Step 1: Problem setup.
House numbers on one side are consecutive odd integers starting from 301. On the other side, they are consecutive even integers starting from 302. Let "n" represent the number of houses on each side.

Step 2: Sum of odd-numbered houses.
Using the arithmetic progression formula, the sum is: n × (n + 300).

Step 3: Sum of even-numbered houses.
Similarly, the sum of even-numbered houses is: n × (n + 301).

Step 4: Calculating the difference in sums.
Given that the difference between the sums is 27:
301n - 300n = 27, which simplifies to n = 27.

Step 5: Final conclusion.
The number of houses on each side of the road is 27.

Step 1: Simplify the given equation.
Starting with:
(p/q)^p/q = (p/q)^{(p/q - 1)}
Rewriting as:
q^q / p^q = p^{p/q - 1}.
Equating the powers of p and q:
q^p = p^q.

Step 2: Verification.
The relationship q^p = p^q satisfies the given equation.

Step 1: Analyze the given sequence.
The sequence shows a pattern where each number is one less than a power of 2.

Step 2: Express each term.
3 = 2² - 1, 7 = 2³ - 1, 15 = 2⁴ - 1, X = 2⁵ - 1 = 31.
The subsequent terms follow the same pattern: 63 = 2⁶ - 1, 127 = 2⁷ - 1, 255 = 2⁸ - 1.

Step 3: Conclusion.
The missing term X is 31.

Step 1: Understand the motion of the second and minute hands.
The second-hand completes one full revolution (360 degrees) in 60 seconds, while the minute-hand completes one revolution in 3600 seconds (1 hour).

Step 2: Calculate the crossings in one minute.
In one minute, the second-hand crosses the minute-hand exactly once.

Step 3: Calculate the crossings between 12:05:00 and 12:55:00.
The time interval between 12:05:00 and 12:55:00 is 50 minutes. Hence, the second-hand and minute-hand will cross each other exactly 50 times during this period.

Step 4: Conclusion.
The total number of crossings is 50.

Step 1: Analyze the grammar.
Each blank requires a verb that agrees with the subject and fits the tense of the sentence.

• (i) holds: Matches the singular subject "athletics."
• (ii) waits: Agrees with the singular subject "crowd."
• (iii) culminate: Fits the progression of actions leading to a conclusion.
• (iv) pivots: Aligns with the description of the athlete's motion.

Step 1: Problem Setup.
We are tasked with finding the number of unique arrangements in a circular table where twins are always seated together.

Step 2: Circular Arrangements Formula.
Since the twins must be next to each other, treat each pair as a single unit, resulting in 3 units for arrangement.
The formula for arrangements is: Total arrangements = (n-1)!, where n is the number of units.

Step 3: Substitution and Simplification.
For 3 units: Arrangements = (3-1)! = 2! = 2.
Each twin can switch places within their pair, resulting in additional 2³ = 8 arrangements.

Step 4: Final Answer.
Total arrangements = 2 × 8 = 12.

Step 1: Understanding Capacity Factor.
The Capacity Factor is the ratio of actual electricity generation to the maximum possible electricity generation over a given time.

Step 2: Calculate Capacity Factor for Each Technology.
From the given data:

• T1: CF = 14,000 ÷ (20 × 1000) = 0.7 (70%)
• T2: CF = 9,000 ÷ (25 × 1000) = 0.36 (36%)
• T3: CF = 8,000 ÷ (30 × 1000) = 0.267 (26.7%)
• T4: CF = 7,000 ÷ (35 × 1000) = 0.2 (20%)

Step 3: Conclusion.
The highest Capacity Factor is for T1, which is 70%.

Step 1: Analyze the given array.
The rule specifies that the number in each cell indicates the count of crosses (X) in its immediate neighbors. This limits the placement of crosses in adjacent cells.

Step 2: Identify constraints from neighboring numbers.
Examine the numbers in the third column, as these dictate the possible placement of crosses in the empty fourth column.

Step 3: Calculate the maximum number of crosses.
By observing the constraints, it is possible to place 2 crosses in the empty column without violating the numbers in the third column.

Step 4: Conclusion.
The maximum number of crosses in the empty column is 2.

Step 1: Use the trigonometric relationship.
During the half-moon phase, the Earth-Moon-Sun form a right triangle. Using the tangent of the Moon-Earth-Sun angle θ = 89.85°:
tan(θ) = Earth-Moon distance ÷ Earth-Sun distance.

Step 2: Rearrange the formula.
Earth-Sun distance = Earth-Moon distance ÷ tan(θ).

Step 3: Substitute the values.
With θ = 89.85°, tan(θ) ≈ 0.002618.
Earth-Sun distance ÷ Earth-Moon distance = 1 ÷ 0.002618 ≈ 382.

Step 4: Conclusion.
The ratio of Earth-Sun to Earth-Moon distances is closest to 382.

Step 1: Analyze Amma’s tone.
The passage illustrates Amma’s strong feelings about women’s rights and her vocal dissatisfaction with the inequality she faced. While she continues her role as a mother and wife, her complaints and dissatisfaction reflect a sense of protest.

Step 2: Key analysis.

• Amma’s strong feelings and complaints about being taken for granted indicate she is protesting her situation.
• She does not accept her condition passively, ruling out "resignation."
• Her dissatisfaction does not suggest compromise or contentment but aligns with an underlying "protest."

The passage describes the tightness and discomfort experienced by the speaker. The use of the words "feet," "shoes," and "pain" clearly indicates that the answer should relate to footwear. Thus, the correct choice is:

• (i) patent-leather shoes
• (ii) shoes
• (iii) patent-leather shoes
• (iv) feet

In this context, "ignite" refers to awakening or inspiring inner energy and positivity. The word "encourage" best matches the meaning of "ignite" here, as it implies motivating or instilling energy for constructive efforts.

Option (B) uses proper punctuation rules for dialogue and quoted speech:

• The quoted statement is enclosed in single quotation marks.
• Commas are correctly placed after "book" and "said."
• The internal quotation maintains proper punctuation for clarity.

The correct tense sequence is:

• (i) "had" indicates a past effect attributed to Darwin's work.
• (ii) "has" signifies the continuing influence of this work on the development of environmental politics in the present.

Step 1: Identify the relationship.
The relationship between ‘Music’ and ‘Notes’ is that Notes are the basic components or elements that constitute Music.
Similarly, in the case of ‘House: Bricks,’ Bricks are the basic components used to construct a House.

Step 2: Evaluate other options.

• (A) Water: Cold drink – Water is an ingredient, not a structural component.
• (B) Paper: Class Notes – Class Notes are written on Paper but are not structural components of Paper.
• (D) Graphite: Charcoal – Graphite is a material in Charcoal but does not constitute the entire structure.

Thus, the correct answer is (C) House: Bricks.

Step 1: Assign numerical values to letters.
Assign values based on their position in the alphabet: \( A = 1, B = 2, C = 3, \ldots, Z = 26 \).

Step 2: Calculate for given examples.

• For "RAMAN": \( R = 18, A = 1, M = 13, A = 1, N = 14 \). Sum = \( 18 + 1 + 13 + 1 + 14 = 47 \). Adding \( +5 \), code = \( 52 \).
• For "MAP": \( M = 13, A = 1, P = 16 \). Sum = \( 13 + 1 + 16 = 30 \). Adding \( +3 \), code = \( 33 \).

Step 3: Apply the pattern to "CLICK."
For "CLICK": \( C = 3, L = 12, I = 9, C = 3, K = 11 \). Sum = \( 3 + 12 + 9 + 3 + 11 = 38 \). Adding \( +5 \), code = \( 43 \).

Thus, the correct answer is (B) 43.

Step 1: Match assumptions with statements.

• 1: Suffering is because of wants – Matches "Desire is the cause of suffering."
• 2: Life is not always full of suffering – Matches "Life has suffering" (not always).
• 3: The eightfold path can reduce suffering – Matches "Desire can be reduced by following the noble eightfold path."
• 4: Suffering is caused by life – Not valid; life itself is not the cause, desire is.

Thus, only assumptions 1, 2, and 3 are valid.

Step 1: Analyze the coding pattern.
"KARAMCHAND" is divided into pairs: KA, RA, MC, HA, ND. Each letter in a pair is shifted two steps backward in the alphabet.

Step 2: Apply the pattern to "CREATION."
Divide "CREATION" into pairs: CR, EA, TI, ON. Shift each letter two steps backward:

• CR → AT
• EA → CC
• TI → RK
• ON → MP

Step 3: Combine the results.
Code for "CREATION": ATCCRKMP.

Step 1: Understand the rule.
The arrangement rule involves two processes:

1. Words are arranged in alphabetical order from left to right in each step.
2. Numbers are arranged in descending order from right to left in each step.

Step 2: Apply the rule to the input.
Input: cb kb eb 58 49 23 38 jb nb gb 69 82
Step-by-step arrangement:

• Step 1: eb cb kb 49 23 38 jb nb gb 69 82 58
• Step 2: eb cb gb kb 23 38 jb nb 82 69 58 49
• Step 3: eb cb gb jb kb 38 nb 82 69 58 49 23
• Step 4: eb cb gb jb kb nb 82 69 58 49 38 23

Step 3: Determine the position of 58 in Step 4.
In Step 4, the arrangement is: eb cb gb jb kb nb 82 69 58 49 38 23.
The number 58 is third from the right.

Step 1: Analyze the given codes.

• 'points': Found in multiple phrases: "kv."
• 'earned': Found in two phrases: "gv."
• 'maximum': Found in one phrase: "gb."

Step 2: Combine the codes.
The code for 'earned maximum points' is gv gb kv.

Step 1: Analyze the argument.
The passage argues that structural brain changes, not size, correlate with increased intelligence in humans.

Step 2: Evaluate the options.

• (A) Weakens the argument by directly refuting the hypothesis of region-specific development.
• (B) Irrelevant to the argument as it speculates on Neanderthals' extinction without addressing structural brain changes.
• (C) Speculative and unrelated to the argument about brain structure and intelligence.
• (D) Does not directly refute the argument but presents a potential counterexample to structural brain development.

Thus, the correct answer is (A).

Step 1: Analyze the narrator's tone and purpose.
The narrator reflects on their writing style and choices, showing a self-conscious tone. They also openly communicate their preferences and experiences, demonstrating a confessional style.

Step 2: Eliminate incorrect options.

• (B) Apologetic and regretful – There is no evidence of regret in the passage.
• (D) Egotistical and vain – The narrator does not display any sense of arrogance or vanity.

Thus, the correct tones are (A) Self-conscious and (C) Confessional and communicating.

Step 1: Analyze the problem.
The problem relates to student absenteeism post-pandemic. Logical solutions involve understanding and addressing underlying reasons.

Step 2: Evaluate the options.

• (A) Disciplinary action – Reactive and does not address the root cause.
• (B) Counselling sessions – Proactive and addresses potential challenges faced by students.
• (C) Surveys – Necessary to understand the reasons for absenteeism.
• (D) Changing course content – Premature and speculative without understanding the problem.

Thus, the most appropriate actions are (B) Counselling sessions and (C) Surveys.

Step 1: Analyze the passage.

• (A) Supported by the goal to inform educators about "brain science related to emotion and learning."
• (B) Incorrect; the author offers strategies but does not explicitly state applying "our learnings."
• (C) Valid, as the passage highlights the uniqueness of "integrating the lens of emotion and the brain."
• (D) Logical inference, as the author emphasizes supporting emotions for learning.

Thus, the correct statements are (A), (C), and (D).

Step 1: Analyze the statement.
- A's mother is the daughter of B's mother. This means that B's mother is A's grandmother.
- Therefore, B is either A's maternal uncle or maternal aunt, depending on B's gender.

Step 2: Conclusion.
Since the gender of B is not specified, both options Uncle (A) and Aunt (B) are plausible. Thus, the correct answer is A or B.

Step 1: Understanding Cārvāka philosophy.
Cārvāka, a materialistic school of Indian philosophy, equates liberation (\textit{apavargah}) with death (\textit{marana}), as it represents the cessation of suffering and the end of life.

Key Points:
1. Cārvāka rejects notions of afterlife, karma, and spiritual liberation (\textit{mukti}).
2. Liberation (\textit{apavargah}) is not equated with sensory pleasure or wealth but with the natural end of life: death.

Step 1: Key concept of Satkāryavāda.
Satkāryavāda asserts that the effect pre-exists in a subtle form within its material cause. Supported by:
- Sāṅkhya and some Vedānta traditions.

Contrasting views:
- Asatkāryavāda: Effect is newly produced (Nyāya-Vaiśeṣika).
- Ajātivāda and Vivartavāda: Metaphysical positions, unrelated to cause-effect pre-existence.

Key distinctions in Advaita Vedānta:
1. Absolute Brahman (\textit{Parabrahman}): Unconditioned, indeterminate, without attributes.
2. Phenomenal Brahman (\textit{Aparabrahman}): Conditioned, determinate, with attributes, referred to as \textbf{Īśvara (God)}.

Eliminating other options:
- \textbf{Jīva (Individual self):} Represents the soul, not Brahman.
- \textbf{Ātman (Self):} Refers to the individual essence or consciousness.
- \textbf{Jagat (World):} Represents the physical universe.

Understanding Pradeśa:
In Jaina philosophy, Pradeśa refers to the smallest indivisible unit of \textbf{matter} (\textit{pudgala}).

Key points:
1. Matter (\textit{pudgala}) consists of infinitely small units called Pradeśas.
2. Incorrect options: - \textbf{(A)} Self or soul (\textit{jīva}): Conscious, non-material.
- \textbf{(B)} Space (\textit{ākāśa}): Provides the area for existence.
- \textbf{(C)} Motion (\textit{dharma}): Medium enabling movement.

Key Explanation:
- The Navya Nyāya (new school of Indian logic) was founded by Gangeśa Upādhyāya.
- His seminal work, Tattvachintāmaṇi, formalized the principles of Navya Nyāya.
- While Udayana and Jayanta Bhaṭṭa made significant contributions to earlier Nyāya traditions, Gautama (Gotama) founded the classical Nyāya school.

Thus, the correct answer is (C) Gangeśa.

Explanation:
- Chapter 2 (Verses 54–72) of the Bhagavadgītā describes the qualities of a Sthitaprajña, a person with steady wisdom and equanimity.
- Such a person is unaffected by desires, emotions, or external circumstances.

Incorrect Options:
- (A) Karmayogi: Refers to someone who performs actions selflessly.
- (C) Jñāni: Refers to a person with knowledge of the Self.
- (D) Lokasaṃgraha: Relates to the welfare of the world, not individual wisdom.

Explanation:
1. Deterrent Theory: Justifies capital punishment as a means to prevent future crimes.
2. Retributive Theory: Supports capital punishment as a way to exact revenge for heinous crimes.
3. Reformative Theory: Incompatible with capital punishment, as it focuses on rehabilitating the offender.

Key Points:
- William James is known for his pragmatist view of truth, where it is defined by its practical utility.
- The quote reflects his idea that "truth" and "rightness" are verified by their expedience and usefulness.

Eliminating Incorrect Options:
- (B) John Dewey: A pragmatist, but his emphasis was on education and democracy.
- (C) Richard Rorty: Neo-pragmatist but focused on different aspects of utility.
- (D) C. S. Peirce: Emphasized long-term convergence of belief, not expediency.

Explanation:
- Aristotle associates phronesis (practical wisdom) with ethical decision-making and living a virtuous life.
- Other options relate to Aristotle's broader philosophical works but do not align with phronesis. For instance: - (B) Metaphysics relates to first principles and existence.
- (C) "Being qua Being" concerns ontology.
- (D) Syllogisms are part of logical reasoning, unrelated to ethics.

Explanation:
Pythagoras regarded numbers as the fundamental principles of reality, not material entities. Numbers define:
- Relationships and patterns (e.g., harmony in music based on numerical ratios).
- The structural organization of the cosmos.

Incorrect Options:

Thus, the correct answer is (B) As constituting the formal or relational structure.

Explanation:
In Plato’s metaphysics:
- Particulars are imperfect, transient instances of the eternal, perfect Forms.
- The relationship is called Participation, where particulars “participate” in the universal Forms (e.g., a beautiful object participates in the Form of Beauty).

Incorrect Options:

Thus, the correct answer is (D) Participation.

Explanation:
In the argument:
- Middle term ("misers") is not distributed (i.e., does not refer to all instances) in either premise.
- Without a distributed middle term, the connection between major (moneylenders) and minor (capitalists) terms is invalid.

Incorrect Options:

Thus, the correct answer is (C) Fallacy of undistributed middle.

Explanation:
In Husserl's phenomenology:
- The 'natural attitude' involves everyday, unreflective engagement with the world.
- The 'phenomenological attitude' is achieved by bracketing (epoche), where preconceived notions and assumptions are set aside.
- This method allows focus on the essence of experiences.

Thus, the correct answer is (B) By the use of bracketing or epoche.

Explanation:
In Śaiva-siddhānta, the core entities are:
1. Pati (God or Śiva): The divine being.
2. Paśu (soul): The bound self.
3. Pāśa (bondage): Ignorance and karma that bind the soul.

Incorrect:

Thus, the correct answer is (B, C, D).

Explanation:
Tagore’s vision of the ‘Supreme Man’ requires the following:
1. Engaging in imagination to transcend mundane life (\textbf{A}).
2. Acting with great purpose to align with the Spirit (\textbf{B}).
3. Finding joy through suffering and sacrifice, reflecting spiritual elevation (\textbf{C}).

Incorrect:

Thus, the correct answers are (A, B, C).

Explanation:
In Wittgenstein’s \textit{Tractatus Logico-Philosophicus}:
- A proposition is a logical picture of facts, representing reality through its logico-pictorial form.
- This structure aligns with the state of affairs it describes.

Incorrect:

Thus, the correct answer is (A) Logico-Pictorial Form.

Explanation:
In \textit{The Ethics of Ambiguity}:
- Subjectivity is both for-oneself (autonomous) and for others (social) (\textbf{D}).
- It is neither pure interiority nor pure exteriority but involves a dynamic interplay (\textbf{A, B are incorrect}).
- While subjectivity presupposes freedom, its characterization is not limited to radical freedom (\textbf{C is incorrect}).

Thus, the incorrect notions are (A, B, C).

Explanation:
Sub-contrary propositions satisfy these conditions:
1. Both cannot be false.
2. Both can be true.
Given \textbf{Some celestial bodies are not shining entities}, its sub-contrary is:
\textbf{Some celestial bodies are shining entities.}

Thus, the correct answer is (C) Some celestial bodies are shining entities.

Explanation:
Rāmānuja’s critique focuses on the lack of a proper locus for Māyā (\textbf{Avidyā}):
1. Māyā cannot reside in Brahman (pure consciousness).
2. Māyā cannot reside in Jīva (created by Māyā).
This logical challenge is termed Āśrayānupapatti, meaning "lack of proper locus."

Thus, the correct answer is (B) Āśrayānupapatti.

Explanation:
Logical Positivism emphasizes the following epistemological tenets:
1. The rejection of synthetic a priori knowledge (Option B).
2. Scientific theories as hypotheses extending beyond finite experience (Option C).
3. Verification as a criterion for meaningful statements (Option D).
However, Logical Positivism does not assert that empirical experience is the only source of knowledge (Option A), as it includes logical-mathematical truths within its framework.

Thus, the correct answer is (A).

Explanation:
Jiddu Krishnamurti's philosophy of education emphasizes the following:
1. The individual’s development is prioritized over rigid educational systems.
2. Education’s purpose is to understand life holistically (Option B).
3. Emphasis on understanding and learning rather than technical training (Option C).
4. Avoidance of fixed ideals that restrict present comprehension (Option D).
Option A contradicts his core philosophy, as he strongly opposes prioritizing the system over the individual.

Thus, the correct answer is (A).

Explanation:
According to John Locke:
1. Primary qualities (e.g., shape, size) are inherent to objects and perceptible by multiple senses (Option C).
2. Secondary qualities (e.g., color, taste) are subjective and depend on perception, often tied to a single sense (Option D).
3. Qualities in objects produce ideas in our mind, which represent them but are not exact images (Option A is incorrect).
4. The term ‘qualities’ refers to powers in objects that cause ideas in us (Option B).

Thus, the correct answer is (A).

Explanation:
The passage describes a consistent correlation:
- Good rainfall in Konkan (July) is linked with rain in Vidarbha (September).
- The absence of good rainfall in Konkan is linked to the expectation of little or no rain in Vidarbha.
This is an example of the Method of Concomitant Variation, which establishes a correlation between two events by observing variations in one event alongside variations in another.
Other methods:
- Method of Agreement: Identifies common factors in multiple cases of an effect.
- Method of Difference: Contrasts cases where the effect is present or absent.
- Method of Residues: Involves isolating the cause of an effect after accounting for known causes.

Explanation:
- Nyāya and Vaiśeṣika accept paratah-prāmāṇya, meaning that the validity of knowledge is established by external factors or sources.
- Mīmāṃsā and Vedānta generally uphold svatah-prāmāṇya, the intrinsic validity of knowledge.
Thus, the correct answer is Nyāya (C) and Vaiśeṣika (D).

Explanation:
In Yogasūtra (1:7), Patañjali identifies the following as valid means of knowledge (pramāṇa):
1. Pratyakṣa (Perception): Direct sensory experience.
2. Anumāna (Inference): Logical deduction based on observation.
3. Āptavacana (Testimony of reliable sources).
Arthāpatti (Presumption) and Upamāna (Comparison) are not included as independent pramāṇas in Patañjali's system.

Explanation:
The correct combinations of Buddhist philosophical schools and their respective thinkers are:
1. (a) Mādhayamika: Associated with (ii) Nāgārjuna, as Nāgārjuna was the founder of the Mādhayamika school, emphasizing the philosophy of emptiness (\textit{śūnyatā}).
2. (b) Yogācāra: Associated with (i) Vasubandhu, a prominent proponent of the Yogācāra or the "mind-only" school.
Incorrect options:
- (c) Sarvāstivāda and (iii) Sariputta: Sarvāstivāda was not directly associated with Śāriputra.
- (d) Sautrāntika and (iv) Ānanda: Sautrāntika is not primarily linked with Ānanda.
Thus, the correct matches are:
(a) Mādhayamika → Nāgārjuna
(b) Yogācāra → Vasubandhu

Explanation:
According to S. Radhakrishnan, intuitive knowledge:
1. Leads to the integration of the mind with reality (A). Intuition bridges the gap between the self and the universal reality.
2. Provides the knowledge of being (B). Intuition allows one to experience the essence of existence.
Incorrect options:
- (C): Logical knowledge pertains to intellect, not intuition.
- (D): Intuition dissolves the difference between knowledge of a thing and being, not emphasizing it.
Thus, the correct answers are (A, B).

Explanation:
In Sāṅkhya philosophy, bāhyakaraṇa (external instruments) are:
1. The five sensory organs (Jñānendriyas): Eyes, ears, nose, tongue, and skin (A).
2. The five motor organs (Karmendriyas): Hands, feet, speech, excretion, and reproduction (B).
Incorrect options:
- (C): Mind (Manas) is considered an internal organ, not an external one.
- (D): Includes both Jñānendriyas and Manas, but Manas is not part of bāhyakaraṇa.
Thus, the correct answers are (A, B).

Explanation:
Sri Aurobindo describes the "power" of Saccidānanda (existence, consciousness, and bliss) that creates the world as the dynamic force responsible for the manifestation of the phenomenal universe.
1. Māyā: Māyā is the creative power of the Supreme Being, responsible for manifesting the diversity of the phenomenal world while maintaining unity in existence. It aligns with the description in the passage.
2. Incorrect options:
- Involution: Refers to the descent of the Supreme Consciousness but is not explicitly the "power" here.
- Evolution: Describes the ascent of consciousness, not the creative force.
- Integral Yoga: A practical philosophy, not the metaphysical "power" mentioned.
Thus, the correct answer is (A) Māyā.

Explanation:
Dr. B.R. Ambedkar’s views in the passage highlight:
1. Dhamma is necessary for liberty (C): As it consists of Prajna (understanding) and Karuna (love), both critical for societal growth and individual freedom.
2. Prajna checks superstition (D): As understanding, Prajna prevents superstition and is a cornerstone of Dhamma.
Incorrect options:
- (A): The passage does not describe Dhamma, Prajna, and Karuna as aspects of Religion but rather as components of Dhamma.
- (B): Both Karuna and Dhamma are essential; the passage does not prioritize Karuna over Dhamma.
Thus, the correct answers are (C, D).

Explanation:
Bertrand Russell differentiates between:
1. Knowledge by acquaintance: Direct experience or perception of objects.
2. Knowledge by description: Knowledge of things not directly experienced, derived through inference.
Russell asserts:
- Description involves inference and the use of concepts, making (A) and (D) incorrect.
- Physical objects and other people's minds are often known by description, supporting (B).
- Description is ultimately reducible to acquaintance (C), as descriptions depend on direct experiences.
Thus, the correct answers are (B), (C).

Explanation:
Cultural relativism asserts:
- Moral values are relative to specific cultures (A, B).
- There is no universal or intercultural basis for judging moral values (C).
- It does not deny the existence of moral values entirely, making (D) incorrect.
Thus, the correct answers are (A, B, C).

Explanation:
Correct associations:
1. Thomas Hobbes: Described the state of nature as "nasty, brutish, and short" (A).
2. J.J. Rousseau: Argued "Man is born free, but everywhere he is in chains" (C).
Incorrect associations:
- (B): Economics as the base structure is a Marxist idea, not Locke's.
- (D): Marx did not describe the state of nature as total freedom and equality.
Thus, the correct answers are (A, C).

Explanation:
Rene Descartes’ philosophy introduces the concept of innate ideas, which are ideas inherent in the human mind, not derived from external experiences or constructed by oneself.
1. (A): Incorrect. Descartes believed that innate ideas are inherent in the mind and are a fundamental part of the self.
2. (B): Correct. Innate ideas are not adventitious (not derived from sensory experience).
3. (C): Incorrect. Innate ideas are not produced by the self; they pre-exist in the mind.
4. (D): Correct. Innate ideas are possessed purely by virtue of our nature.
Thus, the correct answers are (B, D).

Explanation:
David Hume divides perceptions into two distinct classes:
1. Impressions: Vivid, direct sensory experiences, including sensations and emotions (D).
2. Ideas: Fainter copies of impressions (B).
Incorrect statements:
- (A): Ideas and impressions are distinct classes, not one.
- (C): Ideas do not directly involve emotions; these are part of impressions.
Thus, the correct answers are (B, D).

Explanation:
Immanuel Kant distinguishes between analytic and synthetic propositions and introduces synthetic a priori judgements.
1. (A): Correct. "All bodies are extended" is an analytic judgement because the predicate is contained within the subject.
2. (B): Correct. "All bodies are heavy" is synthetic because it adds new information not inherent in the subject.
3. (C): Incorrect. "A straight line is the shortest one" is a synthetic a priori proposition, not analytic.
4. (D): Correct. The law of conservation of matter is synthetic a priori, as it adds universal and necessary knowledge.
Thus, the correct answers are (A, B, D).

Explanation:
Hegel's view on Spirit (Geist):
1. (A): Incorrect. Spirit's development manifests in concrete reality.
2. (B): Correct. Spirit's struggle to know itself is central to Hegel's dialectical process.
3. (C): Correct. Spirit progresses from potentiality to actuality in history.
4. (D): Correct. History is the unfolding of reason or logic.
Thus, the correct answers are (B, C, D).