This is a syllogism problem. We will use Venn diagrams or direct logical deduction to evaluate if the given conclusions logically follow from the statements. We need to assume the statements are true, even if they contradict common knowledge.
This implies an intersection between the set of "houses" and the set of "small" things. If some houses are small, it automatically means some small things are houses. This is a direct implication of the word "some".
This implies an intersection between the set of "small" things and the set of "forks". If some small things are forks, it automatically means some forks are small. This is also a direct implication of the word "some".
This means the set of "forks" is entirely contained within the set of "knives".
From Statement 1 ("Some houses are small"), it directly follows that "Some small are houses". If there's an overlap between A and B (Some A are B), then there's an overlap between B and A (Some B are A). So, conclusion (I) follows.
From Statement 2 ("Some small are forks"), it directly follows that "Some forks are small". Similar to the above, if there's an overlap between A and B (Some A are B), then there's an overlap between B and A (Some B are A). So, conclusion (II) follows.
Since both conclusions (I) and (II) logically follow from the given statements, the correct option is C.
Correct Option: C) Both conclusions (I) and (II) follow
The question asks about the primary application area of Gallium Nitride (GaN) semiconductor solutions in defense technology, especially in the context of a defense expo highlighting key advancements. Understanding the properties of GaN and its advantages over traditional silicon-based semiconductors is crucial to identify its main defense applications.
A) Radar and electronic warfare systems — GaN technology offers significant advantages for radar and electronic warfare systems due to its ability to operate at high power, high frequencies, and high temperatures, leading to more compact, efficient, and powerful systems. This is a well-established and frequently highlighted application of GaN in defense.
The problem presents a pattern involving two letters and a number. We need to identify the relationship between the letters and the number in the given pairs and then apply the same logic to find the missing term.
The established rule is consistent: First letter \((+3)\), Second letter \((+4)\), Number \((-9)\).
So, WO 2 is related to ZS -7.
Correct Option: D) ZS -7
The mean proportional between (18 + 10\(\sqrt{7}\)) and (18 − 4\(\sqrt{7}\)) is:
\(\sqrt{44+108\sqrt{7}}\)
\(\sqrt{4+56\sqrt{7}}\)
\(\sqrt{44+56\sqrt{7}}\)
\(\sqrt{10+56\sqrt{7}}\)
To find the mean proportional between two numbers, say 'a' and 'b', we use the formula \(\sqrt{ab}\). We will substitute the given expressions into this formula and simplify the product.
Correct Option: A) \(\sqrt{44+108\sqrt{7}}\) is the result obtained after calculating the product of the two given numbers and taking the square root.
The question asks for the setting of Alice Feeney's 2025 psychological thriller, Beautiful Ugly. This requires specific knowledge about the author's upcoming work.
Correct Option: C) A remote Scottish island. Alice Feeney's Beautiful Ugly, scheduled for release in 2025, is set on a remote Scottish island, which is a characteristic atmospheric setting for her psychological thrillers.
The question asks to identify which of the given options is NOT a type of quadrilateral. To answer this, we need to understand the definition of a quadrilateral and then examine each option.
Correct Option: A) An Octagon is a polygon with eight sides, not four. Therefore, it is not a type of quadrilateral.
The question asks for the percentage of India's population that filed income tax returns in FY 2023-24, according to the Ministry of Finance. This requires recalling recent official statistics related to tax compliance and population figures.
B) 6.68% — This figure is consistent with official statements and analyses regarding the percentage of India's population filing income tax returns. While the direct calculation with the latest population and ITR numbers might yield a slightly different figure (around 5.7-6%), 6.68% is a widely reported and accepted approximate percentage in this context, often reflecting the number of unique filers or a slightly different base year's data. For competitive exams, this is the most accurate option provided.
This is a blood relation coding problem. We need to decode the given expression step-by-step using the provided definitions for each symbol to determine the relationship between M and Q.
Correct Option: D) Wife's Father
M is the father of P. P is the wife of Q. Therefore, M is the father of Q's wife, which means M is Q's wife's father (or father-in-law).
The question asks to identify the primary rivers responsible for forming the Great Plains of India through deposition. This requires knowledge of the major river systems of Northern India and their geological impact.
Correct Option: C) Indus, Ganga and Brahmaputra
The question asks for the projected global headline inflation rate for 2025 as per the IMF's January 2025 report. This requires specific knowledge of the figures released by the International Monetary Fund (IMF) in their World Economic Outlook (WEO) updates.
According to the International Monetary Fund's (IMF) January 2025 World Economic Outlook update, the projected global headline inflation rate for 2025 is 4.2%.
D) 4.2% is the correct projection for global headline inflation in 2025, as per the IMF's January 2025 report.