The question asks for the best corollary to the provided passage. A corollary is a direct consequence or a natural conclusion drawn from a statement. We need to analyze the passage's main points and then evaluate which option logically follows from them.
A) The passage clearly states that while the non-agricultural economy experienced consistent growth from the 1980s to the 2000s (a period of economic reforms), the agricultural sector suffered relative stagnation after the 1980s. This directly implies that the benefits of economic reforms, which largely propelled the non-agricultural sector, did not reach or impact the agricultural sector as effectively or quickly.
The question asks to identify valid assumptions that could reduce/contain the divergence between agricultural and non-agricultural economies. We need to evaluate each statement (I and II) based on its practical implications and whether it is a realistic or desirable solution in the Indian context, especially considering the socio-economic realities and past experiences with such policies.
D) Neither I nor II
The passage discusses how the handloom industry is traditionally linked to cultural heritage, which influences public policy. However, it also highlights that this narrow definition of tradition is being challenged, as it often discounts or stifles the identities and histories of large sections of the population. Consequently, many people ignore handlooms when promoted solely as a traditional industry. The task is to identify the statement that best reflects the author's logical and rational message.
Correct Option: A) We need to free the handloom industry from the limited narrative linked to preserving cultural heritage. This option directly addresses the central problem identified by the author: the restrictive and contested definition of tradition that causes large sections of the population to ignore handlooms. The author argues that this limited narrative is counterproductive.
This question asks us to evaluate the validity of two assumptions based on an unprovided passage. Since the passage is not given, we must assume that the question implies that the passage does NOT explicitly state or strongly imply these assumptions. In critical reasoning questions, assumptions are unstated premises that must be true for the argument to hold. Without the passage, we cannot confirm if these assumptions are supported or contradicted. Therefore, we must consider if these statements are universally true or if they are likely to be directly stated or strongly implied in a typical passage discussing the handloom sector.
Correct Option: D) Neither I nor II
We need to find the count of natural numbers from 1 to 100 that are not divisible by 2, 3, 5, 7, and 9. First, we can simplify the set of divisors. Since any number divisible by 9 is also divisible by 3, we only need to consider divisibility by 2, 3, 5, and 7. We will use the Principle of Inclusion-Exclusion to find the numbers divisible by at least one of these primes and then subtract this count from the total number of integers (100).
C) 22 ā This is the correct count obtained by applying the Principle of Inclusion-Exclusion.
To find the ratio of the maximum value of \((x+y)\) to the minimum value of \((x-y)\), we first need to determine the maximum possible value for \((x+y)\) and the minimum possible value for \((x-y)\) given the ranges for \(x\) and \(y\).
Determine the maximum value of \((x+y)\):
Given the ranges \(4 \le x \le 8\) and \(2 \le y \le 7\), to maximize the sum \((x+y)\), we should choose the maximum possible values for both \(x\) and \(y\).
Determine the minimum value of \((x-y)\):
To minimize the difference \((x-y)\), we should choose the minimum possible value for \(x\) and the maximum possible value for \(y\).
Calculate the ratio:
The ratio required is the maximum value of \((x+y)\) to the minimum value of \((x-y)\).
Compare with options:
The calculated ratio is \(-5\). Let's check the given options.
Since \(-5\) is not among options A, B, or C, the correct option is D.
D) None of the above. The calculated ratio is \(-5\), which is not listed in options A, B, or C.
We need to find the number of possible values for the prime number \(k\) such that when added to the square of another prime number \(p\), the result \((p^2 + k)\) is also a prime number less than 30. We will systematically test prime values for \(p\) and then find corresponding prime values for \(k\).
B) 5