UPSC NDA-1 Archives

31. Suppose the force of gravitation between two equal masses is F. If eac

Suppose the force of gravitation between two equal masses is F. If each mass is doubled keeping the distance of separation between them unchanged, the force would become

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2 F

4 F

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UPSC NDA-1 – 2016

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According to Newton’s Law of Universal Gravitation, the force of gravitation (F) between two masses (m₁ and m₂) separated by a distance (r) is given by the formula:
F = G * (m₁ * m₂) / r²
where G is the gravitational constant.
Initially, we have two equal masses, let’s call them m. So, m₁ = m and m₂ = m. The force is F = G * (m * m) / r² = G * m² / r².
Now, each mass is doubled, so the new masses are m₁’ = 2m and m₂’ = 2m. The distance of separation (r) remains unchanged.
The new force (F’) is:
F’ = G * (m₁’ * m₂’) / r²
F’ = G * (2m * 2m) / r²
F’ = G * (4 * m²) / r²
We can rewrite this as:
F’ = 4 * (G * m² / r²)
Since F = G * m² / r², we have F’ = 4 * F.
The force becomes four times the original force.

The gravitational force between two masses is directly proportional to the product of their masses. If both masses are doubled, their product becomes (2m) * (2m) = 4m², quadrupling the force, assuming the distance remains constant.

The gravitational force is also inversely proportional to the square of the distance between the centres of the masses. If the distance were, for example, doubled instead of the masses, the force would become F/4.

32. Arrange the following centres of AIIMS from East to West : 1. Rishik

Arrange the following centres of AIIMS from East to West :

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1. Rishikesh
2. New Delhi
3. Patna
4. Bhubaneswar

Select the correct answer using the code given below :

4-3-1-2

4-1-3-2

3-4-2-1

3-2-1-4

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To arrange the cities from East to West, we need to consider their relative longitudes.
1. Rishikesh (Uttarakhand) – Approx. Longitude 78.3° E
2. New Delhi (Delhi) – Approx. Longitude 77.2° E
3. Patna (Bihar) – Approx. Longitude 85.1° E
4. Bhubaneswar (Odisha) – Approx. Longitude 85.8° E
Ordering from East to West (decreasing longitude):
Bhubaneswar (85.8° E) is the most East.
Patna (85.1° E) is West of Bhubaneswar.
Rishikesh (78.3° E) is West of Patna.
New Delhi (77.2° E) is West of Rishikesh and the most West.
So, the East to West order is 4, 3, 1, 2.

Arranging locations East to West requires comparing their longitudes. Locations further East have higher longitudes (in the Eastern Hemisphere).

The exact locations of AIIMS centres within these cities would provide precise coordinates, but the cities’ approximate locations are sufficient for this relative ordering. Bhubaneswar AIIMS (established 2012), Patna AIIMS (established 2012), Rishikesh AIIMS (established 2012), New Delhi AIIMS (established 1956). The question asks for the centres of AIIMS, implying the locations of the institutes themselves.

33. One of the main causes of air pollution in cities is emissions from ve

One of the main causes of air pollution in cities is emissions from vehicles like cars and trucks. Cars emit various pollutants which are bad for human health when inhaled, like

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1. Nitrogen oxides (NO_x)
2. Carbon monoxide (CO)
3. Carbon dioxide (CO₂)
4. Benzene

Which of the above pollutants are not tolerated by human beings even at very low levels ?

1 and 4 only

1 and 2 only

1, 2 and 3 only

1, 2 and 4 only

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The question asks which pollutants are *not* tolerated by human beings *even at very low levels*. This typically refers to substances with high toxicity or carcinogenicity at trace concentrations.
1. Nitrogen oxides (NOx): Respiratory irritants, contribute to smog. Can cause respiratory problems at relatively low concentrations.
2. Carbon monoxide (CO): Highly toxic gas. Binds to haemoglobin more strongly than oxygen, impairing oxygen transport. Even low levels in inhaled air can be dangerous, especially over time.
3. Carbon dioxide (CO₂): A greenhouse gas and a natural component of air (around 400 ppm). It is not toxic at these ambient levels. High concentrations (e.g., > 5000 ppm or more) can cause adverse health effects or suffocation, but it is tolerated at “very low levels” (ambient levels).
4. Benzene: A volatile organic compound and a known human carcinogen. Exposure to benzene, even at very low concentrations over time, is linked to increased risk of cancer (e.g., leukemia).
Considering the criteria “not tolerated even at very low levels”, CO and Benzene are clear candidates due to their high toxicity/carcinogenicity at low exposures. NOx are also significant respiratory hazards at lower concentrations than CO₂. CO₂ is relatively non-toxic at typical atmospheric concentrations. Thus, NOx, CO, and Benzene fit the description better than CO₂.

Certain pollutants like carbon monoxide (CO), benzene, and nitrogen oxides (NOx) pose health risks even at low exposure levels due to their toxicity, carcinogenicity, or irritant properties, whereas carbon dioxide (CO₂) is harmful primarily at high concentrations.

The term “tolerated at very low levels” is relative, but in the context of common air pollutants from vehicles, CO, NOx, and Benzene are regulated and considered hazardous at much lower concentrations than CO₂. CO₂ is regulated more as a climate change gas than a direct air toxic at ambient urban levels.

34. Which one of the following is not a chemical change?

Which one of the following is not a chemical change?

Ripening of fruits

Curdling of milk

Freezing of water

Digestion of food

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UPSC NDA-1 – 2016

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A chemical change involves a change in the chemical composition of a substance, resulting in the formation of new substances with different properties. A physical change alters the form or appearance of a substance but not its chemical identity.
A) Ripening of fruits: Involves complex chemical reactions that change color, sweetness, texture, and aroma (e.g., conversion of starch to sugars, breakdown of pigments). This is a chemical change.
B) Curdling of milk: Usually caused by the action of acids or enzymes on milk proteins (casein), causing them to coagulate and separate from the liquid whey. This is a chemical change.
C) Freezing of water: Water changes from liquid state to solid state (ice). The chemical composition remains H₂O. This is a change of state, which is a physical change.
D) Digestion of food: Involves the breakdown of complex food molecules (carbohydrates, proteins, fats) into simpler molecules by enzymes. These are chemical reactions. This is a chemical change.
Therefore, freezing of water is not a chemical change; it is a physical change.

Chemical changes result in new substances; physical changes do not change the chemical composition.

Changes of state (melting, freezing, boiling, condensation, sublimation) are common examples of physical changes. Burning, rusting, cooking, and decomposition are examples of chemical changes.

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35. The phosphorus used in the manufacture of safety matches is

The phosphorus used in the manufacture of safety matches is

Red phosphorus

Black phosphorus

White phosphorus

Scarlet phosphorus

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UPSC NDA-1 – 2016

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Safety matches utilize red phosphorus. Red phosphorus is a less reactive allotrope of phosphorus compared to white phosphorus. The striking surface of a safety matchbox contains red phosphorus, powdered glass, and a binder. The match head contains oxidizing agents (like potassium chlorate), fuel (like sulfur or antimony trisulfide), and a binder. When the match head is struck against the striking surface, the friction generates heat and converts a tiny amount of red phosphorus to white phosphorus, which ignites spontaneously in the presence of the oxidizing agent on the match head. This then ignites the fuel in the match head, starting the flame.

Red phosphorus is used in safety matches due to its relatively low reactivity and non-toxicity compared to white phosphorus.

White phosphorus is highly toxic and pyrophoric (ignites spontaneously in air), which led to its ban in matches in many countries. Black phosphorus and scarlet phosphorus are other allotropes of phosphorus, but red phosphorus is the one commonly used in safety matches.

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36. Density of water is

Density of water is

maximum at 0°C

minimum at 0°C

maximum at 4°C

minimum at – 4°C

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Water exhibits an anomalous expansion property. Unlike most substances which become denser as they cool (contracting), water’s density increases as it cools from boiling point down to 4°C. However, when cooled further from 4°C down to 0°C, it expands and its density decreases. At 0°C, when it freezes into ice, its density drops significantly. Therefore, the density of water is maximum at 4°C.

Water has maximum density at 4°C. This anomalous expansion is crucial for aquatic life in cold climates, as ice floats and water at 4°C remains at the bottom of lakes, preventing them from freezing solid.

The density of pure water at standard atmospheric pressure is approximately 999.97 kg/m³ at 0°C, 1000 kg/m³ at 4°C, and decreases gradually as temperature increases beyond 4°C. Ice (solid water) has a density of about 917 kg/m³.

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37. A container is first filled with water and then the entire water is re

A container is first filled with water and then the entire water is replaced by mercury. Mercury has a density of 13·6 × 10³ kg/m³. If X is the weight of the water and Y is the weight of the mercury, then

X = Y

X = 13·6 Y

Y = 13·6 X

None of the above

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UPSC NDA-1 – 2016

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The weight of an object is given by W = m * g, where m is the mass and g is the acceleration due to gravity. The mass of a substance filling a container of volume V is given by m = ρ * V, where ρ is the density of the substance.
For water, the weight X is given by X = ρ_water * V * g.
For mercury, the weight Y is given by Y = ρ_mercury * V * g.
The density of water is approximately 1.0 × 10³ kg/m³.
The density of mercury is given as 13.6 × 10³ kg/m³.
Taking the ratio of the weights:
Y / X = (ρ_mercury * V * g) / (ρ_water * V * g)
Y / X = ρ_mercury / ρ_water
Y / X = (13.6 × 10³) / (1.0 × 10³) = 13.6
Therefore, Y = 13.6 X.

Weight depends on mass and gravitational acceleration. Mass is proportional to density for a fixed volume. The ratio of weights for the same volume of different substances is equal to the ratio of their densities.

The density of water varies slightly with temperature and pressure, but 1000 kg/m³ is a standard value at 4°C. The acceleration due to gravity (g) is the same for both substances in the same location, so it cancels out in the ratio.

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38. Directions : The following 05 (Five) items consist of two statements,

Directions : The following 05 (Five) items consist of two statements, Statement I and Statement II. Examine these two statements carefully and select the answers to these items using the code given below :
Code :

Both the Statements are individually true and Statement II is the correct explanation of Statement I.
Both the Statements are individually true but Statement II is not the correct explanation of Statement I.
Statement I is true but Statement II is false.
Statement I is false but Statement II is true.

55.
Statement I: India has wide variation in population density.
Statement II: Factors like agricultural productivity and history of settlements have greatly influenced the population density pattern in India.

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Both the Statements are individually true and Statement II is the correct explanation of Statement I.

Both the Statements are individually true but Statement II is not the correct explanation of Statement I.

Statement I is true but Statement II is false.

Statement I is false but Statement II is true.

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The correct answer is A) Both the Statements are individually true and Statement II is the correct explanation of Statement I.

Statement I is true. India exhibits vast differences in population density across states and regions, ranging from very high densities in fertile plains (e.g., Bihar, West Bengal, Uttar Pradesh) and urban areas to much lower densities in mountainous states (e.g., Arunachal Pradesh, Himachal Pradesh), arid regions, or dense forest areas.
Statement II is true. Several factors influence this variation. Highly fertile agricultural lands (supporting high agricultural productivity) and areas with a long history of stable settlements (often linked to resource availability like water and fertile land) tend to have higher population densities. Other factors like industrial development, urbanization, climate, terrain, and access to resources also play significant roles in shaping population distribution patterns. Statement II lists the key factors that explain *why* the variation described in Statement I exists.

The population density of India as a whole is among the highest in the world. Understanding the factors contributing to the uneven distribution is crucial for planning and development policies.

39. Directions : The following 05 (Five) items consist of two statements,

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Both the Statements are individually true and Statement II is the correct explanation of Statement I.
Both the Statements are individually true but Statement II is not the correct explanation of Statement I.
Statement I is true but Statement II is false.
Statement I is false but Statement II is true.

54.
Statement I: Plantation farming has mostly been practised in humid tropics.
Statement II: The soil of humid tropics is highly fertile.

Both the Statements are individually true and Statement II is the correct explanation of Statement I.

Both the Statements are individually true but Statement II is not the correct explanation of Statement I.

Statement I is true but Statement II is false.

Statement I is false but Statement II is true.

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The correct answer is C) Statement I is true but Statement II is false.

Statement I is true. Plantation farming, focusing on commercial crops like tea, coffee, rubber, cocoa, etc., is predominantly practiced in humid tropical and subtropical regions because these crops thrive in such climates (warm temperatures, high rainfall).
Statement II is false. The soils of humid tropics are generally *not* highly fertile. Due to high temperatures and heavy rainfall, organic matter decomposes rapidly, and soluble nutrients are heavily leached away through a process called laterization. This often leaves behind soils rich in iron and aluminum oxides (like Oxisols and Ultisols), which are typically low in fertility and require significant fertilization for sustained agriculture, especially for nutrient-demanding plantation crops.

Despite the low inherent soil fertility, tropical regions support dense forests because nutrients are quickly taken up and stored in the living biomass. When these forests are cleared for agriculture, the limited nutrients in the soil are quickly depleted. Plantation farming in these areas often relies on large inputs of fertilizers and careful management practices.

40. Directions : The following 05 (Five) items consist of two statements,

Both the Statements are individually true and Statement II is the correct explanation of Statement I.
Both the Statements are individually true but Statement II is not the correct explanation of Statement I.
Statement I is true but Statement II is false.
Statement I is false but Statement II is true.

53.
Statement I: Volcanic eruption is accompanied by earthquakes.
Statement II: Volcanoes erupt water vapours and dust particles in the atmosphere.

Both the Statements are individually true and Statement II is the correct explanation of Statement I.

Both the Statements are individually true but Statement II is not the correct explanation of Statement I.

Statement I is true but Statement II is false.

Statement I is false but Statement II is true.

Answer is Right!

Answer is Wrong!

This question was previously asked in

UPSC NDA-1 – 2016

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The correct answer is B) Both the Statements are individually true but Statement II is not the correct explanation of Statement I.

Statement I is true. Volcanic eruptions are frequently preceded by or accompanied by earthquakes. These are often seismic events directly related to the movement of magma beneath the surface, the fracturing of rocks due to pressure buildup, or the rapid release of pressure during the eruption.
Statement II is also true. Volcanoes erupt various materials including gases (primarily water vapour), ash, dust particles, lava, and rock fragments.
However, Statement II (what volcanoes erupt) does not explain *why* volcanic eruptions are accompanied by earthquakes (Statement I). The earthquakes are caused by processes happening *before* or *during* the eruption related to magma dynamics and rock mechanics, not by the mere expulsion of water vapour and dust.

Volcanic earthquakes are distinct from tectonic earthquakes, although both involve ground shaking. Volcanic earthquakes are typically shallower and more localized around volcanic structures. They can be indicators of impending eruptions.

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