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Questions and Answers
Considering the geopolitical landscape of 7th-century India, which of the following factors most likely contributed to the rise of numerous independent kingdoms after the disintegration of the Gupta Empire?
Considering the geopolitical landscape of 7th-century India, which of the following factors most likely contributed to the rise of numerous independent kingdoms after the disintegration of the Gupta Empire?
- The weakening of central authority exacerbated by invasions and internal power struggles, leading to regional assertion of sovereignty by former Gupta feudatories. (correct)
- The deliberate dismantling of centralized military infrastructure by the later Gupta rulers to promote local governance.
- A widespread adoption of a uniform legal code that inadvertently fostered regional autonomy among the administrative divisions.
- Diminished trade routes due to natural disasters, compelling regions to become economically self-reliant and politically independent.
Given the established feudal structure of ancient Indian kingdoms, which action by Harsha Vardhana would have MOST effectively consolidated his rule and ensured long-term stability across his newly formed kingdom?
Given the established feudal structure of ancient Indian kingdoms, which action by Harsha Vardhana would have MOST effectively consolidated his rule and ensured long-term stability across his newly formed kingdom?
- Implementing a centralized currency system to facilitate trade and reduce regional economic disparities.
- Reforming the administrative structure to incorporate loyal regional chieftains into a hierarchical system of governance, thus co-opting potential rivals. (correct)
- Commissioning the construction of extensive irrigation networks to boost agricultural productivity and foster economic dependence on the central authority.
- Establishing a new, syncretic religious order to unify diverse populations and legitimize his authority.
If the Mantri Parishad's (Council of Ministers) support was crucial for Harsha Vardhana's ascension, what prevailing sociopolitical condition does this detail MOST strongly imply about the nature of monarchical succession in that era?
If the Mantri Parishad's (Council of Ministers) support was crucial for Harsha Vardhana's ascension, what prevailing sociopolitical condition does this detail MOST strongly imply about the nature of monarchical succession in that era?
- The monarch's power was absolute and unconditional, with the Council's support being purely ceremonial and devoid of any practical implication.
- The absence of a clear-cut succession law or the existence of multiple legitimate claimants could lead to reliance on the Council's consensus for validation. (correct)
- The monarch was elected by the Mantri Parishad from among eligible royal family members, making their support a mere formality.
- Monarchical succession was strictly determined by primogeniture, necessitating the Council's endorsement to circumvent established laws.
Judging from the information available, which of the subsequent developments in Indian history would have been MOST contrary to the political trajectory initiated by Harsha Vardhana?
Judging from the information available, which of the subsequent developments in Indian history would have been MOST contrary to the political trajectory initiated by Harsha Vardhana?
Given the historical context and Harshavardhana's efforts to consolidate power, what strategic advantage would control over both Prayag and Kanauj confer upon a ruler in 7th century India?
Given the historical context and Harshavardhana's efforts to consolidate power, what strategic advantage would control over both Prayag and Kanauj confer upon a ruler in 7th century India?
Considering the patterns of dynastic alliances and conflicts during the Post-Gupta period, what strategic imperative MOST likely drove Graha Varman's marriage to Rajyashri of the Pushyabhuti family of Thaneshwar?
Considering the patterns of dynastic alliances and conflicts during the Post-Gupta period, what strategic imperative MOST likely drove Graha Varman's marriage to Rajyashri of the Pushyabhuti family of Thaneshwar?
If Ishana Varman adopted the title Maharajadhiraja, what shift in Maukhari dynastic policy does this action MOST likely represent, compared to the preceding three kings who held only the title Maharaja?
If Ishana Varman adopted the title Maharajadhiraja, what shift in Maukhari dynastic policy does this action MOST likely represent, compared to the preceding three kings who held only the title Maharaja?
Given the prominence of figures like Hieun-Tsang, and assuming patterns of cultural exchange, what impact would the presence of such travelers MOST likely have had on governance under rulers such as Harsha?
Given the prominence of figures like Hieun-Tsang, and assuming patterns of cultural exchange, what impact would the presence of such travelers MOST likely have had on governance under rulers such as Harsha?
Considering the geographical locations and the historical context, what strategic objective would MOST logically explain Prabhakara Vardhan's campaigns against the Hunas, Gurjaras, and other regional powers?
Considering the geographical locations and the historical context, what strategic objective would MOST logically explain Prabhakara Vardhan's campaigns against the Hunas, Gurjaras, and other regional powers?
If Harsha was reluctant to accept the responsibilities of kingship, yet brought 'a majority of the regions of northern India under his management/control,' what inference can be justifiably drawn regarding the administrative structures in place?
If Harsha was reluctant to accept the responsibilities of kingship, yet brought 'a majority of the regions of northern India under his management/control,' what inference can be justifiably drawn regarding the administrative structures in place?
Considering the context of the 6th century AD, what specific advantage did situating the Pushyabhuti kingdom in Srikanta Janapada (modern Haryana) MOST likely confer upon its rulers?
Considering the context of the 6th century AD, what specific advantage did situating the Pushyabhuti kingdom in Srikanta Janapada (modern Haryana) MOST likely confer upon its rulers?
If Sarva Varman's ascension to the throne marked a shift, establishing 'a strong presence of Maukharis in Madhya Desha,' what primary change in geopolitical focus did this likely entail for the Maukhari kingdom?
If Sarva Varman's ascension to the throne marked a shift, establishing 'a strong presence of Maukharis in Madhya Desha,' what primary change in geopolitical focus did this likely entail for the Maukhari kingdom?
Supposing the title 'Maharaja' was granted to the first three Maukhari kings, what inherent limitation, in terms of political signaling, would this title impose on their ability to project power and influence compared to rulers claiming titles like 'Maharajadhiraja'?
Supposing the title 'Maharaja' was granted to the first three Maukhari kings, what inherent limitation, in terms of political signaling, would this title impose on their ability to project power and influence compared to rulers claiming titles like 'Maharajadhiraja'?
Considering the common motivations of ancient rulers, what primary incentive MOST likely drove Ishana Varman to engage in battles with the Andhras and Gaudas, and the Guptas of Magadha?
Considering the common motivations of ancient rulers, what primary incentive MOST likely drove Ishana Varman to engage in battles with the Andhras and Gaudas, and the Guptas of Magadha?
Given that Adiya Vardhan, Rajya Vardhan, and Nara Vardhan of the Pushyabhuti dynasty held the title 'Maharaja', but Prabhakara Vardhan adopted the title 'Param Bhattarak Maharajadhiraja', what profound transition in the dynasty's standing does this title change BEST illustrate?
Given that Adiya Vardhan, Rajya Vardhan, and Nara Vardhan of the Pushyabhuti dynasty held the title 'Maharaja', but Prabhakara Vardhan adopted the title 'Param Bhattarak Maharajadhiraja', what profound transition in the dynasty's standing does this title change BEST illustrate?
Flashcards
Post-Gupta Kingdoms
Post-Gupta Kingdoms
Kingdoms that emerged after the Gupta empire disintegrated in the 6th century AD.
The Maukharis
The Maukharis
A dynasty that rose to prominence after the Gupta empire; their capital was Kannauj.
Maharaja Title
Maharaja Title
Title given to the first three kings of the Maukhari dynasty.
Ishana Varman
Ishana Varman
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Sarva Varman
Sarva Varman
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Graha Varman
Graha Varman
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The Pushyabhutis
The Pushyabhutis
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Prabhakara Vardhan
Prabhakara Vardhan
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Hunas and Gurjaras
Hunas and Gurjaras
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Rajya Vardhan
Rajya Vardhan
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Harsha Vardhana
Harsha Vardhana
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Hieun-Tsang's Writings
Hieun-Tsang's Writings
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'Siladitya'
'Siladitya'
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Prayag and Kanauj assemblies
Prayag and Kanauj assemblies
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Study Notes
- Stability in closed loop systems can be determined by analyzing the open loop transfer function, denoted as G(s).
- Stability assessment involves determining the number of unstable poles using the frequency response of G(s).
Example Scenario
- G(s) = 1/(s-1) represents an open loop transfer function.
- H(s) = G(s) / (1 + G(s)) = 1/s illustrates the closed loop transfer function, which in this case is stable even though the open loop system is unstable.
Nyquist Plot Overview
- It is a graphical representation of G(jω) on the complex plane across the frequency range of negative infinity to positive infinity.
- Plotting from 0 to positive infinity is sufficient due to the property G(jω) = G(-jω)* and the plot is then completed based on symmetry.
- The Nyquist plot allows deduction of the stability of a closed loop system.
Nyquist Criterion Explained
- N is defined as the number of clockwise encirclements of the -1 point by the Nyquist plot of G(s).
- P is the number of unstable poles in G(s), which represents the open loop system.
- Z is the number of unstable poles in the closed loop system, represented by G(s) / (1 + G(s)).
- The relationship between these variables is given by Z = N + P.
- Closed loop system achieves stability if and only if N = -P.
Nyquist Criterion Considerations
- A "Nyquist contour" is needed; use a semi-circle of infinite radius (R → ∞) enclosing the right half of the complex plane.
- Indentations around poles on the imaginary axis are necessary if present in G(s).
Applying the Nyquist Criterion - Example
- Consider G(s) = 1/(s-1).
- Nyquist contour includes the pole at s = 1.
- Semi-circle at infinity maps to the origin.
- If the Nyquist plot encircles -1 once clockwise, then N = 1.
- Given P = 1, Z = N + P = 1 + (-1) = 0, indicating the closed loop system is stable.
Robust Stability
- Assumes models are not perfectly accurate due to uncertainties.
- Controllers should be designed to maintain stability despite these uncertainties across a range of plant models.
Uncertainty Types
- Unstructured uncertainty indicates limited knowledge about the model inaccuracies:
- Additive uncertainty represents the transfer function as G(s) + W(s)Δ(s).
- Multiplicative uncertainty represents the transfer function as G(s)(1 + W(s)Δ(s)).
- Here, Δ(s) is any stable transfer function where the infinity norm of Δ(s) is less than or equal to 1 (||Δ(s)||_∞ ≤ 1).
- W(s) is a weighting function adjusting for the frequency content of the uncertainty.
- Structured uncertainty indicates partial knowledge, such as a pole or zero.
Robust Stability Assessment
- For multiplicative uncertainty G(s) → G(s)(1 + W(s)Δ(s)).
- The closed loop transfer function is T(s) = G(s) / [1 + G(s)K(s)].
- A sufficient condition to maintain stability for all Δ(s) where ||Δ(s)||∞ ≤ 1 requires the infinity norm of W(s)T(s) to be less than 1 (||W(s)T(s)||∞ < 1).
Robust Stability - Example
- System specified by G(s) = 1/(s+1) and K(s) = 1.
- Uncertainty weighted by W(s) = (0.5s) / (s+2).
- Closed loop transfer function then is T(s) = 1 / (s+2).
- Ensuring robust stability requires ||W(s)T(s)||_∞ = sup over ω |W(jω)T(jω)| and that this result must be less than 1.
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