is of the order of 1Å, whereas the wavelength of gamma rays is of the order of 10–3Å, so statement 1 is incorrect. X-rays are less penetrating than gamma rays, hence statement 2 is also incorrect. Both X-Rays and Gamma Rays are indeed electromagnetic waves and they both travel with the speed of light, making statements 3 and 4 correct. Therefore, the correct option is only 3 & 4.
