UPSC NDA-1

31. A fuse wire must be

A fuse wire must be

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conducting and of low melting point
conducting and of high melting point
insulator and of high melting point
insulator and of low melting point
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The correct option is A) conducting and of low melting point. A fuse wire must possess these properties to function correctly as a safety device.
– A fuse wire is designed to protect electrical circuits and appliances from damage due to excessive current.
– It is connected in series with the circuit, so it must be able to conduct electricity under normal operating conditions. Thus, it must be **conducting**.
– When the current flowing through the circuit exceeds a specified limit (the fuse rating), the fuse wire heats up due to the Joule effect (heat = I²Rt).
– To break the circuit and stop the excessive current flow, the fuse wire must melt when it gets too hot. This requires it to have a **low melting point**.
– If the fuse wire had a high melting point or was an insulator, it would not serve its purpose as a safety device.
Fuse wires are typically made of materials like tin, lead, or an alloy of tin and lead, which have relatively low melting points compared to the wires used in the rest of the circuit (like copper). The thickness and material of the fuse wire are carefully chosen to ensure it melts at the desired current level. Modern circuits often use circuit breakers instead of fuses, which are resettable switches that automatically trip when current is too high.

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32. LIGO stands for

LIGO stands for

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Laser Interferometer Gravitational wave Observatory
Light Interferometer Gravitational wave Observatory
Light Induced Gravity Observer
Laser Induced Gascous Optics
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The correct option is A) Laser Interferometer Gravitational wave Observatory. LIGO is a major scientific collaboration dedicated to detecting gravitational waves.
– LIGO stands for Laser Interferometer Gravitational-Wave Observatory.
– It is a large-scale physics experiment and observatory designed to detect cosmic gravitational waves and to develop gravitational-wave science as an astronomical tool.
– LIGO consists of two large observatories in the United States (Livingston, Louisiana, and Hanford, Washington) that work in tandem.
LIGO achieved the first direct detection of gravitational waves on September 14, 2015, from the merger of two black holes. This detection, announced in February 2016, confirmed a major prediction of Einstein’s general theory of relativity and opened a new window on the universe, leading to the Nobel Prize in Physics in 2017.

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33. When a beam of white light passes through a glass prism, the colour of

When a beam of white light passes through a glass prism, the colour of light beam that deviates the least is

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Blue
Red
Green
Violet
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The correct option is B) Red. When white light passes through a glass prism, red light deviates the least.
– When white light passes through a prism, it undergoes dispersion, splitting into its constituent colors because the refractive index of the prism material is different for different wavelengths (colors) of light.
– This phenomenon is called dispersion. The spectrum of white light in order of increasing wavelength (and decreasing frequency) is Violet, Indigo, Blue, Green, Yellow, Orange, Red (VIBGYOR).
– The deviation experienced by light passing through a prism is related to the refractive index of the material for that color. Generally, refractive index decreases with increasing wavelength.
– Longer wavelengths (like red) are refracted less, meaning they deviate less from their original path.
– Shorter wavelengths (like violet) are refracted more, meaning they deviate the most.
– Therefore, red light deviates the least, and violet light deviates the most.
The angle of deviation (δ) for a prism is related to the angle of incidence, angle of the prism (A), and the refractive index (μ) of the prism material by complex formulas, but generally, for a given prism angle and angle of incidence, a higher refractive index leads to a greater angle of deviation. Since μ is higher for shorter wavelengths (violet) and lower for longer wavelengths (red), violet deviates more than red. This is why the colors are separated when white light passes through a prism.

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34. The formula for conversion between Fahrenheit and Celsius is °F=X+(1.8

The formula for conversion between Fahrenheit and Celsius is
°F=X+(1.8×°C)
What is factor X ?

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32
22
98
42
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The correct option is A) 32. The formula for converting Celsius to Fahrenheit is °F = (1.8 × °C) + 32.
– The standard formula for temperature conversion from Celsius (°C) to Fahrenheit (°F) is °F = (°C × 9/5) + 32.
– Since 9/5 is equal to 1.8, the formula can be written as °F = (1.8 × °C) + 32.
– The given formula is °F = X + (1.8 × °C).
– Comparing the standard formula with the given formula, we can see that X must be 32.
The Fahrenheit and Celsius scales have different reference points and different increments per degree. The freezing point of water is 0°C or 32°F. The boiling point of water is 100°C or 212°F. The factor 1.8 (or 9/5) accounts for the different degree sizes, and the factor 32 accounts for the different zero points. The inverse formula for converting Fahrenheit to Celsius is °C = (°F – 32) / 1.8 or °C = (°F – 32) × 5/9.

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35. ‘Black hole’ is a

‘Black hole’ is a

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huge black star which has zero acceleration due to gravity on its surface
star which has moderate acceleration due to gravity on its surface
star which has collapsed into itself and has large acceleration due to gravity on its surface
star which has collapsed into itself and has zero acceleration due to gravity on its surface
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The correct option is C) star which has collapsed into itself and has large acceleration due to gravity on its surface. This describes the nature of a black hole.
– A black hole is not a regular star; it is the result of the gravitational collapse of a very massive star after it exhausts its nuclear fuel.
– This collapse compresses the mass into an extremely small volume, resulting in incredibly dense matter.
– The gravitational pull becomes so strong that nothing, not even light, can escape from within a certain boundary called the event horizon.
– The “surface” (event horizon) of a black hole is characterized by an extremely large acceleration due to gravity (often conceptualized by the escape velocity exceeding the speed of light).
– Options A, B, and D are incorrect because a black hole is not a typical star, and it has extremely large, not zero or moderate, acceleration due to gravity at its boundary.
Black holes are predicted by Einstein’s theory of general relativity. They are regions of spacetime exhibiting such strong gravitational effects that nothing—not even particles and electromagnetic radiation such as light—can escape from inside their event horizon. The point of infinite density at the center of a black hole is called the singularity.

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36. Which one of the following statements regarding a thermos flask is NOT

Which one of the following statements regarding a thermos flask is NOT correct?

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The walls of flask are separated by vacuum and made of glass which is a poor conductor of heat
The glass walls themselves have shiny surfaces
The surface of inner wall radiates good amount of heat and the surface of outer wall absorbs some of heat that is radiated from the inner wall
The cork supports are poor conductors of heat
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The correct option is C) The surface of inner wall radiates good amount of heat and the surface of outer wall absorbs some of heat that is radiated from the inner wall. This statement is NOT correct regarding a thermos flask.
– A thermos flask is designed to minimize heat transfer by conduction, convection, and radiation.
– To minimize heat transfer by radiation, the surfaces of the inner and outer glass walls are made shiny (often silvered). Shiny surfaces are poor emitters and poor absorbers of thermal radiation.
– Statement A is correct: Vacuum between walls minimizes conduction and convection; glass is a poor conductor.
– Statement B is correct: The glass walls have shiny surfaces to reduce radiation.
– Statement D is correct: Cork or plastic supports minimize conduction through the neck.
– Statement C is incorrect because the shiny inner wall surface is designed to radiate a *poor* amount (low emissivity) of heat, not a “good amount”. While the outer wall would absorb some radiated heat, the primary mechanism to reduce radiative transfer is the low emissivity/absorptivity of the surfaces.
Heat transfer in a thermos flask is minimized through several features: vacuum (prevents conduction/convection), silvered/shiny surfaces (reduces radiation), poor conducting stopper (prevents conduction/convection), and supports made of insulating material (prevents conduction). The effectiveness relies on minimizing all three modes of heat transfer.

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37. In the given velocity (V) versus time (t) graph, accelerated and decel

In the given velocity (V) versus time (t) graph, accelerated and decelerated motions are respectively represented by line segments

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CD and BC
BC and AB
CD and AB
AB and CD
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In a velocity-time graph, accelerated motion is represented by a line segment with a positive slope (velocity increasing with time), and decelerated motion (or retardation) is represented by a line segment with a negative slope (velocity decreasing with time).
Line segment CD has a positive slope, indicating that velocity is increasing with time, which is accelerated motion. Line segment AB has a negative slope, indicating that velocity is decreasing with time, which is decelerated motion.
Line segment BC represents motion with constant velocity, meaning zero acceleration. The question asks for accelerated motion followed by decelerated motion, which corresponds to segments CD and AB respectively.

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38. 1 dyne (a unit of force in CGS system) equals to

1 dyne (a unit of force in CGS system) equals to

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$10^3$ g cm/s²
$10^{-3}$ g cm/s²
$10^5$ kg m/s²
$10^{-5}$ kg m/s²
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1 dyne, a unit of force in the CGS system, is equal to $10^{-5}$ kg m/s² in the SI system.
– The CGS unit of force is the dyne, defined as 1 g ⋅ cm/s².
– The SI unit of force is the Newton (N), defined as 1 kg ⋅ m/s².
– To convert dyne to Newton, we convert the units:
– 1 gram (g) = $10^{-3}$ kilogram (kg)
– 1 centimeter (cm) = $10^{-2}$ meter (m)
– So, 1 dyne = 1 g ⋅ cm/s² = ($10^{-3}$ kg) ⋅ ($10^{-2}$ m) / s² = $10^{-3} \times 10^{-2}$ kg ⋅ m/s² = $10^{-5}$ kg ⋅ m/s².
Therefore, 1 dyne = $10^{-5}$ N. Conversely, 1 Newton = $10^5$ dyne. Understanding unit conversions between different systems like CGS and SI is fundamental in physics.

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39. The figure shown above gives the time (t) versus position (x) graphs o

The figure shown above gives the time (t) versus position (x) graphs of three objects A, B and C. Which one of the following is the correct relation between their speeds $V_A$, $V_B$ and $V_C$, respectively at any instant (t > 0)?

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”$V_A
”$V_A
”$V_A
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The speeds of the three objects are represented by the slope of their position-time graphs. The correct relation between their speeds is $V_A > V_B > V_C$.
– In a position-time (x-t) graph, the velocity (speed if motion is in one direction without change in direction) is given by the slope of the graph ($\Delta x / \Delta t$).
– A steeper slope indicates a higher speed, and a less steep slope indicates a lower speed.
– Examining the graph, the line for object A has the steepest slope.
– The line for object B has a slope less steep than A but steeper than C.
– The line for object C has the least steep slope.
– Since all slopes are positive, the objects are moving in the positive direction. The magnitude of the slope represents the speed.
All three graphs are straight lines, indicating that the objects are moving with constant velocities (uniform motion). If the lines were curved, the slope would change over time, indicating changing velocity (acceleration).

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40. The Sun is seen little before it rises and for a short while after it

The Sun is seen little before it rises and for a short while after it sets. This is because of

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total internal reflection
atmospheric refraction
apparent shift in the direction of Sun
dispersion
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The phenomenon of seeing the Sun slightly before it rises and after it sets is caused by atmospheric refraction.
– Light from the Sun bends as it passes through the Earth’s atmosphere, which is denser near the surface.
– When the Sun is below the horizon, the light rays from it are refracted (bent) downwards as they enter the atmosphere, making the Sun appear to be above the horizon to an observer.
– This effect causes the Sun to be visible for a few minutes before its geometrical sunrise and after its geometrical sunset.
The amount of refraction depends on atmospheric conditions, but it typically makes the Sun appear about 0.5 degrees higher than its true position on the horizon. This also contributes to the apparent flattening of the Sun’s disc when it is very low on the horizon.

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