This question tests the conversion of direct speech to indirect speech.


Step 1: The reporting verb is "told," which is in the past tense.


Step 2: The verb in the direct speech is "am thinking," which is the present continuous tense.


Step 3: According to the rules of grammar, when the reporting verb is in the past tense, the present continuous tense in direct speech changes to the past continuous tense in indirect speech.


Step 4: Therefore, "am thinking" becomes "was thinking".


Step 5: The pronoun "I" changes to "he" to refer to Rafi, and "this weekend" changes to "that weekend".


Step 6: The complete sentence in indirect speech is: "Rafi told Mary that he was thinking of watching a film that weekend."
Quick Tip: In direct to indirect speech conversion, if the reporting verb is in the past tense, the tense of the verb in the reported speech must shift backwards. For example, Present Simple becomes Past Simple, Present Continuous becomes Past Continuous, and Present Perfect becomes Past Perfect.

This is an analogy question that relies on identifying the relationship between words.


Step 1: Analyze the relationship in the second pair: "Enforce : Relax".


Step 2: "Enforce" means to compel observance of a rule. "Relax" means to make a rule less strict. These words are antonyms (opposites).


Step 3: The same relationship must apply to the first pair. We need to find the antonym of "Permit".


Step 4: "Permit" means to allow something. The opposite action is to disallow or prohibit it.


Step 5: From the options, "Forbid" means to refuse to allow something. It is the correct antonym.


Step 6: The complete analogy is Permit : Forbid :: Enforce : Relax.
Quick Tip: In word analogy questions (A : B :: C : D), first, establish the precise relationship between C and D. Then, apply that same relationship to find the missing word related to A. Common relationships include synonyms, antonyms, cause-and-effect, part-to-whole, and degree.

This problem requires calculating the probability of two independent events.


Step 1: The first event is getting a '1' on the first roll. The probability of this event, P(A), is \(\frac{1}{6}\).


Step 2: The second event is getting a '4' on the second roll. The outcome of the second roll is independent of the first.


Step 3: The probability of the second event, P(B), is also \(\frac{1}{6}\).


Step 4: The probability of two independent events occurring together is the product of their individual probabilities.


Step 5: P(A and B) = P(A) \(\times\) P(B).


Step 6: P(A and B) = \(\frac{1}{6} \times \frac{1}{6} = \frac{1}{36}\).
Quick Tip: For problems involving multiple independent events, remember the multiplication rule of probability: The probability that all events occur is the product of their individual probabilities. An event is independent if its outcome is not affected by the outcomes of other events.

Step 1: Let the total number of tobacco users be 100 for simplicity.


Step 2: The number of users advised to stop is 65% of 100, which is 65.


Step 3: The number of users who attempted to stop is 3 out of 10, which is 30% of 100, or 30.


Step 4: We need to analyze the group of 65 users who were advised. Let's consider the maximum possible overlap between the 'advised' and 'attempted' groups to test the options with certainty.


Step 5: Assume all 30 users who attempted to stop were from the group of 65 who were advised. This is the maximum overlap.


Step 6: In this scenario, within the 'advised' group of 65, there are 30 who attempted and (65 - 30) = 35 who did not attempt.


Step 7: A majority of the advised group (65 users) would be more than \(65 / 2 = 32.5\) users.


Step 8: Since 35 (did not attempt) is greater than 32.5, it is certain that a majority of those advised to stop did not attempt to do so. This holds even in this extreme case.
Quick Tip: For logical inference questions with percentages involving overlapping sets, test the extreme scenarios (maximum and minimum possible overlap) to determine what can be concluded with absolute certainty.

The figure can be seen as two large triangles sharing a common diagonal base.


Step 1: Focus on the upper large triangle. It has a single common vertex at the bottom-right.


Step 2: The base of this triangle (the top edge of the parallelogram) is divided into 4 segments. This creates \(4+1=5\) points on the base line.


Step 3: Any two points on the base line, along with the common vertex, form a triangle. The number of ways to choose 2 points from 5 is given by the combination formula \(C(n, k) = \frac{n!}{k!(n-k)!}\).


Step 4: Number of triangles in the upper part = \(C(5, 2) = \frac{5 \times 4}{2 \times 1} = 10\).


Step 5: The lower half of the figure is symmetrical to the upper half. It also has a common vertex (top-left) and a base divided into 4 segments (5 points).


Step 6: Number of triangles in the lower part is also \(C(5, 2) = 10\).


Step 7: The total number of triangles is the sum of triangles from both halves.


Step 8: Total triangles = 10 + 10 = 20.
Quick Tip: For triangle counting problems with a common vertex and a segmented base, use the combination formula. If a base is divided into 'n' segments (meaning n+1 points), the number of triangles sharing a common apex is C(n+1, 2) = \(\frac{n(n+1)}{2}\).

Step 1: From the premises, we know: Eligibility to vote requires successful registration.


Step 2: We also know: No student from Human Sciences successfully registered.


Step 3: From these two facts, we can certainly conclude that no student from Human Sciences is eligible to vote.


Step 4: Now let's analyze the statements.


Step 5: Statement (i) claims all ineligible students are from Human Sciences. This is not certain, as a student from another department could also have failed to register and thus be ineligible.


Step 6: Statement (ii) claims all students from other departments successfully registered. The passage gives no information about other departments, so we cannot be certain of this.


Step 7: Statement (iii) claims all eligible voters are not from Human Sciences. Since we deduced that no Human Sciences student is eligible, it must be true that anyone who is eligible cannot be from Human Sciences. This is a certain inference.


Step 8: Therefore, only statement (iii) can be logically inferred with certainty.
Quick Tip: In logical inference, remember the validity of derived statements. If you know "If P, then Q" is true, you also know its contrapositive "If not Q, then not P" is true. Be wary of the inverse ("If not P, then not Q") and converse ("If Q, then P"), which are not necessarily true.

Step 1: Analyze the graph's behavior. The function passes through the origin (0,0). For \(x > 0\), \(f(x)\) is positive. For \(x < 0\), \(f(x)\) is negative.


Step 2: Evaluate option (A): \(f(x) = x^2 2^{-|x|}\). For any \(x \neq 0\), \(x^2 > 0\) and \(2^{-|x|} > 0\), so \(f(x)\) is always positive. This contradicts the graph.


Step 3: Evaluate option (B): \(f(x) = x 2^{-|x|}\). This function is an odd function. As \(x \rightarrow -\infty\), let \(x = -y\) with \(y \rightarrow \infty\). \(f(-y) = -y \cdot 2^{-y} = -y/2^y \rightarrow 0\). The graph goes to \(-\infty\), so this is incorrect.


Step 4: Evaluate option (C): \(f(x) = |x| 2^{-x}\). For \(x < 0\), \(|x|\) is positive and \(2^{-x}\) is positive (e.g., \(2^{-(-2)} = 4\)). So \(f(x)\) would be positive for \(x < 0\). This contradicts the graph.


Step 5: Evaluate option (D): \(f(x) = x 2^{-x}\).

- At \(x=0\), \(f(0) = 0 \cdot 2^0 = 0\). This matches.

- For \(x > 0\), \(x\) is positive and \(2^{-x}\) is positive, so \(f(x)\) is positive. This matches.

- For \(x < 0\), \(x\) is negative and \(2^{-x}\) is positive, so \(f(x)\) is negative. This matches.

- As \(x \rightarrow -\infty\), let \(x=-y\), \(f(x) = -y \cdot 2^y \rightarrow -\infty\). This matches.

- As \(x \rightarrow \infty\), \(f(x) = x/2^x \rightarrow 0\). This matches.


Step 6: Option (D) matches all key features of the graph.
Quick Tip: When matching a function to a graph, start by checking simple points like the origin (x=0) and the function's behavior at extremes (as x approaches positive and negative infinity). This can often eliminate most incorrect options quickly.

Step 1: The question asks to identify the statement that does NOT follow from the passage.


Step 2: The passage's central theme is that we perceive cancer as modern precisely because modern cell biology uses modern metaphors, like the cell being a "molecular machine," to describe it.


Step 3: Option (A) is directly stated in the first sentence.


Step 4: Option (B) and (C) are directly supported by the sentence "Modern cell biology encourages us to imagine the cell as a molecular machine."


Step 5: Option (D) states that modern cell biology never uses figurative language such as metaphors.


Step 6: This is a direct contradiction to the entire point of the passage, which explicitly discusses the metaphors used by modern cell biology.


Step 7: Therefore, option (D) is the statement that does not follow from the passage.
Quick Tip: In "which of the following is NOT true" questions, carefully scan the passage for direct statements or strong implications. The incorrect option will often be an absolute statement (using words like 'never', 'always', 'all') that directly contradicts a point made in the text.

We determine the unit digit of each term separately.


Step 1: Find the cyclicity of the unit digit for powers of 3. The cycle is 3, 9, 7, 1, which has a length of 4.


Step 2: To find the unit digit of \(3^{999}\), we divide the power 999 by the cycle length 4. \(999 \div 4\) gives a remainder of 3.


Step 3: The unit digit is the 3rd digit in the cycle, which is 7.


Step 4: Find the cyclicity of the unit digit for powers of 7. The cycle is 7, 9, 3, 1, which also has a length of 4.


Step 5: To find the unit digit of \(7^{1000}\), we divide the power 1000 by the cycle length 4. \(1000 \div 4\) gives a remainder of 0.


Step 6: A remainder of 0 means the unit digit is the last digit in the cycle, which is 1.


Step 7: The unit digit of the product is the unit digit of (unit digit of \(3^{999}\)) \(\times\) (unit digit of \(7^{1000}\)).


Step 8: Unit digit = unit digit of (\(7 \times 1\)) = 7.
Quick Tip: To find the unit digit of \(a^n\), find the repeating cycle of the unit digits of powers of \(a\). Then, find the remainder when \(n\) is divided by the length of the cycle. The remainder tells you the position in the cycle (a remainder of 0 corresponds to the last digit in the cycle).

Step 1: The total area of the square is side \(\times\) side = \(6 \times 6 = 36 cm^2\).


Step 2: Observe the figure's symmetry. The shaded area and the unshaded area are created by identical geometric constructions (two semi-circles).


Step 3: If you rotate the figure 180 degrees about its center, the shaded region would exactly cover the unshaded region, and vice-versa.


Step 4: This perfect symmetry implies that the area of the shaded region is equal to the area of the unshaded region.


Step 5: The total area of the square is the sum of the shaded and unshaded areas.


Step 6: Area(Shaded) + Area(Unshaded) = 36.


Step 7: Since Area(Shaded) = Area(Unshaded), we can write 2 \(\times\) Area(Shaded) = 36.


Step 8: Therefore, Area(Shaded) = \(\frac{36}{2} = 18 cm^2\).
Quick Tip: In geometry problems, always look for symmetry first. If a figure is divided into two regions that are symmetrical (e.g., via rotation or reflection), their areas will be equal. This can often lead to a much simpler solution than direct area calculation.

Step 1: The question asks for a single word that means both "spineless" (lacking courage or determination) and "cowardly".


Step 2: Let's analyze the meanings of the given options.


Step 3: (A) Pusillanimous means showing a lack of courage or determination; timid. This is a direct synonym for being cowardly and implies a lack of backbone (spineless). This is a perfect match.


Step 4: (B) Unctuous means excessively flattering or ingratiating. This does not mean cowardly.


Step 5: (C) Obsequious means being overly obedient or servile. While it might imply being spineless, it doesn't necessarily mean cowardly.


Step 6: (D) Reticent means being reserved or not revealing one's thoughts. This is unrelated to cowardice.


Step 7: Therefore, "pusillanimous" is the best word to describe being both spineless and cowardly.
Quick Tip: When asked for the meaning of a word, break down the question into its core components ("spineless" and "cowardly") and evaluate each option against those components. Use the process of elimination for unfamiliar words.

Step 1: The sentence describes a gathering for a specific festival or holiday period.


Step 2: The preposition "at" is used to refer to a point in time, including festivals and holidays like Christmas, Easter, or Diwali. For example, "We exchange gifts at Christmas."


Step 3: The preposition "on" is used for specific days (e.g., "on Diwali day," "on Monday"). The sentence implies the general festival period, not just the single day, making "at" more appropriate.


Step 4: The prepositions "of," "in," and "till" do not fit grammatically or idiomatically in this context.


Step 5: Therefore, "at" is the correct preposition. "The whole family got together at Diwali."
Quick Tip: Remember the common usage of prepositions of time: 'at' for specific times and festival periods (at 5 PM, at Christmas); 'on' for days and dates (on Sunday, on October 31st); 'in' for longer periods like months, years, and seasons (in December, in 2023, in winter).

Step 1: Analyze the context of the passage. It contrasts some "turbulence" with the success of South Indian films, which are performing better than Bollywood films.


Step 2: For blank (i), the success of these films acts as a positive point in a difficult time ("turbulence"). "Redeeming" means compensating for faults or bad aspects, which fits perfectly.


Step 3: For blank (ii), the passage describes the success of films like RRR and K.G.F. "Outperformance" correctly describes their strong performance.


Step 4: For blank (iii), the passage states that southern films traditionally did well in their own regions. "Geographies" is the most appropriate word for these regions.


Step 5: For blank (iv), the passage highlights that the collections of dubbed southern films are now better than Bollywood films. "Eclipsing" means to surpass or overshadow, which accurately describes this situation.


Step 6: Option (B) provides a set of words that are all contextually and tonally appropriate for the passage. The other options contain words that contradict the meaning (e.g., failure, underperformance, falling behind).
Quick Tip: In sentence completion questions with multiple blanks, read the entire passage first to understand the overall tone and meaning. Then, test each option to see if all the words fit logically and consistently. Often, one incorrect word in an option is enough to eliminate the entire option.

Step 1: The first sentence introduces the topic of mobility as both geographical and social.


Step 2: Sentence 2 critiques the "social mobility literature" for failing on the geographical aspect mentioned in sentence 1. This makes it a logical follow-up.


Step 3: Sentence 3 broadens the critique from "social mobility" to "sociology of migration," stating it is also too limited. This naturally follows the critique in sentence 2.


Step 4: Sentence 4 begins with "Further," signaling an elaboration. The author states their own concern with "flows of people," which is a direct response to the limitations mentioned in sentences 2 and 3.


Step 5: Sentence 5 begins with "Moreover," introducing an additional, related idea: the mobility of 'objects' in addition to people. This transitions the topic from people to objects.


Step 6: Sentence 6, the fixed conclusion, directly builds upon the idea of the 'sociology of objects' introduced in sentence 5.


Step 7: The logical flow is 1-2-3-4-5-6. Therefore, the correct order for the jumbled sentences is 2, 3, 4, 5.
Quick Tip: In jumbled paragraph questions, look for logical connectors (like 'Further', 'Moreover', 'However'), pronoun references, and the flow of ideas from general to specific. Start by finding a sentence that logically follows the fixed opening sentence.

Step 1: Let the population in 2020 be P.


Step 2: The population increased by 5% in 2021. The new population is P + (5% of P) = P + 0.05P = 1.05P.


Step 3: The population then decreased by 5% from the 2021 level. The decrease is 5% of 1.05P.


Step 4: Decrease amount = 0.05 \(\times\) 1.05P = 0.0525P.


Step 5: The population in 2022 is the 2021 population minus the decrease: 1.05P - 0.0525P = 0.9975P.


Step 6: The overall change from 2020 to 2022 is the final population minus the initial population: 0.9975P - P = -0.0025P.


Step 7: To express this as a percentage, we calculate (\(\frac{Change}{Initial}) \times 100\).


Step 8: Percentage change = (\(\frac{-0.0025P}{P}) \times 100 = -0.0025 \times 100 = -0.25%\).
Quick Tip: For successive percentage changes (e.g., +x% followed by -y%), you can use the formula: Net % Change = \(x - y - \frac{xy}{100}\). Here, x = 5 and y = 5. So, Change = \(5 - 5 - \frac{5 \times 5}{100} = 0 - \frac{25}{100} = -0.25%\).

Step 1: Analyze the relationship between the words in the given set: Thin, Slim, Slender.


Step 2: These words are all synonyms that describe a person of low body weight or girth. They carry slightly different connotations, often moving from a neutral or potentially negative term (thin) to more positive or elegant terms (slim, slender).


Step 3: Now, evaluate the options to find a set with a similar relationship.


Step 4: (A) Fat: Plump: Voluptuous. These words are synonyms for a person with a higher body weight. They also carry different connotations, moving from a potentially negative term (fat) to a more neutral or positive term (plump) to a distinctly positive and attractive term (voluptuous). This mirrors the relationship in the original set.


Step 5: (B) Short: Small: Petite. These are synonyms for a person of small stature. "Petite" specifically applies to a small and slender build, which overlaps but is not a perfect parallel to the primary relationship of weight/girth synonyms. While similar, (A) is a more direct parallel.


Step 6: (C) Tall: Taller: Tallest. This shows the comparative and superlative degrees of an adjective, which is a grammatical relationship, not a semantic relationship of synonyms with different connotations.


Step 7: (D) Fair: Dark: Wheatish. These are different categories of skin tone, not synonyms for the same idea.


Step 8: The relationship in option (A) most closely reflects the relationship in the given set.
Quick Tip: When analyzing word relationships, consider not just the denotation (literal meaning) but also the connotation (the associated feeling or idea). The relationship might be a group of synonyms with a progression in intensity or positive/negative association.

Step 1: The passage describes a past crisis (pandemic) and the government's response (medical interventions, economic spending, involvement of district authorities). The question asks for plausible future actions.


Step 2: Plausible actions are those that logically follow as a response to such a crisis. These typically involve reviewing past performance and planning for future occurrences.


Step 3: Option (A) suggests making district authorities responsible. While they were involved, making them solely responsible is a specific policy choice that isn't as universally plausible as reviewing and planning.


Step 4: Option (B) suggests reviewing past measures. This is a very plausible action, as governments need to learn from past events.


Step 5: Option (C) suggests setting up a committee to formulate a future management program. This is a proactive, forward-looking, and highly plausible step to be better prepared for the next crisis. It directly addresses minimizing future losses.


Step 6: Option (D) suggests population control. This is an extreme and indirect measure. While population density can be a factor, "population control" is not a standard or direct public health response to a pandemic in the way that planning and review are. It is the least plausible option.


Step 7: Comparing (A), (B), and (C), both (B) and (C) are very plausible. However, (C) is the most comprehensive and constructive future action that synthesizes the lessons from the past (which would be covered by (B)) into a concrete plan. Therefore, it is arguably the most fitting and plausible action.



% Quick tip
\begin{quicktipbox
In questions asking for "plausible actions," evaluate each option based on how logical, common, and direct a response it is to the situation described. Look for standard governmental or organizational procedures in response to crises, such as review, analysis, and future planning.
\end{quicktipbox Quick Tip: In questions asking for "plausible actions," evaluate each option based on how logical, common, and direct a response it is to the situation described. Look for standard governmental or organizational procedures in response to crises, such as review, analysis, and future planning.

Step 1: The question asks for the highest scorer in XH-B1 only. We can ignore all information related to XH-C1 scores.


Step 2: Let's list the relevant comparisons for XH-B1 scores.

1. Balwinder \(<\) Chintu

2. David \(>\) Chintu

3. Emon \(<\) David

4. Emon \(>\) Fulmoni

5. Arif \(<\) Emon

6. Arif \(>\) Fulmoni


Step 3: Combine the inequalities to establish a ranking.

From (2), we have David \(>\) Chintu. From (1), we have Chintu \(>\) Balwinder. Combining these gives: David \(>\) Chintu \(>\) Balwinder.


Step 4: From (5), we have Emon \(>\) Arif. From (6), we have Arif \(>\) Fulmoni. Combining these gives: Emon \(>\) Arif \(>\) Fulmoni.


Step 5: Now we need to relate the two chains. From (3), we know David \(>\) Emon.


Step 6: We can now combine all the information: David is greater than Chintu and David is greater than Emon. Since everyone else scores less than either Chintu or Emon, David must have the highest score among all students.


Step 7: The combined ranking places David at the top: David \(>\) \{Chintu, Emon\ \(>\) \{Balwinder, Arif\ \(>\) Fulmoni. David is clearly the highest scorer.
Quick Tip: In logical puzzles with multiple pieces of information, carefully filter out any irrelevant data. For ranking problems, write down the inequalities and then connect them step-by-step to form a clear hierarchy.

Step 1: We are given the condition \(x > 1\). Let's analyze the expressions for E and F based on this.


Step 2: First, simplify F. Since \(x > 1\), the denominator \((1-x)\) is negative. We can write \(F = \frac{-x}{-(x-1)} = \frac{x}{x-1}\).


Step 3: Now we need to compare \(E = \frac{x}{1+x}\) and \(F = \frac{x}{x-1}\).


Step 4: Since \(x > 1\), the numerator \(x\) is positive. Both denominators, \((1+x)\) and \((x-1)\), are also positive.


Step 5: We are comparing two positive fractions with the same positive numerator. The fraction with the smaller denominator will be the larger one.


Step 6: Let's compare the denominators: \((1+x)\) and \((x-1)\).


Step 7: Since \(1 > -1\), adding \(x\) to both sides gives \(x+1 > x-1\).


Step 8: The denominator of E is larger than the denominator of F. Therefore, the value of fraction E must be smaller than the value of fraction F.


Step 9: So, we can conclude that E \(<\) F.
Quick Tip: When comparing fractions with the same positive numerator, the fraction with the smaller positive denominator is larger. For example, \(\frac{1}{2} > \frac{1}{3}\) because \(2 < 3\). Also, when working with inequalities, plugging in a simple test value (like x=2) can quickly suggest the correct relationship, which you can then prove algebraically.

Step 1: We need to apply the given coding rules to the word "GOODMORNING".


Step 2: Rule for Vowels (A, E, I, O, U): Replace with the next vowel in the sequence A \(\rightarrow\) E, E \(\rightarrow\) I, I \(\rightarrow\) O, O \(\rightarrow\) U, U \(\rightarrow\) A.


Step 3: Rule for Consonants: Replace with the previous consonant in the alphabet (e.g., C \(\rightarrow\) B, D \(\rightarrow\) C).


Step 4: Let's encode the word letter by letter:

- G (consonant): The previous consonant is F.

- O (vowel): The next vowel is U.

- O (vowel): The next vowel is U.

- D (consonant): The previous consonant is C.

- M (consonant): The previous consonant is L.

- O (vowel): The next vowel is U.

- R (consonant): The previous consonant is Q.

- N (consonant): The previous consonant is M.

- I (vowel): The next vowel is O.

- N (consonant): The previous consonant is M.

- G (consonant): The previous consonant is F.


Step 5: Combine the coded letters in order: F U U C L U Q M O M F.


Step 6: This matches option (C).
Quick Tip: For coding-decoding questions, write down the rules clearly and apply them systematically, one letter at a time, to avoid errors. Double-check your work, especially with vowels and consonants that are close to each other in the alphabet.

Step 1: The question asks what can be assumed based on the passage.


Step 2: The passage defines the stranger by what he lacks: he is "no owner of soil" because he is "not organically connected, through established ties of kinship, locality, and occupation".


Step 3: This definition implies that the condition of being a "stranger" (and thus not an "owner of soil") is contingent upon the lack of these specific ties.


Step 4: It can be logically inferred that if the stranger were to establish these ties (of kinship, locality, etc.), he would cease to be a stranger and could therefore become an "owner of soil".


Step 5: Option (C) directly states this logical reversal: becoming an owner is possible through establishing the very ties the stranger is defined by lacking.


Step 6: Option (A) is incorrect because "charm" is mentioned as something he might develop, but not as the mechanism for becoming an owner. Option (B) is too absolute; the passage implies the state is conditional, not permanent. Option (D) contradicts the passage, which treats the physical and figurative senses of "soil" together.
Quick Tip: In reading comprehension, when a concept is defined by a set of negative characteristics (what it is not), a valid assumption is often the positive corollary (what would happen if those characteristics were reversed).

Step 1: Analyze the given relationships to determine the family structure.


Step 2: "B is the only son of D." This means any other male sibling of B cannot be a son of D.


Step 3: "S has one sibling, B." Since B is the only son of D, his sibling S must be the daughter of D. Therefore, S is female.


Step 4: "L is the only son of A and S." Since S is female, S must be L's mother.


Step 5: We have the lineage: L is the child of S, and S is the child of D. This makes D the maternal grandparent of L, and L the grandchild of D.


Step 6: This eliminates the "Paternal" options (A) and (C). The relationship must be maternal.


Step 7: The remaining options are (B) Maternal Grandfather and (D) Maternal Grandmother.


Step 8: The problem statement does not provide any information about the gender of D. D could be male (Grandfather) or female (Grandmother).


Step 9: Therefore, both possibilities (B) and (D) are correct descriptions of a possible relationship between L and D. L is the grandchild, and D is the maternal grandparent (who could be a grandfather or grandmother).
Quick Tip: In blood relation puzzles, pay close attention to phrases like "only son" or "only daughter". "B is the only son of D" implies that any other child of D must be a daughter. This is often the key to solving the puzzle.

Step 1: Sentence 1 sets a scene: ".multitudes are jostling. inside me". A statement of action or intent from "me" should follow.


Step 2: Sentence 4 provides this: "I must commence the business of remaking my life.". This is a strong logical continuation from the introductory feeling in sentence 1. So, the sequence starts with 4.


Step 3: Sentence 4 ends with ".the point at which it really began,". The next sentence should describe this starting point or the manner of beginning. Sentence 2, starting with "and guided only by the memory.", explains how this remaking will be navigated. It connects logically to sentence 4.


Step 4: Sentence 2 introduces "the memory of a large white bedsheet.". Sentence 3 elaborates on this specific image, referring to it as "that holey, mutilated square of linen". The phrase "that. square of linen" clearly refers back to the "bedsheet" in sentence 2. Therefore, 3 must follow 2.


Step 5: The logical sequence of the middle segments is 4-2-3.


Step 6: This sequence connects smoothly to the final sentence (5), which specifies that this starting point (the memory) was long before the narrator's actual birth.
Quick Tip: In sentence arrangement questions, look for pronoun references ("that linen" referring to "a bedsheet") and logical connectors ("and guided by.") to establish clear links between sentences.

Step 1: The question asks how "truth" is understood in the context of the given passage.


Step 2: The passage explicitly defines "Memory's truth" as something that "selects, eliminates, alters, exaggerates, minimizes, glorifies, and vilifies". This means it is not an objective fact but a subjective construction.


Step 3: Evaluate Option (C): "Truth is the product of memory that is fallible, selective and slanted." The words "fallible" (capable of error), "selective" (selects, eliminates), and "slanted" (exaggerates, glorifies, vilifies) are a direct summary of the passage's description of memory. This statement is correct.


Step 4: Evaluate Option (D): "Truth is contingent on the observer and can only be partial." The passage states memory "creates its own reality" and that a person trusts their "own version" more than anyone else's. This shows truth is contingent on the observer (subjective). The fact that it "selects, eliminates" shows it is partial. This statement is also correct.


Step 5: Option (A) is incorrect as the passage describes a non-empirical, subjective truth, the opposite of hard evidence. Option (B) is incorrect because the passage emphasizes how memory alters perception, not the perception itself.


Step 6: Both (C) and (D) accurately reflect the understanding of truth presented in the passage.
Quick Tip: When a reading comprehension question asks for what can be understood or inferred, match the options directly against the explicit descriptions in the text. The best answers will often be paraphrases or summaries of the author's key points.

Step 1: Let 's' be the number of skilled laborers and 'u' be the number of unskilled laborers.


Step 2: From the problem statement, we can form two linear equations.

Equation 1 (Total laborers): \(s + u = 100\)

Equation 2 (Total wage bill): \(40000s + 15000u = 2375000\)


Step 3: Simplify Equation 2 by dividing the entire equation by 1000.
\(40s + 15u = 2375\)


Step 4: From Equation 1, express 'u' in terms of 's': \(u = 100 - s\).


Step 5: Substitute this expression for 'u' into the simplified Equation 2.
\(40s + 15(100 - s) = 2375\)


Step 6: Solve the equation for 's'.
\(40s + 1500 - 15s = 2375\)
\(25s = 2375 - 1500\)
\(25s = 875\)
\(s = \frac{875}{25}\)
\(s = 35\)


Step 7: The number of skilled laborers employed by the firm is 35.
Quick Tip: For word problems involving two variables, set up a system of two linear equations based on the given information. Then, use the substitution or elimination method to solve for the required variable. Simplifying large numbers by dividing by a common factor (like 1000) can make calculations easier.

Step 1: Analyze the given list of words to identify the common category.


Step 2: (1) Lek is the official currency of Albania.


Step 3: (2) Zloty is the official currency of Poland.


Step 4: (4) Drachma was the former currency of Greece.


Step 5: (5) Real is the official currency of Brazil.


Step 6: (3) Diner refers to a type of restaurant, particularly in North America. It is not a unit of currency. (Note: "Dinar" is a currency, but the word given is "Diner").


Step 7: All words except "Diner" are names of currencies (either current or former).


Step 8: Therefore, "Diner" is the odd one out. The option number is 3.
Quick Tip: In "odd one out" questions, the goal is to find the one item that does not belong to the category formed by all the other items. Consider various categories like type, function, origin, etc. Pay close attention to spelling, as a single letter change can alter the meaning entirely (e.g., Diner vs. Dinar).

Step 1: The Sānkhya school of philosophy describes a process of cosmic evolution (sarga).


Step 2: This evolution begins from a single, uncaused cause called Prakṛti (primordial matter/nature). Puruṣa (consciousness) is the witness but does not participate in the evolution.


Step 3: The evolutionary chain proceeds as follows: Prakṛti \(\rightarrow\) Mahat (or Buddhi, intellect) \(\rightarrow\) Ahaṃkāra (ego).


Step 4: From the Sāttvika (pure) aspect of Ahaṃkāra, the Manas (mind) and the five sense organs (jñānendriyas) and five motor organs (karmendriyas) evolve.


Step 5: Although Manas evolves directly from Ahaṃkāra, Ahaṃkāra itself is an evolute of Mahat, which is an evolute of Prakṛti.


Step 6: Therefore, Manas is ultimately an evolute of the original source, Prakṛti. Among the given options, Prakṛti is the correct ultimate origin.
Quick Tip: In Sānkhya philosophy, all manifest reality, including the intellect (buddhi), ego (ahaṃkāra), mind (manas), senses, and elements, are considered evolutes originating from a single source: Prakṛti. Puruṣa is pure consciousness and is distinct from this entire evolutionary chain.

Step 1: Hegel's \textit{Phenomenology of Spirit traces the journey of consciousness towards Absolute Knowing, where Spirit fully recognizes itself.


Step 2: For Hegel, this ultimate self-recognition is not a private, mystical experience or a purely intellectual achievement. It is a social and historical achievement.


Step 3: Absolute Spirit is realized in the life of a community (Sittlichkeit or ethical life) where individuals are both free and mutually recognize each other as free beings within a rational social and political structure.


Step 4: Option (C), "The self-transparency of a society of free individuals," best captures this idea of mutual recognition and rational freedom within a community. It is the state where the universal (the society) and the particular (the individual) are reconciled.


Step 5: The other options represent earlier, incomplete stages of Spirit's development. Devotion (A) involves alienation, scientific knowledge (B) involves an objectifying split between subject and object, and mystical insight (D) is an immediate, non-rational state that Hegel's philosophy moves beyond.
Quick Tip: A key concept in Hegel is that "the real is rational, and the rational is real." He believed that ultimate reality (Absolute Spirit) is not something mystical or transcendent, but is fully realized and understood through reason within the concrete social and historical life of humanity.

Step 1: The Cārvāka school, also known as Lokāyata, is a materialist school of Indian philosophy.


Step 2: Its epistemology accepts direct perception (pratyakṣa) as the only valid source of knowledge and rejects inference and testimony.


Step 3: Consequently, it rejects concepts that cannot be perceived, such as God, soul, afterlife, karma, heaven, and hell.


Step 4: The four traditional puruṣārthas (goals of life) are Dharma (righteous duty), Artha (material prosperity), Kāma (pleasure/desire), and Mokṣa (liberation).


Step 5: Since Cārvāka rejects the metaphysical basis of Dharma and Mokṣa, it denies them as valid goals of life.


Step 6: The school holds that pleasure (Kāma) is the ultimate goal of human existence, and wealth (Artha) is the means to achieve that pleasure.


Step 7: Therefore, the Cārvāka system accepts only Artha and Kāma as the puruṣārthas.
Quick Tip: Remember the core principle of Cārvāka philosophy: "Eat, drink, and be merry." This hedonistic and materialist stance means they only accept the two worldly goals of life: Kāma (pleasure) and Artha (the means to get it). They reject the two metaphysical goals, Dharma and Mokṣa.

Step 1: The \textit{Taittirīya Upaniṣad describes the pañca-koṣa, or five sheaths, that cover the true Self (Ātman). These are concentric layers, from the grossest to the most subtle.


Step 2: The five sheaths are:

1. Annamaya-koṣa: The physical body, made of food.

2. Prāṇamaya-koṣa: The vital life-force or energy sheath.

3. Manomaya-koṣa: The mental sheath, comprising the mind (manas) which deals with thoughts and emotions.

4. Vijñānamaya-koṣa: The intellectual sheath, comprising intellect (buddhi) and ego (ahaṃkāra). This is the seat of wisdom, knowledge, intelligence, and discrimination.

5. Ānandamaya-koṣa: The bliss sheath, the most subtle layer, experienced in deep sleep.


Step 3: The question asks for the sheath of "knowledge and intelligence".


Step 4: Based on the descriptions, the Vijñānamaya-koṣa (from the root 'vijñāna' meaning knowledge/wisdom) is the sheath associated with intellect, knowledge, and intelligence.
Quick Tip: To remember the five koṣas, think of them as layers of a person: Anna (food/body), Prāṇa (breath/life), Manas (mind/emotions), Vijñāna (intellect/wisdom), and Ānanda (bliss/core self). This hierarchy moves from the most external and physical to the most internal and subtle.

Step 1: Swami Vivekananda's concept of 'Universal Religion' is a core part of his teachings, based on Vedanta philosophy.


Step 2: He argued that all religions are different paths leading to the same ultimate reality or God.


Step 3: He made a crucial distinction between "tolerance" and "acceptance".


Step 4: "Tolerance" implies a sense of putting up with something you believe is inferior or wrong. Vivekananda found this attitude patronizing.


Step 5: "Acceptance," on the other hand, means acknowledging the truth in every religion and accepting them as valid paths.


Step 6: He famously stated, "We believe not only in universal toleration, but we accept all religions as true."


Step 7: Therefore, the watch-word for his vision of a universal religion is "Acceptance".
Quick Tip: For Vivekananda's philosophy, remember the key phrase from his Chicago address: "We believe not only in universal toleration, but we accept all religions as true." This highlights his emphasis on 'acceptance' over mere 'tolerance'.

Step 1: K. C. Bhattacharyya's philosophy explores the different ways consciousness relates to the Absolute.


Step 2: He outlines three primary functions of consciousness: knowing, feeling, and willing.


Step 3: Each of these functions has a corresponding 'absolute' or transcendental value which is its ultimate object or realization.


Step 4: The absolute of 'knowing' is Truth. The cognitive function of consciousness seeks and ultimately realizes Truth.


Step 5: The absolute of 'feeling' is Beauty. The affective or emotional function of consciousness realizes Beauty.


Step 6: The absolute of 'willing' is Goodness or Freedom. The conative or volitional function of consciousness realizes Freedom or moral Goodness.


Step 7: Therefore, the 'absolute' of 'knowing' is Truth.
Quick Tip: Remember K. C. Bhattacharyya's triad of consciousness functions and their corresponding absolutes: Knowing corresponds to Truth, Feeling corresponds to Beauty, and Willing corresponds to Goodness/Freedom.

Step 1: The Mīmāṃsā school of Indian philosophy is deeply concerned with epistemology, or the theory of knowledge (pramāṇas).


Step 2: The school split into two main sub-schools, Prābhākara and Bhāṭṭa, which differ on the number of accepted pramāṇas.


Step 3: The Prābhākara school accepts five pramāṇas:

1. Pratyakṣa (Perception)

2. Anumāna (Inference)

3. Upamāna (Comparison)

4. Arthāpatti (Postulation)

5. Śabda (Testimony, especially of the Vedas)


Step 4: The Bhāṭṭa school, along with Advaita Vedānta, accepts a sixth pramāṇa: Anupalabdhi (non-apprehension), which is the means of knowing a negative fact (e.g., "there is no pot on the ground").


Step 5: The Prābhākara school famously rejects Anupalabdhi as an independent pramāṇa. They argue that the knowledge of non-existence is a form of perception of the empty space.


Step 6: Therefore, Anupalabdhi is the one not considered a pramāṇa by the Prābhākara Mīmāṃsakas.
Quick Tip: A key differentiator between the two major Mīmāṃsā schools is their stance on Anupalabdhi (non-apprehension). Prābhākara accepts five pramāṇas and rejects Anupalabdhi. Bhāṭṭa accepts six pramāṇas, including Anupalabdhi.

Step 1: Commodity fetishism is a central concept in Karl Marx's critique of capitalism.


Step 2: The concept describes how, under capitalism, social relationships between people (the producers) are mystified and appear as objective relationships between things (the commodities they produce).


Step 3: The value of a commodity seems to arise from the commodity itself, rather than from the human labor that produced it.


Step 4: As Marx puts it, a commodity is a "mysterious thing" because "the social character of men's labour appears to them as an objective character stamped upon the product of that labour."


Step 5: This means that the product (the commodity) reflects the social relations of the labor that went into it, but it does so in a distorted, "fetishized" way, making it seem like the social relations are properties of the thing itself.


Step 6: Option (C) accurately captures this core idea: the concept is about the reflection (and mystification) of the social character of labor in the commodity.
Quick Tip: For Marx, "fetishism" means treating something man-made as if it had its own intrinsic, almost supernatural, power. Commodity fetishism is when the social relations of production are hidden, and it seems like the market value of goods is a natural property of the goods themselves.

Step 1: W. V. O. Quine's essay "Two Dogmas of Empiricism" is a landmark work in 20th-century philosophy.


Step 2: The two "dogmas" he attacks are (1) the distinction between analytic truths (true by meaning) and synthetic truths (true by fact), and (2) reductionism, the idea that every meaningful statement can be translated into a statement about immediate experience.


Step 3: In place of these, Quine proposes a holistic view of knowledge, often called the "web of belief". Our knowledge is a network of interconnected statements.


Step 4: When we encounter a new experience that conflicts with our web of belief, we can make adjustments anywhere in the web to restore consistency.


Step 5: Quine argues that this applies even to the statements at the center of the web, such as the laws of logic or mathematics. While we are very reluctant to revise these, no statement is, in principle, unrevisable.


Step 6: This leads to his famous conclusion that "no statement is immune to revision."
Quick Tip: Quine's central idea in "Two Dogmas" is holism: our statements about the world face the tribunal of sense experience not individually but as a corporate body. This implies that any statement can be held true if we make drastic enough adjustments elsewhere in the system, meaning no statement is completely safe from revision.

Step 1: Heraclitus is known for the doctrine that "everything flows" (panta rhei). He emphasized that the world is characterized by constant change and a plurality of opposing forces.


Step 2: However, Heraclitus also believed that this constant flux is governed by a unifying principle or universal law, which he called the Logos. So, for him, there is a unity (Logos) underlying the apparent plurality and change.


Step 3: Parmenides, in contrast, argued from pure reason that what-is (Being) must be one, eternal, and unchanging.


Step 4: He concluded that all change, motion, and plurality that we perceive with our senses are illusions. For Parmenides, reality is a single, undifferentiated whole, and he denies the reality of the plurality of things.


Step 5: Option (B) perfectly captures this fundamental contrast. Heraclitus sees a real plurality governed by a deep unity, while Parmenides denies the reality of plurality in favor of an absolute unity.
Quick Tip: A simple way to remember the contrast between Heraclitus and Parmenides is: Heraclitus says "Everything Changes" but is unified by a hidden logic (Logos). Parmenides says "Nothing Changes" and reality is a single, unchanging block; change is an illusion.

Step 1: The ontological difference is the most fundamental concept in Martin Heidegger's philosophy.


Step 2: Heidegger argues that the entire history of Western metaphysics has forgotten this crucial distinction, leading to the "forgetfulness of Being."


Step 3: The distinction is between "Being" (Sein) and "beings" (Seiende).


Step 4: "Beings" (Seiende) refers to all the particular entities that exist in the world: tables, chairs, people, trees, numbers, etc. These are things that are.


Step 5: "Being" (Sein) is not another entity among beings. It is that which makes it possible for any being to be what it is. It is the "is-ness" of beings, the ground of their existence, but not a thing itself.


Step 6: Option (A) correctly and precisely states this foundational distinction. Dasein (B, C) is a specific type of being (the human being) through which the question of Being can be asked, but the difference itself is not with Dasein.
Quick Tip: For Heidegger, the ontological difference is key. Think of it this way: "beings" are the nouns (the things that exist), while "Being" is the verb "to be" itself—not a thing, but the very condition of existence for all things.

Step 1: In Plato's \textit{Republic, he describes the four cardinal virtues of the ideal state (polis): Wisdom, Courage, Moderation, and Justice.


Step 2: He locates Wisdom specifically in the ruling class, the philosopher-kings or guardians.


Step 3: He locates Courage specifically in the warrior class, the auxiliaries.


Step 4: Moderation (sophrosyne), however, is different. Plato describes it as a kind of harmony or agreement between all parts of the state about who should rule and who should be ruled.


Step 5: For the state to be moderate, the rulers, the warriors, and the producers must all agree on their respective roles and accept the rule of the guardians.


Step 6: Because it is an agreement that must be shared by all classes, Plato says that moderation, unlike wisdom and courage, is "stretched throughout the whole" of the city.


Step 7: Therefore, the virtue of moderation is present throughout the republic.
Quick Tip: To remember the virtues in Plato's Republic: Wisdom is in the head (Guardians), Courage is in the chest (Auxiliaries), but Moderation and Justice are virtues of the whole system. Moderation is the agreement of all parts, and Justice is each part doing its own job.

Step 1: Kāśmīra Śaivism is a school of non-dualistic (Advaita) Hindu philosophy that originated in Kashmir. It is known by several names that refer to its key concepts or textual traditions.


Step 2: (B) Trika: This is one of the most common names for the system. It means "the threefold" or "the triad," referring to its central concepts of Śiva (the divine), Śakti (divine energy), and Nara (the individual soul), or other important triads.


Step 3: (A) Pratyabhijñā: This means "recognition" and is the name of the main philosophical school within Kāśmīra Śaivism. Its central tenet is that liberation is achieved through the direct recognition (pratyabhijñā) of one's own self as identical with Śiva.


Step 4: (C) Spanda: This means "vibration" or "divine creative pulse." The Spanda school is another important branch that focuses on the dynamic, vibrating nature of ultimate reality.


Step 5: (D) Vīra-śaivism: This is a distinct school of Śaivism, prominent in Karnataka. It is a qualified non-dualistic (Viśiṣṭādvaita) school and is not another name for Kāśmīra Śaivism.


Step 6: Therefore, Pratyabhijñā, Trika, and Spanda are all names used to refer to Kāśmīra Śaivism or its major sub-systems.
Quick Tip: Kāśmīra Śaivism is a rich tradition with several names. Remember "Trika" (the triad), "Pratyabhijñā" (recognition of the self as Śiva), and "Spanda" (the divine vibration) as key identifiers for this non-dualistic school. Differentiate it from Vīra-śaivism of Karnataka.

Step 1: B. R. Ambedkar was a critical theorist of democracy. He distinguished between "political democracy" (formal structures like voting) and "social democracy" (a way of life based on liberty, equality, and fraternity).


Step 2: He believed that in a society with deep-rooted inequalities like the caste system, political democracy alone was insufficient.


Step 3: Analyze option (A): "Adult suffrage and frequent elections are no bar against the governing class reaching places of power.". This aligns perfectly with Ambedkar's view. He argued that a dominant "governing class" could still maintain power despite formal elections, especially if the "servile classes" (oppressed castes) were not socially and economically empowered. This statement is correct.


Step 4: Analyze option (B): ".volunteering to elect members of the governing class. is a sign of a thriving democracy". This is the opposite of Ambedkar's view. He would see this as a symptom of a failed democracy where the oppressed have internalized their subjugation.


Step 5: Analyze option (C): ".servile classes. may need other safeguards beside adult suffrage.". This is a central tenet of Ambedkar's political philosophy. He championed safeguards like reservations in legislatures and government jobs precisely because he believed suffrage alone was not enough to ensure representation and power for marginalized groups. This statement is correct.


Step 6: Analyze option (D): "Existence of the governing class is consistent with democracy.". Ambedkar's ideal of democracy aimed at the "annihilation of caste" and the hierarchical structures that create a permanent "governing class". Therefore, its existence is inconsistent with his vision of true democracy.
Quick Tip: Ambedkar's core critique of democracy is that formal political equality (one person, one vote) is meaningless without social and economic equality. He argued for strong "safeguards" (like reservations) to protect marginalized communities from the dominance of a "governing class."

Step 1: The question asks to identify statements that are NOT in conformity with Gandhi's passage.


Step 2: Let's analyze the passage's claims.

- Gandhi states "there is no other God than Truth." This supports option (A).

- He says his "devotion to Truth has drawn me into the field of politics." This supports option (B).

- He explicitly refutes the idea of separating religion and politics: ".those who say that religion has nothing to do with politics do not know what religion means." This makes option (C) a direct contradiction of his view.

- He links his political action (driven by Truth/God) to Ahimsa through the concept of self-purification, implying politics must be guided by Ahimsa. This makes option (D) a contradiction.


Step 3: Option (C) states that religion and politics should be separated. The passage argues the exact opposite. So, (C) is not in conformity.


Step 4: Option (D) states Ahimsa and politics do not go hand in hand. Gandhi's entire political philosophy is based on Ahimsa, which he links to Truth/God. The passage implies his politics is an application of these principles. So, (D) is not in conformity.


Step 5: Therefore, statements (C) and (D) are the ones not in conformity with the passage.
Quick Tip: For questions asking what is "NOT" true or "NOT in conformity," carefully look for direct contradictions. The passage will often make a strong claim, and one of the incorrect options will state the exact opposite of that claim.

Let's break down the premises into logical statements.


Step 1: Premise 1: Soli likes logic OR Soli likes biology (L \(\lor\) B).


Step 2: Premise 2: IF Soli likes logic THEN Soli is not a happy person (L \(\rightarrow\) \(\neg\)H).


Step 3: Premise 3: Soli does NOT like biology (\(\neg\)B). (The information about Rupinder is not relevant to Soli's happiness).


Step 4: From Premise 1 (L \(\lor\) B) and Premise 3 (\(\neg\)B), we can use the rule of disjunctive syllogism. Since one of the options (B) is false, the other must be true. Therefore, we can conclude that Soli likes logic (L). This confirms that option (D) is a correct conclusion.


Step 5: Now that we have concluded that Soli likes logic (L), we can use this with Premise 2 (L \(\rightarrow\) \(\neg\)H).


Step 6: Using the rule of modus ponens (if P is true, and P implies Q, then Q is true), since L is true, we can conclude that Soli is not a happy person (\(\neg\)H). This confirms that option (A) is also a correct conclusion.


Step 7: There is no information to conclude anything about Rupinder's happiness, so (B) and (C) are incorrect.
Quick Tip: This is a classic logic problem using two fundamental rules of inference. 1. Disjunctive Syllogism: If you know (P or Q) is true and you know P is false, you can conclude Q is true. 2. Modus Ponens: If you know (If P then Q) is true and you know P is true, you can conclude Q is true.

Step 1: This question tests knowledge of Aristotle's core ethical concepts.


Step 2: Analyze option (A). This refers to Aristotle's "function argument" (ergon argument). Aristotle argues that to understand the good (and virtue) for a human being, we must first understand the unique function of a human being, which he identifies as rational activity. So, understanding function is essential to understanding virtue. This statement is correct.


Step 3: Analyze option (B). For Aristotle, a virtuous act must be chosen through a process of practical reasoning or deliberation (bouleusis) about how to achieve the good in a particular situation. The choice itself is a "deliberate desire." This statement is correct.


Step 4: Analyze option (C). Aristotle explicitly rejects this Socratic idea. He argues that knowing what is good is not enough; one becomes virtuous by repeatedly doing virtuous acts and developing the right habits and character traits, not just by intellectual knowledge. This statement is incorrect.


Step 5: Analyze option (D). This is Aristotle's famous Doctrine of the Mean. He defines moral virtue as a state of character concerned with choice, lying in a mean relative to us, this being determined by a rational principle. For example, courage is the mean between cowardice and rashness. This statement is correct.
Quick Tip: Remember Aristotle's three key ideas about virtue: 1. The Function Argument (ergon): Virtue is excellence in performing our unique function (reason). 2. Habituation: We become virtuous by practice, not just by study. 3. The Doctrine of the Mean: Virtue is an intermediate state between two vices (excess and deficiency).

Step 1: This is a direct question about David Hume's theory of the association of ideas.


Step 2: In his \textit{Inquiry, Hume argues that while our thoughts can seem random, they are connected by certain principles of association. He identifies three such principles.


Step 3: The first principle is Resemblance. A picture naturally leads our thoughts to the original. This matches option (A).


Step 4: The second principle is Contiguity in time or place. The mention of one apartment in a building naturally introduces an inquiry concerning the others. This matches option (B).


Step 5: The third principle is Cause and Effect. When we think of a wound, we can scarcely forbear reflecting on the pain which follows it. This matches option (D).


Step 6: "Juxtaposition" (C) is a general term for placing things side-by-side. While related to contiguity, it is not one of Hume's specific three principles.


Step 7: Therefore, Resemblance, Contiguity, and Cause and Effect are the correct principles according to Hume.
Quick Tip: Remember Hume's three principles of association of ideas with the acronym "RCC": Resemblance, Contiguity, and Cause and Effect. He believed these are the universal principles that govern how our thoughts are connected.

Step 1: Patañjali's Yogasūtra (Chapter 2, Sutra 3) lists five kleśas, which are the root causes of all human suffering.


Step 2: The five kleśas are:

1. Avidyā (Ignorance or false knowledge) - The root cause from which the others spring.

2. Asmitā (Egoism, identifying the self with the non-self).

3. Rāga (Attachment or craving for pleasure).

4. Dveṣa (Aversion or repulsion from pain).

5. Abhiniveśa (Clinging to life or fear of death).


Step 3: Comparing the options to this list:

- (B) Avidyā is the first kleśa.

- (C) Rāga is the third kleśa.

- (D) Asmitā is the second kleśa.


Step 4: (A) Mātsarya, meaning jealousy, envy, or rivalry, is considered a negative mental state in yogic philosophy, but it is not one of the five primary kleśas listed by Patañjali.


Step 5: Therefore, Mātsarya is the correct answer as it is not one of the five kleśas.
Quick Tip: To remember the five kleshas, think of the acronym "ARADA": Avidyā (Ignorance), Rāga (Attachment), Asmitā (Ego), Dveṣa (Aversion), and Abhiniveśa (Fear of Death). Ignorance (Avidyā) is the root of the other four.

Step 1: Jaina metaphysics classifies reality into different substances (dravyas). A primary classification is based on whether they have spatial extension.


Step 2: The term "astikāya" means "having a body" or "having extension in space". Substances that occupy multiple points in space are called astikāya.


Step 3: The five astikāya dravyas are:

1. Jīva (living souls)

2. Pudgala (matter)

3. Dharma (the medium of motion)

4. Adharma (the medium of rest)

5. Ākāśa (space)


Step 4: The term "anastikāya" means "without a body" or "without spatial extension". There is only one such substance.


Step 5: Kāla (Time) is considered a real substance (dravya), but it does not extend in space. It is conceived as a succession of moments, not a spatial entity.


Step 6: Therefore, Time (kāla) is the single anastikāya dravya.
Quick Tip: In Jaina metaphysics, remember the "5+1" structure of substances (dravyas). Five have spatial extension (astikāya): soul, matter, motion, rest, and space itself. The "+1" is Time (kāla), the only substance without spatial extension (anastikāya).

Step 1: Husserl's \textit{Cartesian Meditations, particularly the fifth, addresses the problem of solipsism (the idea that only one's own mind is sure to exist).


Step 2: The phenomenological method begins with the "reduction" (epoché), where we bracket the external world to focus on consciousness itself. This leads to the "transcendental sphere of ownness" (my own conscious experience).


Step 3: A potential problem is that this seems to trap us in our own minds, cutting us off from others (solipsism). This is what option (B) suggests.


Step 4: However, the entire purpose of the fifth meditation is to show that this is not the case. Husserl argues that it is precisely from within my own sphere of consciousness that I "constitute" the Other (the alter ego) through a process of analogical apperception or "pairing."


Step 5: I experience the Other's body as similar to my own, and I infer a conscious life like my own connected to that body. The Other is experienced as another center of consciousness.


Step 6: Thus, the reduction to my ownness is the necessary starting point for understanding how the experience of others is possible. It does not cut me off from the other; it is the very basis for encountering the other phenomenologically. This makes option (A) correct.
Quick Tip: In Husserl's phenomenology, the "reduction" to one's own consciousness is not an end but a beginning. It's a methodological step to show how the world, including other people, is constituted as a phenomenon for consciousness. It's the solution to solipsism, not the cause of it.

Step 1: Let's analyze the structure of the Nyāya inference (anumāna).

- Pakṣa (subject): Sparrow

- Sādhya (major term, what is to be proven): Birdness

- Hetu (middle term, the reason): Having wings


Step 2: A valid hetu must be present in the pakṣa, present in all similar cases (sapakṣa), and absent in all dissimilar cases (vipakṣa).


Step 3: The hetu "having wings" is present in the pakṣa "sparrow". So, it's not Svarūpāsiddhi. The pakṣa "sparrow" exists, so it's not Āśrayāsiddhi.


Step 4: The hetu must be absent in all vipakṣas (things that are not birds). However, the reason "having wings" is also present in many non-birds, such as bats and insects. These are vipakṣas where the hetu is present.


Step 5: The fallacy of Sādhāraṇa-anaikāntika (the common or "too-wide" reason) occurs when the hetu is present in both sapakṣas (other birds) and vipakṣas (non-birds like insects).


Step 6: Since "having wings" is too common and does not uniquely indicate "birdness," the inference is fallacious. This specific type of fallacy is called Sādhāraṇa-anaikāntika.
Quick Tip: In Nyāya logic, the fallacy of Sādhāraṇa-anaikāntika (common strayer) happens when the reason (hetu) is too broad. Think of it as "guilt by association." The reason is present where the property-to-be-proved is, but it's also present where the property-to-be-proved isn't. Example: "Socrates is mortal because he is a mammal." (The reason "mammal" is too broad, as all mammals are mortal).

Step 1: The Vaiśeṣika school analyzes reality into categories called padārthas. We need to break down the sentence "Dhavala is a white cow" into these categories.


Step 2: "Dhavala" refers to a specific, individual cow. This individual is a Substance (dravya).


Step 3: "White" is a characteristic of this cow. Color is a Quality (guṇa).


Step 4: "Cow" refers to the class or universal nature of "cowness" that Dhavala partakes in. This is the Universal (sāmānya).


Step 5: There is a relationship between the substance (the cow Dhavala) and its quality (whiteness), and also between the substance and its universal (cowness). This inseparable relationship is called Inherence (samavāya). The whiteness inheres in the cow, and cowness inheres in the cow.


Step 6: Therefore, to understand the full meaning of the sentence, we need to account for the Substance, the Quality, the Universal, and the relationship of Inherence that binds them.


Step 7: Option (C) includes all four of these necessary padārthas. The other options are incomplete or include irrelevant categories like Action (karma) or Absence (abhāva).
Quick Tip: When analyzing a simple descriptive sentence in the Vaiśeṣika system, look for four key things: the thing itself (Substance), its property (Quality), its class (Universal), and the "glue" that holds them together (Inherence).

Step 1: Gottlob Frege made a crucial distinction between the "sense" (Sinn) and "reference" (Bedeutung) of an expression.


Step 2: The "sense" of an expression is its mode of presentation or the thought it expresses. It is the way in which we think about the object.


Step 3: The "reference" of an expression is the actual object in the world that the expression picks out or refers to.


Step 4: Let's apply this to the expression "the largest prime number".


Step 5: Does it have a sense? Yes. We understand what the words mean. It expresses a clear concept or thought: the prime number that is greater than all other prime numbers. We can think about it and discuss its properties.


Step 6: Does it have a reference? No. Euclid's theorem proves that the set of prime numbers is infinite. Therefore, there is no object in the mathematical world that corresponds to this description. The expression fails to refer to anything.


Step 7: Therefore, the expression "the largest prime number" has a sense, but it does not have a reference.
Quick Tip: For Frege, Sense is "what you know" when you understand an expression, while Reference is "what the expression picks out" in the world. It is possible for an expression to be perfectly meaningful (have a sense) but not actually refer to anything (have no reference), like "the current king of France" or "a unicorn".

Step 1: The question asks about Socrates' explanation of beauty in Plato's dialogue, the \textit{Phaedo. This is where Plato introduces his Theory of Forms.


Step 2: Socrates rejects conventional explanations for beauty, such as a thing's color or shape (rejecting option A). He calls these "stupid" explanations.


Step 3: He also rejects subjective explanations that beauty is just in the eye of the beholder (rejecting option B).


Step 4: His new, "safe" explanation is that a beautiful thing is beautiful because it "participates" in, or shares in, the Form of Beauty (the Beautiful-in-itself).


Step 5: He uses the term "parousia," which means "presence," to describe this relationship. The Form of the Beautiful is, in some way, "present" in the particular beautiful object, and this presence is the cause of the object's beauty.


Step 6: Option (C) perfectly captures this central idea of the Theory of Forms as the cause of qualities in particular things. Option (D) is too extreme; Plato does not say beautiful things are illusions, but that their beauty is derived from the Form.
Quick Tip: In Plato's Theory of Forms, any property (like beauty, justice, or largeness) that a particular object has is caused by that object's "participation" in the corresponding ideal, eternal Form. A beautiful flower is beautiful because the Form of Beauty is "present" in it.

Step 1: Descartes' method of doubt proceeds in stages. The evil genius (or malicious demon) argument is the final and most radical stage of doubt.


Step 2: The argument is designed to call into question even those beliefs that seem most certain and are not dependent on the senses, namely the truths of mathematics and logic.


Step 3: The evil genius hypothesis supposes that a powerful, evil being could be deceiving Descartes, making him believe that mathematical propositions are true when they are in fact false.


Step 4: Let's analyze the statements.

- I, III, IV, VI are empirical claims based on sense perception. These are already cast into doubt by the earlier dream argument.

- V and VII are statements about internal mental states. Descartes argues he cannot be deceived about the fact that he is thinking or wishing (Cogito, ergo sum).

- II ("The sum of the angles of a triangle is 180 degrees") and VIII ("2+2=4") are a priori truths of mathematics. These are the specific targets of the evil genius argument. Descartes wonders if the demon could be deceiving him even about these fundamental certainties.


Step 5: Therefore, the evil genius is postulated to deny the certainty of statements like II and VIII.
Quick Tip: Remember the stages of Descartes' doubt: 1. Doubt from Senses (senses sometimes deceive us). 2. Dream Argument (doubts the existence of the external world). 3. Evil Genius Argument (doubts even a priori truths of mathematics). The Cogito ("I think, therefore I am") is the only thing that survives this final stage.

Step 1: In Kant's ethics, an "imperative" is a command of reason. It tells a will what it ought to do.


Step 2: A perfectly rational will, which Kant calls a "holy will" or "divine will," always acts in accordance with reason. Its actions are necessarily aligned with the moral law. Therefore, it does not experience the moral law as a command or an "ought." It is not subject to imperatives.


Step 3: The human will, however, is imperfectly rational. We have inclinations and desires that can conflict with reason. Therefore, we experience the moral law as a command we ought to follow, i.e., as an imperative. This confirms that (B) is a true statement.


Step 4: Let's evaluate the options to see which are NOT true.

- (A) "Every will, even the divine will is subject to imperatives". This is false. The divine will is not subject to imperatives because it cannot act otherwise than rationally.

- (C) ".the divine will is subject to the categorical imperative". This is false, for the same reason as (A). The divine will is the categorical imperative in action, but it is not subject to it as a command.

- (D) ".categorical imperative which comes from God". This is false. For Kant, the categorical imperative comes from reason itself (autonomy), not from an external authority like God (heteronomy).


Step 5: Since the question asks for statements that are NOT true, options (A), (C), and (D) are all incorrect descriptions of Kant's philosophy.
Quick Tip: For Kant, an "imperative" is only necessary for an imperfect will (like ours). A "holy will" (God's will) is perfectly rational, so it automatically does what is right without needing to be commanded. Thus, God is not subject to imperatives. Also, the moral law comes from reason itself (autonomy), not from God (heteronomy).

Step 1: Aristotle, in his \textit{Physics, outlines his theory of the Four Causes, which are four types of explanation for why something is the way it is.


Step 2: The four causes are:

1. The Material Cause: The matter out of which something is made.

2. The Formal Cause: The form, essence, or pattern of a thing. The 'what-it-is-to-be'.

3. The Efficient Cause: The agent that brings something about. The source of the change.

4. The Final Cause: The purpose or end for which something exists. The 'that-for-the-sake-of-which'.


Step 3: Let's apply these to the statue of Poseidon.

- (A) Bronze: This is the matter the statue is made from. This is the Material Cause.

- (B) The sculptor: This is the agent who made the statue. This is the Efficient Cause.

- (C) The plan to have a bronze statue of Poseidon installed in a temple: The "plan" represents both the form (Formal Cause - the idea of a statue of Poseidon) and the purpose (Final Cause - to be installed in a temple, for worship, etc.). This statement covers both.

- (D) The space in the temple: This is the location of the statue, not one of Aristotle's four causes for its existence.


Step 4: Therefore, the bronze (material), the sculptor (efficient), and the plan/purpose (formal/final) are all Aristotelian causes of the statue.
Quick Tip: To remember Aristotle's Four Causes, use the example of a statue: 1. Material (what's it made of? - bronze), 2. Formal (what is it? - a statue of a god), 3. Efficient (who made it? - the sculptor), and 4. Final (why was it made? - to be worshiped).

Step 1: The question asks about the number of dharmas (ultimate elements of reality) in two major schools of early Buddhism: Sautrāntika and Sarvāstivāda (also known as Vaibhāṣika).


Step 2: The Sarvāstivāda school is known for its extensive Abhidharma analysis. It posits a comprehensive list of 75 dharmas, which are categorized as conditioned (saṃskṛta) and unconditioned (asaṃskṛta).


Step 3: The Sautrāntika school was a reaction against the complex realism of the Sarvāstivādins. They were critical of the extensive list of dharmas and proposed a more streamlined list. They generally accepted a list of 43 dharmas.


Step 4: So, the correct pair for (Sautrāntika, Sarvāstivāda) is (43, 75).


Step 5: The question asks for the pairs that do NOT give the correct numbers. We need to find the options that are NOT (43, 75).

- (A) 75 and 43: This is (Sarvāstivāda, Sautrāntika). It is incorrect because the order is reversed.

- (B) 43 and 75: This is (Sautrāntika, Sarvāstivāda). This is the correct pair.

- (C) 43 and 0: This is incorrect.

- (D) 0 and 43: This is incorrect.


Step 6: Therefore, the pairs that are NOT the correct (Sautrāntika, Sarvāstivāda) pair are (A), (C), and (D).
Quick Tip: A key difference in early Buddhist Abhidharma is the dharma list. Remember: Sarvāstivāda ("everything exists") has a large, comprehensive list (75 dharmas). Sautrāntika was a more critical school and had a reduced list (43 dharmas).

Step 1: The core doctrine of Śankara's Advaita Vedānta is non-dualism: the ultimate reality (Brahman) is one and without a second. The individual self (Ātman) is identical to Brahman.


Step 2: Analyze option (A): "Not ontologically different from Brahman". Ontology deals with the nature of being or reality. In ultimate reality, the jīva (as Ātman) is non-different from Brahman. This statement is correct.


Step 3: Analyze option (B): "Empirically different from Brahman due to the limiting adjuncts.". Śankara explains the apparent difference between the jīva and Brahman as a product of ignorance (avidyā), which creates "limiting adjuncts" or upādhis (body, mind, senses). From the empirical or transactional standpoint (vyāvahārika), the jīva appears different and limited. This statement is also correct.


Step 4: Analyze option (C): "Ontologically real and one with Brahman". The self (Ātman) is ontologically real (it is not an illusion, its essence is Being itself) and, as stated before, it is one with Brahman. This statement is correct.


Step 5: Analyze option (D): "A part of Brahman". Śankara strongly refutes the idea that Brahman has parts (pariṇāmavāda). He upholds the doctrine of vivartavāda (apparent transformation). The jīva is not a part of Brahman, but is Brahman itself appearing as limited. To say it is a "part" would imply Brahman is divisible, which is contrary to Advaita. This statement is incorrect.
Quick Tip: In Advaita Vedānta, remember the two levels of reality: 1. Ultimate (Pāramārthika): Jīva IS Brahman (non-different, ontological identity). 2. Empirical (Vyāvahārika): Jīva APPEARS different from Brahman due to limiting adjuncts (upādhis). Advaita is not that the jīva is a part of Brahman, but that the jīva is Brahman whole and entire.

Step 1: Mohammad Iqbal's philosophy, particularly in "The Reconstruction of Religious Thought in Islam," discusses intuition as a valid source of knowledge, distinct from sense perception and reason.


Step 2: Analyze option (A): Iqbal characterizes religious experience, which is a form of intuition, as a direct, unmediated encounter with the Ultimate Reality (God). It is an immediate form of knowledge. This statement is correct.


Step 3: Analyze option (B): While intuition is a personal, subjective experience, Iqbal argues it is not merely subjective. It is a genuine encounter with an objective Reality that is independent of the individual's mind. So, it has an objective content. This statement is correct.


Step 4: Analyze option (C): Iqbal, drawing from Sufi and Islamic tradition, often associates this intuitive faculty with the "qalb" or heart. The heart is seen as an organ of supra-rational cognition, a deeper level of consciousness than the intellect. This statement is correct.


Step 5: Analyze option (D): Iqbal makes a clear distinction between the discursive, analytical knowledge of the intellect (aql) and the immediate, holistic knowledge of intuition (ishq/qalb). He sees them as different, though complementary, faculties. Attributing intuition to the mind and intellect is contrary to his distinction. This statement is incorrect.
Quick Tip: For Iqbal, "intuition" (often linked to the "heart") is a higher form of cognition than intellect. It provides immediate, direct knowledge of Reality. While a deeply personal experience, he insists it's not a mere subjective feeling but has objective cognitive value.

Step 1: Sandra Harding is a key figure in feminist standpoint theory and philosophy of science.


Step 2: Standpoint theory argues that knowledge is socially situated. The perspectives of marginalized or oppressed groups (like women) can provide a more complete and less distorted view of reality than the perspectives of dominant groups.


Step 3: A common misconception is that this negates objectivity (Option C). Harding argues the opposite. She critiques traditional notions of objectivity as being weak because they ignore the social values and biases of the researchers (who have historically been from a dominant group).


Step 4: Harding advocates for "strong objectivity." Strong objectivity requires researchers to critically examine their own social positions and the underlying assumptions of their research programs. By starting from the "standpoint" of the marginalized, whose lives are directly impacted by these assumptions, we can achieve a more rigorous and truly objective account of the world.


Step 5: Therefore, her project involves grounding feminist science not in subjectivity, but in a "strongly objective" framework (Option D). Option (A) describes feminist empiricism, a different position. Option (B) is what she argues against; science is not value-free.
Quick Tip: For Sandra Harding, "standpoint" does not mean abandoning objectivity for subjectivity. It means achieving a "stronger" objectivity by critically examining the social positions and hidden assumptions that shape scientific inquiry. The view from the margins, she argues, is more objective because it sees more.

Step 1: J.S. Mill addresses the apparent conflict between justice and utility in his work \textit{Utilitarianism. He argues that justice is not an independent standard but is grounded in utility.


Step 2: Analyze option (A). Mill argues that the rules of justice (like rights, fairness, etc.) protect our most vital interests, namely security. Since security is the most fundamental requirement for human well-being, the utility of upholding justice is exceptionally high. He calls them "the most sacred and binding part of all morality." Thus, standards of justice stand higher in the scale of social utility than other considerations. This statement is valid.


Step 3: Analyze option (B) and (D). These suggest that utility (expediency) overrides justice easily. Mill argues against this. While justice is based on utility, it is based on the highest and most important kind of utility, not mere short-term expediency. The distinction is real and crucial, not imaginary. These statements are invalid.


Step 4: Analyze option (C). Mill is still a utilitarian. This means that in extreme cases, the overall good (utility) could require overriding a specific rule of justice. He gives examples like it being permissible to steal food to save a life. In such cases, a specific social duty (saving a life) can overrule a general maxim of justice (do not steal). This statement is valid.
Quick Tip: Mill's view on justice is nuanced: Justice is not an abstract principle but is based on the highest form of utility—the utility of security and rights, which are essential for long-term happiness. While these rules are paramount, they are not absolute and can be overruled by the principle of utility itself in exceptional cases.

Step 1: This question involves Bertrand Russell's Theory of Descriptions and the scope ambiguity of negation. The proposition is "The F is not G".


Step 2: Let "The F" be "The prime number between 7 and 11". Since there is no prime number between 7 and 11, this is a definite description that fails to denote.


Step 3: Russell's theory analyzes "The F is G" as: "There is exactly one F, and that F is G".


Step 4: The negation "The F is not G" is ambiguous.

- Primary Occurrence of "The F": It is NOT the case that (The F is G). This means \(\neg\)[There is exactly one F, and that F is G]. This proposition is TRUE if "The F is G" is false. Since there is no such prime, "The F is G" is false, making the whole negated proposition TRUE. This corresponds to (A) and (C).

- Secondary Occurrence of "The F": There is exactly one F, and that F is NOT G. This proposition asserts the existence of "The F" and would be FALSE because there is no prime between 7 and 11. This corresponds to (B).
Quick Tip: Russell's key idea for sentences with negation and definite descriptions is scope ambiguity. "The King of France is not bald" can mean either (1) "There exists a King of France, and he is not bald" (False, because he doesn't exist) or (2) "It is not true that [there exists a King of France who is bald]" (True, because the inner statement is false).

Step 1: Analyze Premise (ii): \(\neg(p \supset s)\).


Step 2: Apply the rule of Material Implication, which states that \((A \supset B)\) is equivalent to \((\neg A \lor B)\).


Step 3: So, \(\neg(p \supset s)\) is equivalent to \(\neg(\neg p \lor s)\).


Step 4: Apply De Morgan's Theorem, which states that \(\neg(A \lor B)\) is equivalent to \((\neg A \cdot \neg B)\).


Step 5: So, \(\neg(\neg p \lor s)\) is equivalent to \((\neg\neg p \cdot \neg s)\), which simplifies to \((p \cdot \neg s)\).


Step 6: From this, we can use the rule of Simplification to deduce that \(p\) is true.


Step 7: Now, take Premise (i): \(p \supset (q \cdot r)\).


Step 8: Since we have deduced that \(p\) is true, we can apply the rule of Modus Ponens. If \(p\) is true and \(p\) implies \((q \cdot r)\), then \((q \cdot r)\) must be true.


Step 9: From the conclusion \((q \cdot r)\), we can again use the rule of Simplification to deduce that \(q\) is true, and also that \(r\) is true.


Step 10: Therefore, both \(q\) and \(r\) can be deduced from the premises.
Quick Tip: A key step in many logic problems is to simplify negated implications. Remember that \(\neg(P \supset Q)\) is logically equivalent to \((P \cdot \neg Q)\). This often provides a positive assertion that can be used to unlock the rest of the proof.

Let's trace the deduction from the premise \(\neg(p \supset (q \lor r))\) to the conclusion \(\neg q\).


Step 1: Start with the premise: \(\neg(p \supset (q \lor r))\).


Step 2: Apply Material Implication to the inner expression: \(\neg(\neg p \lor (q \lor r))\).


Step 3: Apply De Morgan's Theorem to the whole expression: \(\neg\neg p \cdot \neg(q \lor r)\).


Step 4: Apply Double Negation: \(p \cdot \neg(q \lor r)\).


Step 5: Apply De Morgan's Theorem to the second part: \(p \cdot (\neg q \cdot \neg r)\).


Step 6: By the rule of Simplification, we can deduce \((\neg q \cdot \neg r)\).


Step 7: By another application of Simplification, we can deduce \(\neg q\).


Now let's check the options. The sequence we derived is: Material Implication \(\rightarrow\) De Morgan's \(\rightarrow\) Double Negation \(\rightarrow\) De Morgan's \(\rightarrow\) Simplification \(\rightarrow\) Simplification. This sequence is not listed exactly. Let's re-examine the given options.


Option (A): Material Implication \(\rightarrow\) \(\neg(\neg p \lor (q \lor r))\). De Morgan's Th. \(\rightarrow\) \(\neg\neg p \cdot \neg(q \lor r)\). Commutation \(\rightarrow\) \(\neg(q \lor r) \cdot \neg\neg p\). Simplification \(\rightarrow\) \(\neg(q \lor r)\). De Morgan's Th. \(\rightarrow\) \(\neg q \cdot \neg r\). Simplification \(\rightarrow\) \(\neg q\). This sequence is valid.


Option (C): This seems more complex but may be a valid alternative path. However, the path derived initially is much more direct and aligns with the logic in Option (A). Without exploring every possible permutation of rules, (A) presents a clear and correct pathway. The question allows for multiple sequences. Let's assume there is a valid path for C as well, even if less direct. The core transformation \(\neg(P \supset Q) \equiv P \cdot \neg Q\) is the key.

Our direct path: Mat. Imp. \(\rightarrow\) De Morgan's \(\rightarrow\) DN \(\rightarrow\) De Morgan's \(\rightarrow\) Simp. This is a very standard derivation. The options given may add redundant steps like Commutation. Given the clarity of path (A), it is a correct answer.
Quick Tip: The key transformation to remember is that the negation of a conditional, \(\neg(P \supset Q)\), is equivalent to the conjunction of the antecedent and the negation of the consequent, \((P \cdot \neg Q)\). Applying this rule simplifies the premise immediately.

Step 1: The passage uses the famous analogy of a thread to explain the concept of "family resemblances". Wittgenstein argues that concepts like "game" or "number" are not defined by a single essential property common to all examples.


Step 2: He compares this to a thread. The thread's strength comes from the overlapping of many short fibres, not from one single fibre that runs the entire length.


Step 3: Analyze option (A): The "one fibre. that runs through its whole length" is the analogy for the mistaken idea of a single common property or essence (e.g., something that is common to all numbers). Wittgenstein uses this analogy to critique that idea. This statement correctly interprets the analogy.


Step 4: Analyze option (B): The "overlapping of many fibres" is the positive part of the analogy. This represents the network of criss-crossing similarities and relationships that connect all the members of a concept-family. This is exactly what he means by "family resemblance." This statement correctly interprets the analogy.


Step 5: Analyze option (C): The entire point of the analogy is to argue against the idea that there must be one common thing (the single long fibre). He finds this insistence absurd, as illustrated by the thread's strength coming from overlaps, not a single core. This statement is a correct implication of his argument.


Step 6: Analyze option (D): This is a direct contradiction of Wittgenstein's point. "Family resemblance" is his alternative to the idea of a "common property". They are opposing concepts, not different ways of describing the same thing. This statement is incorrect.
Quick Tip: Wittgenstein's "family resemblance" is a critique of essentialism. Instead of looking for one thing that all games (or numbers, etc.) have in common, he tells us to "look and see" the complicated network of overlapping similarities. Think of the thread: strength comes from many overlaps, not one continuous fibre.

Step 1: This question is about Kant's famous claim that mathematical judgments are synthetic a priori.


Step 2: An "analytic" judgment is one where the predicate is already contained in the concept of the subject (e.g., "All bachelors are unmarried"). An "a priori" judgment is one known independently of experience.


Step 3: A "synthetic" judgment is one where the predicate adds new information to the subject. Kant's radical claim is that there can be judgments that add new information but are also known a priori.


Step 4: Analyze option (A): Kant argues that if you analyze the concept of "7", the concept of "5", and the concept of "the union of the two", you will not find the concept "12" contained within them. You are just thinking of two numbers and the operation of joining them. This statement is a core part of his argument. Correct.


Step 5: Analyze option (B): To get from the concept of 7+5 to the concept of 12, Kant says we must go beyond the concepts and appeal to something else: intuition (Anschauung). We must construct the synthesis in our minds, perhaps by visualizing five fingers or five dots and adding them one by one to a group of seven. This act of construction in intuition is what makes the judgment synthetic. Correct.


Step 6: Analyze option (C): This is the logical consequence of (A) and (B). Analytic propositions are known purely through an analysis of concepts and do not require any appeal to intuition. Since Kant argues 7+5=12 does require intuition, it cannot be analytic. Correct.


Step 7: Analyze option (D): This suggests an empirical way of learning math (by imitation). Kant is arguing that the judgment is a priori, meaning its justification is independent of any particular experience or observation, so this is incorrect.
Quick Tip: Kant's big idea for math: "7 + 5 = 12" is not analytic because the concept "12" is not hiding inside the concept "7+5". You have to do something in your mind—use your intuition to count or construct—to synthesize the two concepts and arrive at the new concept, "12". Since this is a universal mental construction, it's a priori, not empirical.

Step 1: This question addresses key concepts from Jean-Paul Sartre's existentialist masterpiece, \textit{Being and Nothingness.


Step 2: Analyze option (A): "Bad faith" (mauvaise foi) is Sartre's term for the act of self-deception where we lie to ourselves to escape the anguish of our absolute freedom. We pretend we are objects (being-in-itself) determined by our situation, roles, or past, thus denying our freedom to choose (being-for-itself). This statement is a perfect definition of bad faith. Correct.


Step 3: Analyze options (B) and (C): For Sartre, human consciousness (the for-itself) is precisely the source of nothingness in the world. Consciousness is not a thing; it is a "hole in being," a capacity to negate, to question, to desire what is not. This "nothingness" is the very structure of our freedom. Therefore, to assert the existence of nothingness (as introduced by consciousness) is to assert the existence of human freedom. Option (C) is correct, and (B) is incorrect.


Step 4: Analyze option (D): While the terms seem opposite, Sartre's ontology is about their intricate relationship. The for-itself (which "is not what it is and is what it is not") introduces nothingness into the heart of being-in-itself. They are dialectically related, not simply mutually exclusive. This statement is an oversimplification and thus incorrect in the context of Sartre's system.
Quick Tip: For Sartre, remember these core equations: Human Consciousness = For-itself = Nothingness = Freedom. Objects = In-itself = Being. "Bad Faith" is when the For-itself pretends to be an In-itself to flee from the responsibility of its own freedom.