UPSC NDA-2 Archives

41. Buckminster fullerene, which looks like a football, is an allotropic f

Buckminster fullerene, which looks like a football, is an allotropic form of

Phosphorus

Sulfur

Carbon

Tin

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Buckminster fullerene, which looks like a football, is an allotropic form of Carbon.

Allotropes are different structural modifications of an element. Carbon exists in several allotropic forms, including diamond, graphite, graphene, and fullerenes. Buckminster fullerene, also known as C60, is the most well-known fullerene molecule, consisting of 60 carbon atoms arranged in a spherical structure resembling a soccer ball (truncated icosahedron).

Fullerenes were discovered in 1985 by Robert Curl, Harold Kroto, and Richard Smalley, who were awarded the Nobel Prize in Chemistry in 1996 for their work. Other allotropes of carbon like diamond and graphite are well-known for their distinct physical properties arising from different atomic arrangements. Phosphorus, Sulfur, and Tin also have allotropes, but fullerenes are specific to Carbon.

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42. Which one of the following alloys contains a non-metal as one of its c

Which one of the following alloys contains a non-metal as one of its constituent ?

Brass

Bronze

Amalgam

Steel

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Steel is an alloy that contains a non-metal, Carbon, as one of its primary constituents.

An alloy is a mixture of metals or a mixture of a metal and another element. Brass is an alloy of copper and zinc (both metals). Bronze is typically an alloy of copper and tin (both metals). An amalgam is an alloy of mercury with another metal (both mercury and the other element are metals). Steel is primarily an alloy of iron and carbon, where carbon is a non-metal. The carbon content in steel ranges from about 0.2% to 2.1% by weight.

The presence of carbon significantly alters the properties of iron, increasing its strength and fracture resistance compared to pure iron. The amount of carbon affects the steel’s properties; for instance, higher carbon content generally leads to harder and stronger steel but also makes it more brittle.

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43. Galvanization is a method of protecting iron from rusting by coating w

Galvanization is a method of protecting iron from rusting by coating with a thin layer of

Gallium

Aluminum

Zinc

Silver

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Galvanization is a method of protecting iron from rusting by coating it with a thin layer of Zinc.

Galvanization works by providing a barrier coating of zinc to prevent corrosive substances from reaching the underlying iron or steel. More importantly, zinc acts as a sacrificial anode. This means that zinc is more reactive than iron and will corrode preferentially, even if the coating is scratched and the iron is exposed.

Rusting is the corrosion of iron, which occurs when iron reacts with oxygen and water. Zinc protects iron through both barrier protection and sacrificial protection. Other metals like aluminum or silver are not typically used for galvanization of iron; aluminum is sometimes used in different protective coatings (like anodizing for aluminum itself), and silver is too expensive and not suitable for this application.

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44. Sita, 1·5 m high, stands before a plane mirror fixed on a wall to view

Sita, 1·5 m high, stands before a plane mirror fixed on a wall to view her full image. What should be the minimum height of the plane mirror so that Sita can view her image fully ?

0·50 m

0·35 m

0·75 m

0·25 m

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The minimum height of the plane mirror required for a person to view their full image is half of the person’s height.

For a person of height H standing in front of a plane mirror, the minimum height of the mirror needed to see the entire image is H/2. This is because of the law of reflection; light rays from the top of the head and the bottom of the feet reflect off the mirror into the observer’s eyes. The reflection point for the feet is halfway between the feet and the eyes’ height, and similarly for the top of the head.

In this case, Sita’s height is 1.5 m. The minimum mirror height is 1.5 m / 2 = 0.75 m. The position of the mirror is also important; the bottom edge of the mirror should be at a height halfway between the person’s eyes and their feet.

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45. The heating element in an electric iron is usually made of

The heating element in an electric iron is usually made of

Constantan

Tungsten

Nichrome

Copper

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The heating element in an electric iron is usually made of Nichrome.

Nichrome is an alloy primarily composed of nickel and chromium. It is chosen for heating elements because it has a high electrical resistance, allowing it to efficiently convert electrical energy into heat. It also has a high melting point and resistance to oxidation at high temperatures, ensuring durability and safety during operation.

Other materials like Constantan also have high resistance but are less commonly used for high-temperature heating elements compared to Nichrome. Tungsten has a very high melting point and is used for filaments in incandescent light bulbs, but not typically for resistive heating elements like those in irons or toasters. Copper has low resistance and is used for electrical wiring, not for generating heat.

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46. The potential difference between the two end terminals of an electric

The potential difference between the two end terminals of an electric heater is 220 V and the current through it is 0·5 A. What would be the current through the heater if the potential difference across the terminals of the heater is reduced to 120 V ?

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1·0 A

0·5 A

0·27 A

0·7 A

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Assuming the resistance of the electric heater remains constant, the current through it would be approximately 0.27 A when the potential difference is reduced to 120 V.

– We can use Ohm’s Law, which states that the voltage (V) across a resistor is directly proportional to the current (I) flowing through it, provided the temperature and other physical conditions remain unchanged (V = I * R).
– First, calculate the resistance (R) of the heater using the initial conditions: V1 = 220 V, I1 = 0.5 A.
– R = V1 / I1 = 220 V / 0.5 A = 440 ohms.
– Now, use this resistance to find the new current (I2) when the potential difference (V2) is 120 V.
– V2 = I2 * R
– 120 V = I2 * 440 ohms
– I2 = 120 V / 440 ohms = 12 / 44 A = 3 / 11 A.
– Calculating the decimal value: 3 / 11 ≈ 0.2727 A.

In reality, the resistance of a heater element made of materials like nichrome increases with temperature. However, standard Ohm’s Law problems involving fixed resistors or devices like heaters typically assume constant resistance unless otherwise specified. The calculated current represents the value based on this common assumption.

47. The flash of lightning is seen before the thunderstorm is heard. It ve

The flash of lightning is seen before the thunderstorm is heard. It verifies that

sound travels much faster than light

light travels much faster than sound

light and sound both travel with same speed

intensity of flash of lightning is very high during thunderstorm

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The fact that the flash of lightning is seen before the thunderstorm is heard verifies that light travels much faster than sound.

– Lightning and thunder occur simultaneously as a result of an electrical discharge in the atmosphere.
– Light (the flash) and sound (the thunder) are both produced by the same event.
– We see the light almost instantly because the speed of light in air is extremely high (approximately 3 x 10^8 m/s).
– We hear the thunder later because the speed of sound in air is much lower (approximately 343 m/s at 20°C).
– The time delay between seeing the flash and hearing the thunder is directly proportional to the distance of the thunderstorm.

For every 3 seconds delay between the flash and the thunder, the thunderstorm is approximately 1 kilometer (or 5 seconds per mile) away. This difference in speeds makes it possible to estimate the distance to a thunderstorm.

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48. The streaming of light beams coming from the Sun through trees is said

The streaming of light beams coming from the Sun through trees is said to have suggested that light travels in straight line. The particles on the path of light beams are visible to us because

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dust particles in the air reflect light into our eyes

dust particles in the air scatter light into our eyes

dust particles in the air refract light into our eyes

dust particles in the air polarize light into our eyes

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The particles on the path of light beams coming from the Sun are visible to us because dust particles in the air scatter light into our eyes.

– In a perfectly clean atmosphere, a beam of light passing through it would be invisible from the side. We see light when it enters our eyes.
– When light encounters particles in the air, such as dust, smoke, or water droplets, it interacts with them.
– Scattering occurs when light waves are deflected in various directions by these particles.
– Some of the scattered light is directed towards our eyes, making the path of the light beam visible.
– This phenomenon is related to the Tyndall effect, which is the scattering of light by particles in a colloid or suspension.

Reflection typically occurs from surfaces, refraction is the bending of light as it passes from one medium to another, and polarization is the restriction of the direction of oscillation of light waves. While dust particles can reflect and refract light, scattering is the primary mechanism by which the path of a light beam through a dusty or smoky medium becomes visible.

49. A microphone converts

A microphone converts

electrical signals to sound waves

sound waves to electrical signals

microwaves to sound waves

sound waves to microwaves

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A microphone converts sound waves into electrical signals.

– A microphone is a transducer, a device that converts one form of energy into another.
– Its function is to capture sound (which consists of variations in air pressure) and transform it into a corresponding electrical voltage or current signal.
– Different types of microphones use different principles (e.g., electromagnetic induction in dynamic microphones, capacitance change in condenser microphones) to achieve this conversion.
– The electrical signal produced by a microphone can then be amplified, recorded, or transmitted.

Conversely, a loudspeaker or headphone is a transducer that performs the opposite function: it converts an electrical signal into sound waves.

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50. A bullet of mass 10 g is horizontally fired with velocity 300 m s$^{-1

A bullet of mass 10 g is horizontally fired with velocity 300 m s$^{-1}$ from a pistol of mass 1 kg. What is the recoil velocity of the pistol?

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0·3 m s$^{-1}$

3 m s$^{-1}$

−3 m s$^{-1}$

−0·3 m s$^{-1}$

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The recoil velocity of the pistol is -3 m/s.

– This problem can be solved using the principle of conservation of linear momentum.
– The total momentum of the system (pistol + bullet) before firing is zero, as both are at rest.
– According to the conservation of momentum, the total momentum of the system after firing must also be zero.
– Let $m_b$ and $v_b$ be the mass and velocity of the bullet, and $m_p$ and $v_p$ be the mass and recoil velocity of the pistol.
– Momentum before firing = 0
– Momentum after firing = $m_b v_b + m_p v_p$
– By conservation of momentum: $m_b v_b + m_p v_p = 0$
– Given: $m_b = 10 \text{ g} = 0.01 \text{ kg}$, $v_b = 300 \text{ m/s}$, $m_p = 1 \text{ kg}$.
– Substituting the values: $(0.01 \text{ kg})(300 \text{ m/s}) + (1 \text{ kg}) v_p = 0$
– $3 \text{ kg} \cdot \text{m/s} + v_p \text{ kg} = 0$
– $v_p = -3 \text{ m/s}$

The negative sign for the recoil velocity indicates that the pistol moves in the opposite direction to the bullet. The magnitude of the recoil velocity is 3 m/s. This demonstrates Newton’s third law of motion (action-reaction) applied to momentum conservation.