The vast network of railways that helped people meet their family and relatives was pioneered during the latter half of which of the following centuries in India?
The question asks about the period when the railway network in India was pioneered, specifically in the latter half of a particular century. This requires knowledge of Indian history, particularly the development of infrastructure during the British Raj.
A) 19th. The first railway line in India was laid in 1853, which falls in the latter half of the 19th century. The subsequent rapid expansion of the railway network also occurred predominantly during this period.
The question asks to identify the crop that the Harappans were the first in Eurasia to cultivate. This requires knowledge of the agricultural practices of the Indus Valley Civilization (Harappan Civilization) and the historical timeline of crop cultivation in Eurasia.
D) Cotton — The Harappans were indeed the first in Eurasia to cultivate cotton. Evidence suggests they were growing cotton as early as 2500 BCE, making them pioneers in its cultivation and use for textiles.
The question asks to identify the best description of the state of Indian industries under British rule. This requires recalling the economic policies and their impact on India's industrial sector during the colonial period.
D) Systematic decline of traditional industries. British colonial policies, characterized by discriminatory tariffs and the influx of cheap machine-made goods from Britain, led to the destruction of India's vibrant traditional handicraft industries, such as textiles, pottery, and metalwork. This process is often referred to as 'de-industrialization'.
The question asks to identify the country ranked as the most innovative in the 2024 Global Innovation Index (GII). This requires knowledge of the latest GII report findings.
Correct Option: B) Switzerland
Switzerland has consistently ranked as the top innovative country in the Global Innovation Index for many years, including the 2024 report. Its strong performance is attributed to its robust innovation ecosystem, high-quality institutions, excellent human capital and research, and sophisticated business environment.
The question asks to identify the Indian state with the largest forest cover (area-wise) according to the 'India State of Forest Report 2023' (ISFR 2023). This requires knowledge of the findings of the latest forest report published by the Forest Survey of India (FSI).
B) Madhya Pradesh has the largest forest cover (area-wise) in India as per the ISFR 2021 (which is the latest available report, despite the question mentioning ISFR 2023).
The question asks to identify the type of case that Lok Adalats generally do NOT handle. Lok Adalats are alternative dispute resolution forums in India that primarily deal with civil disputes and compoundable criminal cases. The key is to understand their jurisdiction and the nature of cases they can resolve through compromise and settlement.
Correct Option: A) Murder trials
Mechanical energy is the sum of kinetic energy and potential energy. The dimensional formula for energy is the same as that for work, as work done is a form of energy transfer. We can derive the dimensional formula for work or kinetic energy to find the dimensional formula for mechanical energy.
Recall the formula for Work or Kinetic Energy:
Work done (\(W\)) is defined as Force (\(F\)) multiplied by displacement (\(d\)):
\[ W = F \times d \]Kinetic energy (\(KE\)) is given by:
\[ KE = \frac{1}{2} m v^2 \]Potential energy (\(PE\)) is given by:
\[ PE = mgh \]Since mechanical energy is the sum of kinetic and potential energy, its dimension will be the same as the dimension of kinetic energy or potential energy.
Determine the dimensional formula for Force (\(F\)):
Force is mass (\(m\)) times acceleration (\(a\)):
\[ F = m \times a \]The dimensional formula for mass is \([M]\).
The dimensional formula for acceleration is \([L T^{-2}]\), as acceleration is change in velocity per unit time (\(L T^{-1} / T\)).
So, the dimensional formula for Force is:
\[ [F] = [M] \times [L T^{-2}] = [M L T^{-2}] \]Determine the dimensional formula for Work (\(W\)):
Work is Force times displacement (\(d\)). The dimensional formula for displacement is \([L]\).
\[ [W] = [F] \times [d] = [M L T^{-2}] \times [L] = [M L^2 T^{-2}] \]Alternatively, using Kinetic Energy:
Kinetic energy \(KE = \frac{1}{2} m v^2\).
The constant \(\frac{1}{2}\) is dimensionless.
The dimensional formula for mass (\(m\)) is \([M]\).
The dimensional formula for velocity (\(v\)) is \([L T^{-1}]\).
So, the dimensional formula for \(v^2\) is \([L T^{-1}]^2 = [L^2 T^{-2}]\).
Therefore, the dimensional formula for Kinetic Energy is:
\[ [KE] = [M] \times [L^2 T^{-2}] = [M L^2 T^{-2}] \]Conclusion:
Since mechanical energy has the same dimensions as work or kinetic energy, its dimensional formula is \([M L^2 T^{-2}]\).
D) [M¹L²T⁻²] is the correct dimensional formula for mechanical energy, which is consistent with the dimensions of work and kinetic energy.
A) [ML²T⁻³]: This dimensional formula represents power, which is work done per unit time (\(W/T\)). \([M L^2 T^{-2}] / [T] = [M L^2 T^{-3}]\).
B) [M¹L²]: This dimensional formula does not correspond to any standard physical quantity related to energy. It lacks the time dimension.
C) [M²L²T⁻¹]: This dimensional formula does not correspond to any standard physical quantity. The exponents for mass and time are incorrect for energy.
The question asks to identify the tetravalent dengue vaccine planned for local manufacturing in India under the 'Make-in-India' initiative, as per a Times of India report from April 2025. This requires knowledge of recent developments in vaccine manufacturing and public health initiatives in India.
Correct Option: D) QDENGA (TAK-003)
The question asks about a specific directive issued by the Supreme Court of India on 15 May 2025, concerning the establishment of dedicated courts for particular types of cases. This requires knowledge of recent judicial pronouncements and their focus areas.
The question asks what happens when a user attempts to create a new folder with the exact same name as an existing folder in the same directory. This is a fundamental concept in operating system file management.
Correct Option: A) It gives an error.