UPSC Geoscientist Archives

21. A steel rod having radius r and length L gets stretched along its leng

A steel rod having radius r and length L gets stretched along its length by ΔL, when a force F is applied to it. If another rod made of the same material having radius 2r and length L is subjected to the same force F, then the elongation observed for the second rod is

4ΔL

2ΔL

ΔL /4

ΔL /2

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According to Hooke’s Law, for a material under tensile stress, Young’s Modulus (Y) is given by Y = Stress / Strain.
Stress = F/A, where F is the force applied and A is the cross-sectional area.
Strain = ΔL/L, where ΔL is the elongation and L is the original length.
So, Y = (F/A) / (ΔL/L) = (F * L) / (A * ΔL).
Rearranging for elongation, ΔL = (F * L) / (A * Y).
The cross-sectional area of a rod with radius r is A = πr².
For the first rod: ΔL₁ = (F * L) / (πr² * Y).
For the second rod: Radius is 2r, length is L, material is the same (Y is the same), and the force is F.
The cross-sectional area of the second rod is A₂ = π(2r)² = 4πr².
The elongation for the second rod is ΔL₂ = (F * L) / (A₂ * Y) = (F * L) / (4πr² * Y).
Substituting the expression for ΔL₁ into the equation for ΔL₂:
ΔL₂ = (1/4) * [(F * L) / (πr² * Y)] = (1/4) * ΔL₁.
Thus, the elongation observed for the second rod is ΔL/4.

Elongation under a given force is inversely proportional to the cross-sectional area of the rod, assuming the material, length, and force are constant. Area is proportional to the square of the radius.

This problem assumes the material behaves elastically and obeys Hooke’s Law. Young’s modulus is a property of the material. The force applied must be within the elastic limit of the material.

22. Which one of the following semi-conductors possesses the highest value

Which one of the following semi-conductors possesses the highest value of band gap Eg?

GaAs

PbS

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The band gap (Eg) values for the given semiconductors are approximately:
Si (Silicon): ~1.1 eV (indirect band gap)
Ge (Germanium): ~0.67 eV (indirect band gap)
GaAs (Gallium Arsenide): ~1.42 eV (direct band gap)
PbS (Lead Sulfide): ~0.37 eV (direct band gap)
Comparing these values, GaAs has the highest band gap among the options.

The band gap is the energy difference between the top of the valence band and the bottom of the conduction band. This value is a key characteristic of semiconductor materials.

Semiconductors are classified by their band gap, which can be direct or indirect. A larger band gap generally means the material is less conductive. Materials with larger band gaps (e.g., GaN, SiC) are used in high-power, high-temperature, and high-frequency applications, as well as in blue/UV light emitters.

23. Which one of the following schematic graphs correctly represents quali

Which one of the following schematic graphs correctly represents qualitatively the variation of resistivity ρ with respect to temperature T for a semiconductor?

Graph (a)

Graph (b)

Graph (c)

Graph (d)

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The correct answer is (B) Graph (b).

For a semiconductor, resistivity generally decreases as temperature increases. This is because increasing thermal energy excites more electrons into the conduction band and creates more holes in the valence band, increasing the number of free charge carriers available for conduction. More charge carriers lead to higher conductivity and thus lower resistivity. Graph (b) qualitatively shows this inverse relationship where resistivity decreases with increasing temperature.

In contrast, for a typical metal, resistivity increases with increasing temperature due to increased scattering of electrons by lattice vibrations. Insulators have very high resistivity that changes significantly with temperature, usually decreasing as temperature increases, but starting from a much higher value than semiconductors. Graph (a) represents the behavior of a metal, while graphs (c) and (d) do not represent the typical qualitative behavior of a semiconductor over a relevant temperature range.

24. Consider the following statements: 1. Ajanta paintings depict storie

Consider the following statements:

1. Ajanta paintings depict stories from the Jatakas.
2. Ajanta paintings depict scenes of court-life, processions, men and women at work, festivals, etc.

Which of the statements given above is/are correct?

1 only

2 only

Both 1 and 2

Neither 1 nor 2

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The correct answer is (C) Both 1 and 2.

Statement 1 is correct. A significant portion of the Ajanta paintings are illustrations of the Jataka tales, which recount the previous lives of the Buddha in human and animal forms, depicting moral lessons.
Statement 2 is also correct. Besides the religious themes, the Ajanta paintings provide a rich panorama of the life of the people during the Gupta period and beyond. They depict various scenes of daily life, including court durbars, processions, hunting scenes, dancers, musicians, women applying makeup, and people of different social strata engaged in various activities, offering valuable historical and cultural insights.

The Ajanta Caves contain Buddhist rock-cut cave monuments dating from the 2nd century BCE to about 480 CE. The paintings are primarily from the Vakataka period (roughly 4th to 6th centuries CE). They are renowned for their artistic quality and their portrayal of religious narratives and contemporary life.

25. Chronologically arrange the following events : 1. Invasion of Alexande

Chronologically arrange the following events :
1. Invasion of Alexander
2. Indo-Greek Rule in the North-West
3. Accession of Kanishka
4. Accession of Chandragupta Maurya
Select the correct answer using the code given below.

4-3-1-2

2-3-4-1

3-4-1-2

1-4-2-3

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The correct answer is (D) 1-4-2-3.

Let’s establish the approximate dates for each event:
1. Invasion of Alexander: 326 BCE.
2. Indo-Greek Rule in the North-West: Started around the late 3rd/early 2nd century BCE (after the decline of the Mauryas) and lasted until the 1st century BCE/1st century CE.
3. Accession of Kanishka: Debated, but commonly placed around 78 CE (start of Shaka Era) or mid-2nd century CE. Kanishka was a Kushan ruler.
4. Accession of Chandragupta Maurya: Founded the Mauryan Empire around 321 BCE, shortly after Alexander’s withdrawal from parts of India.

The chronological order is: Alexander’s invasion (326 BCE), followed immediately by Chandragupta Maurya’s rise to power (c. 321 BCE), then the establishment of Indo-Greek rule after the Mauryan decline (post 185 BCE), and finally the accession of Kanishka much later (1st/2nd century CE).
Thus, the correct order is 1 – 4 – 2 – 3.

Alexander’s invasion weakened some existing powers in the North-West, facilitating Chandragupta Maurya’s expansion. The Mauryan Empire declined around 185 BCE, after which the Indo-Greeks established kingdoms in the North-West. The Kushan Empire, to which Kanishka belonged, emerged later, replacing the Indo-Greeks and other regional powers.

26. Who among the following revolutionaries founded the Hindustan Socialis

Who among the following revolutionaries founded the Hindustan Socialist Republican Army?

Ashfaqullah

Batukeshwar Dutta

Ram Prasad Bismil

Chandra Shekhar Azad

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The correct answer is (D) Chandra Shekhar Azad.

The Hindustan Socialist Republican Army (HSRA) was founded in 1928 at Feroz Shah Kotla in Delhi. It was a transformation of the earlier Hindustan Republican Association (HRA). Chandra Shekhar Azad was a prominent leader and organizer of the HSRA, along with Bhagat Singh, Sukhdev, and Rajguru.

Ram Prasad Bismil and Ashfaqullah Khan were key founders of the original Hindustan Republican Association (HRA) in 1924, but they were executed in 1927 before the formation of the HSRA. Batukeshwar Dutta was a revolutionary associated with Bhagat Singh and the HSRA but was not a founder. Chandra Shekhar Azad remained active until his death in an encounter in 1931.

27. Nil Darpan, which deals with the condition of Indigo planters, was wri

Nil Darpan, which deals with the condition of Indigo planters, was written by

Michael Madhusudan Dutta

Bankim Chandra Chatterjee

Lal Behari Dey

Dinabandhu Mitra

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The correct answer is (D) Dinabandhu Mitra.

‘Nil Darpan’ (The Mirror of Indigo) is a famous Bengali play written by Dinabandhu Mitra in 1860. The play vividly depicted the oppressive treatment of Indian indigo farmers by the British planters and highlighted their suffering and revolt, significantly influencing public opinion and contributing to the Indigo Rebellion (1859-1860).

Michael Madhusudan Dutta was a pioneering figure in Bengali drama and poetry. Bankim Chandra Chatterjee is renowned for his novel ‘Anandamath’, which contains the song ‘Vande Mataram’. Lal Behari Dey was a Bengali journalist and writer known for works like ‘Bengal Peasant Life’.

28. Who among the following was the Viceroy of India in 1905, when the Par

Who among the following was the Viceroy of India in 1905, when the Partition of Bengal was announced?

Lord Ripon

Lord Canning

Lord Curzon

Lord Minto

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The correct answer is (C) Lord Curzon.

The Partition of Bengal was announced in 1905. Lord Curzon served as the Viceroy of India from 1899 to 1905 and was the key figure responsible for implementing the partition, which aimed to divide the large province of Bengal for administrative reasons, though it was widely perceived as an attempt to curb the growing nationalist movement.

Lord Ripon (1880-1884) was known for the Ilbert Bill and repealing the Vernacular Press Act. Lord Canning (1856-1862) was the Governor-General during the 1857 Mutiny and became the first Viceroy. Lord Minto (1905-1910) succeeded Curzon and was involved in the Minto-Morley Reforms of 1909.

29. Which one of the following managed ecosystems has the highest amount o

Which one of the following managed ecosystems has the highest amount of standing crop?

Agricultural land

Grazing land

Human habitation

Forest plantation

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The correct answer is (D) Forest plantation.

Standing crop refers to the total biomass present in an ecosystem at a given time. Among the managed ecosystems listed, a forest plantation, especially as it matures, accumulates a very large amount of biomass in the form of trees. This biomass per unit area is significantly higher than that typically found in agricultural land (which is often harvested frequently), grazing land, or areas of human habitation.

While agricultural land can have high productivity (rate of biomass production), its standing crop at any single point in time can be lower than a forest due to harvesting cycles. Grazing lands support grasses and herbs, resulting in relatively lower biomass accumulation. Human habitation areas are dominated by buildings and infrastructure, with limited natural biomass accumulation.

30. The uplift mechanism that takes place when lighter warm moist air mass

The uplift mechanism that takes place when lighter warm moist air mass rises after encountering a colder and denser air mass causes

conventional precipitation

frontal precipitation

cyclonic precipitation

orogenic precipitation

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The correct answer is (B) frontal precipitation.

Frontal precipitation occurs when a warmer, lighter air mass is forced to rise over a colder, denser air mass along a weather front. As the warm, moist air rises, it cools, condenses, and forms precipitation. This uplift mechanism is characteristic of frontal systems like warm fronts and cold fronts.

Conventional precipitation results from the uplift of warm, moist air due to surface heating, often leading to thunderstorms. Cyclonic precipitation is associated with low-pressure systems (cyclones), which often involve frontal systems but the term “cyclonic” refers to the overall system’s circulation. Orogenic precipitation occurs when air is forced to rise over mountains (orographic lift). The description specifically matches the interaction of distinct air masses at a front.