MPSC Prelims 2020 CSAT (Paper II) with Answers & Explanations

Explanation

The central idea of the passage is focused on non-probability sampling. The text begins by defining non-probability sampling and listing its alternative names, such as deliberate, purposive, and judgement sampling. It details the process of how researchers deliberately select items for the sample based on their judgement, explains the risks of bias and personal elements entering the selection process, and discusses the advantages of time and cost savings. Furthermore, it introduces quota sampling as a specific example of this method. Throughout the passage, every paragraph and example serves to describe the characteristics, advantages, limitations, and applications of non-probability sampling, making it the primary focus of the text.

Explanation

Random sampling is a type of probability sampling where every member of the population has an equal, known, and non-zero chance of being selected. This is the opposite of non-probability sampling, where selection is based on the subjective judgment or convenience of the researcher rather than random selection, making it impossible to estimate sampling errors or ensure every element has a specifiable chance of inclusion.

Explanation

According to the passage, the reliability of the results obtained from an analysis of a deliberately selected sample depends on the qualities of the investigators conducting the inquiry. The text explicitly states that such results can be tolerably reliable if the investigators are impartial, work without bias, and have the necessary experience to make sound judgments. This directly aligns with statement (a) regarding being unbiased and statement (b) regarding being experienced.

Explanation

Under non-probability sampling, the selection of the sample is not randomized but is instead deliberately determined by the investigator. The researcher's judgment is vital because their choice regarding which items to include in the sample is supreme. The organizers purposively select specific units of the population that they believe are typical and representative of the entire universe, making the researcher's subjective discretion the primary force behind the composition of the sample.

Explanation

The passage explicitly states that in non-probability sampling, the items for the sample are selected deliberately by the researcher, meaning that the choice of the researcher concerning the items remains supreme. Additionally, it highlights that the judgment of the organisers of the study plays an important part in this sampling design, confirming that the choice of the researcher is highly significant in non-probability sampling.

Explanation

According to the passage, Henry Ford and Rudolf Diesel expected motor cars to run on fuel obtained from plants. However, crude oil was cheaper and won the competition in those days, leading to petrol becoming popular and shattering their dream.

Explanation

According to the passage, nature takes crores of years to produce crude oil, which directly validates Conclusion (A). Additionally, the passage states that bio-fuel does not emit toxic gases like nitrogen oxide, which highlights that conventional crude oil fuels release such harmful emissions, thereby validating Conclusion (B).

Explanation

According to the second paragraph of the passage, Brazil took the lead in the bio-fuel sector, which confirms statement (a). The third paragraph of the passage explicitly states that Germany is the largest producer of biodiesel in Europe, confirming statement (c). The third paragraph also specifies that ethanol in America is obtained from maize rather than sugarcane, which makes statement (b) incorrect.

Explanation

All four statements are explicitly supported by the provided text. The passage states that the most important thing is that conventional car engines can be run on bio-fuel, validating statement a. It mentions that gasoline cars are slowly disappearing according to technicians, validating statement b. It notes that bio-fuel emits low carbon dioxide and no toxic gases like nitrogen oxide, confirming that pollution is minimized, which validates statement c. Finally, it states there is no need to change the vehicle engines for bio-fuel, validating statement d. Since all statements are correct, the option indicating all of them is the right choice.

Explanation

Biofuels are liquid or gaseous fuels produced from biomass, which primarily consists of vegetation, agricultural crops, and plant residues. Because they are derived from renewable biological sources rather than fossilized organic matter, their combustion releases fewer harmful pollutants and greenhouse gases like carbon monoxide and sulfur dioxide into the atmosphere, resulting in cleaner air and reduced environmental pollution. Furthermore, integrating biofuels into the energy mix directly substitutes and blends with traditional petroleum-based fuels, which decreases the overall demand for and consumption of finite crude oil reserves.

Explanation

Under Section 351 of the Indian Penal Code, an assault is committed when a person makes a gesture or preparation with the intention or knowledge that it will cause another person present to apprehend that criminal force is about to be used against them.

The act of unloosing the muzzle of a ferocious dog is a preparatory act. By doing this with the intention of causing Y to believe that the dog is about to be set upon Y, A creates an apprehension of imminent criminal force in the mind of Y. This scenario directly corresponds to Illustration (b) of Section 351, which explicitly classifies such an act as assault.

Explanation

According to Section 350 of the Indian Penal Code, a person is said to use criminal force if they intentionally use force to any person, without that person's consent, in order to commit any offence, or intending or knowing it to be likely to cause injury, fear, or annoyance to that person.

In this scenario, A intentionally pushes against Y in the street, which means A uses force by causing motion to Y using his own bodily power under Section 349. Since this force is used intentionally, without Y's consent, and with the specific intention of causing injury to Y, all the essential ingredients of criminal force are met. This directly corresponds to the illustration of criminal force under Section 350 of the Indian Penal Code.

Explanation

Under Section 349, force is used when a person causes motion to any substance that is in contact with what another person is wearing. Pulling a woman's veil changes the motion of the veil she is wearing, which constitutes force. Under Section 350, criminal force is established when force is used intentionally, without consent, and with the knowledge that it is likely to cause annoyance or fear. Pulling up a woman's veil without her consent, knowing it is likely to annoy her, fits this definition.

The explanation under Section 351 specifies that mere words do not amount to an assault. A verbal statement expressing an intention to give a beating, without any accompanying gesture or preparation, does not constitute an assault.

Explanation

According to Section 350 of the Indian Penal Code, a person uses criminal force when they intentionally use force to another person without that person's consent, intending or knowing it to be likely that such force will cause injury, fear, or annoyance. By pouring boiling water into the bath without Y's consent and with ill intention, A intentionally uses his own bodily power to cause motion in the boiling water, bringing it into contact with Y and affecting Y's sense of feeling. Since this act is done intentionally without consent and with the knowledge that it will cause injury or annoyance, it satisfies all the statutory requirements to constitute the offence of criminal force.

Explanation

According to Section 349 of the Indian Penal Code, force is caused in one of three specified ways. The first is by the person's own bodily power, which corresponds directly to statement (a). The second is by disposing any substance in such a manner that the motion, change of motion, or cessation of motion takes place without any further act on his part or on the part of any other person, which corresponds to statement (b). Statement (c) is incorrect because the third method specified in Section 349 is by inducing any animal to move, change its motion, or cease to move, whereas statement (c) uses the phrase by not inducing. Therefore, only statements (a) and (b) are included in the definition of force.

Explanation

Under the PM-KISAN scheme, the government provides income support of ₹ 6,000 per year to eligible landholding farmer families. This financial benefit is released in three equal instalments of ₹ 2,000 each, disbursed every four months directly into the bank accounts of the beneficiaries. This confirms both that the annual income support is ₹ 6,000 and that it is released in instalments.

Explanation

The passage highlights that the PM-Kisan scheme faced significant implementation hurdles, resulting in only half of the targeted 140 million farmers receiving benefits. These hurdles include slow internet connections, Aadhaar-based enrolment issues, and messy land records, which shows that the implementation of the scheme suffers from basic lacunae, making statement (a) correct.

Furthermore, the text notes that future disbursals are likely to exclude farmers who fail to link their accounts with Aadhaar, and identifies messy land records as a key factor slowing down the programme. To streamline the identification of beneficiaries and ensure direct benefit transfer, the integration and effective linking of Aadhaar with land records is crucial, making statement (b) correct.

Explanation

Under the PM-KISAN scheme, the government provides direct income support of ₹6,000 per year to eligible farmers, paid in three equal cash transfers of ₹2,000 every four months. This direct cash transfer is designed to provide financial support to farmers to help them meet their agricultural and domestic needs, thereby raising their overall income level.

Explanation

According to the provided passage, during the first instalment period of the PM-Kisan scheme spanning from December 2018 to March 2019, nearly 70.2 million farmers received a total cash transfer of ₹ 14,055 crore.

Explanation

According to the fourth paragraph of the passage, the farm ministry informed a parliamentary panel that the PM-KISAN programme has been slowed down by Aadhaar-based enrolment and cash transfers, messy land records, and slow internet connections in many rural centres. These points directly correspond to Aadhaar-based registration, incomplete land records, and inadequate internet connectivity, which means all three factors serve as implementation hurdles for the scheme.

Explanation

According to Newton's law of gravitation and Newton's second law of motion, when a ball of mass m is dropped near the Earth of mass Me, both objects exert an equal and opposite gravitational force on each other and accelerate toward their mutual center of mass.

The acceleration of the ball toward the Earth is: a_ball = GMe/R²

The acceleration of the Earth toward the ball is: a_Earth = Gm/R²

The relative acceleration with which the ball and the Earth move toward each other is the sum of their individual accelerations: a_rel = a_ball + a_Earth = G(Me + m)/R²

A ball with a larger mass m increases the sum (Me + m), which makes the relative acceleration a_rel larger. Consequently, the distance between the ball and the Earth decreases at a faster rate.

The exact free-fall time t for two mutually attracting masses to collide is given by: t = (π/2) × √(R³ / (2G(Me + m)))

Since the collision time t is inversely proportional to the square root of the combined mass √(Me + m), the system with the larger mass m will have a shorter fall time. Therefore, the theory predicts that the ball with the larger mass will hit the Earth's surface first.

Explanation

The force of gravity acting on an object of mass m at a height h above the Earth's surface is given by the formula F = G m Me / (Re + h)², where Re is the radius of the Earth, Me is the mass of the Earth, and G is the universal gravitational constant. According to Newton's second law of motion, this gravitational force is also equal to the product of the mass of the object and the acceleration due to gravity g at that height, which is written as F = m g. By equating these two expressions, m g = G m Me / (Re + h)², and dividing both sides by the mass of the object m, we obtain the expression for the acceleration due to gravity as a function of height: g = G Me / (Re + h)².

Explanation

Kepler's Third Law of planetary motion states that the square of the orbital period T of a satellite is directly proportional to the cube of its orbital radius R:

T² ∝ R³

Taking the square root on both sides gives:

T ∝ √(R³)

If the orbital radius R is increased by a factor of 4, the new orbital period T' becomes:

T' ∝ √((4R)³) = √(64R³) = 8√(R³)

Thus, the orbital period of the satellite will increase by a factor of 8.

Explanation

Kepler's second law states that the areal velocity of a satellite, which is the rate at which area is swept out by the position vector relative to the center of force, is constant. Mathematically, this is expressed as dA/dt = constant, which implies that the area swept out is directly proportional to the time interval, A ∝ t.

The area swept out by a satellite in a circular orbit of radius R as it moves through an angle φ is A₁ = R²φ/2. When the satellite moves through an angle of 2φ, the area swept out becomes A₂ = R²(2φ)/2 = 2 A₁. Since the area swept out is doubled, and because area is directly proportional to time, the time required to sweep out this doubled area must also be twice as long. Therefore, the time taken to move through 2φ is double the time that it takes to move through φ.

Explanation

To completely escape the gravitational field of the Earth, the final distance of the rocket from the Earth's center must approach infinity, meaning R → ∞.

Substituting R → ∞ into the given energy equation for the rocket yields the total escape energy required:

E = GmMₑ/Rₑ

This energy is provided entirely by the initial kinetic energy of the rocket at the surface of the Earth, which is given by:

K = ½mv²

By the law of conservation of energy, equating the kinetic energy to the required escape energy gives:

½mv² = GmMₑ/Rₑ

Canceling the mass of the rocket m on both sides:

½v² = GMₑ/Rₑ

v² = 2GMₑ/Rₑ

v = (2GMₑ/Rₑ)^½

Explanation

Algae are autotrophic organisms, which means they synthesize their own food through photosynthesis and are not dependent on other living organisms for sustenance. This makes the former half of the given statement wrong. Algae possess various photosynthetic pigments such as chlorophylls, carotenoids, and phycobilins, which makes the latter half of the statement correct. Because only the first half of the statement is incorrect, statement (d) is the correct evaluation.

Explanation

Pteridophytes are vascular plants that possess well-differentiated vascular tissues (xylem and phloem) but do not produce seeds, reproducing instead via spores. Since pteridophytes are not listed among the first three options, the correct choice is None of the above.

Explanation

In gymnosperms, microspores are produced within specialized structures called microsporangia. These microsporangia are borne on modified, leaf-like structures known as microsporophylls, which are arranged spirally along a central axis to form the male cones or microsporangiate strobili.

Explanation

In bryophytes, the diploid zygote does not immediately undergo meiosis. Instead, it divides mitotically to develop into a multicellular diploid body called a sporophyte. This sporophyte is not free-living but remains physically attached to the photosynthetic gametophyte to derive nourishment from it. Specialized cells within the sporophyte, specifically inside the capsule, undergo meiotic reduction division to produce haploid spores. Upon maturation, these haploid spores are released and germinate to give rise to new gametophytes. Therefore, the haploid spores are produced within the multicellular sporophyte.

Explanation

Chlorophyll is the primary photosynthetic pigment present in all autotrophic green plants. Members of the plant kingdom, including algae, bryophytes, pteridophytes, and gymnosperms, utilize chlorophyll pigments to absorb light energy and perform photosynthesis to manufacture their own food. Therefore, all these plant groups possess chlorophyll pigment in their photosynthetic cells.

Explanation

According to the first sentence of the second paragraph of the passage, the major portion present in sewage is water, which can be used for irrigation. This directly corresponds to statement (d), which is represented by option 4.

Explanation

According to the passage, the most suitable and satisfactory filtration takes place in porous, loamy, or sandy soils, which means porous soil is highly preferred for filtration, making statement (b) incorrect. Additionally, the passage mentions that sewage contains nitrogen, potash, phosphate, and organic acids, which give it a good fertilizer value and help increase the fertility of the soil, making statement (c) incorrect. Therefore, only statements (b) and (c) are incorrect.

Explanation

According to the passage, the bacteria present in the soil attack the sewage and convert its content into plant food. Furthermore, the passage states that when sewage is applied on land, a chemical process of oxidation takes place in which the organic matter of the sewage is oxidised by these bacteria. Therefore, the conversion of sewage into plant food is carried out through chemical action and bacteria.

Explanation

According to the passage, the oxygen required for the aerobic decomposition of sewage is present in different layers of the soil. The decomposition process produces carbon dioxide, which is released by the soil and subsequently interchanged with atmospheric oxygen through wind movements, temperature and pressure differences, and soil drainage. Therefore, statement (b) is correct as it accurately describes this interchange of the produced carbon dioxide with atmospheric oxygen.

Explanation

Statement (a) is correct as the passage explicitly mentions that filtration is the principal physical action involved in the purification of sewage by land treatment. Statement (c) is correct because the passage states that sewage contains nutrients like nitrogen, potash, and phosphate, which have a good fertilizer value, thereby increasing the fertility of the soils. Statement (d) is correct because the passage notes that the organic matter present in sewage undergoes decomposition by aerobic and non-aerobic bacteria.

Explanation

The passage defines political education as the preparation of a citizen to take actions for the realization of the socio-economic objectives of the country. It explicitly states that these overriding objectives in India are the abolition of poverty and the creation of a modern democratic, secular, and socialist society in place of the existing traditional, feudal, hierarchical, and inegalitarian one. Hence, the ultimate objective of political education is to transform the existing social structure to create an egalitarian society.

Explanation

According to the passage, Mahatma Gandhi's main contribution to political education lies in his core philosophy regarding the relationship between the methods employed and the goals achieved. The text explicitly states that he believed the means to be as important as the ends. This principle emphasizes that the actions, strategies, and methods used in any political struggle must be ethical, disciplined, and fully compatible with the ultimate political and social objectives one seeks to achieve.

Explanation

According to the passage, the interference of political parties in the educational system is driven by their own ulterior motives and does not constitute genuine political education. Additionally, the passage highlights that political parties, like other institutions outside the school system, have failed to provide genuine political education in the post-independence era, often focusing instead on agitation and anarchic politics for party or individual aggrandizement.

Explanation

The passage explicitly states that the education system of today continues to support the domination of the privileged groups and the domestication of the underprivileged ones. This directly highlights that the major problem of the current education system is that it perpetuates the domination of the few privileged.

Explanation

According to the passage, while academicians desired political support without political interference, the post-independence reality turned out to be the exact opposite. The educational institutions actually received infinite political interference with little to no genuine political support, as political parties began to interfere with the system for their own ulterior motives rather than supporting constructive educational development.

Explanation

उताऱ्यातील पहिल्या परिच्छेदाच्या शेवटी स्पष्टपणे नमूद केले आहे की, ज्याला आपल्या व्यक्तिमत्त्वाचा परिचय नाही त्यांचा अहंकार हा अज्ञानजन्य अहंकार आहे. म्हणजेच स्वतःच्या व्यक्तिमत्त्वाचा परिचय नसणे हे अज्ञानजन्य अहंकाराचे मुख्य लक्षण आहे.

Explanation

प्रस्तुत उताऱ्याची सुरुवात संत ज्ञानेश्वर महाराजांच्या पसायदानाच्या मुख्य उद्दिष्टाने म्हणजेच मानवाच्या कल्याणासाठी आणि प्रकृतीकडून संस्कृतीकडे वळण्यासाठी केलेल्या प्रार्थनेने होते. संपूर्ण उताऱ्यात पसायदानाच्या माध्यमातून मानवी मनातील अहंकार दूर करणे, त्यागाचे मूल्य अंगीकारणे आणि शेवटी स्वानंद साम्राज्याचा चक्रवर्ती होणे याविषयी सविस्तर मार्गदर्शन केले आहे. संपूर्ण उतारा पसायदानाचा मुख्य संदेश, त्याचे मानवी जीवनातील महत्त्व आणि त्यातील उदात्त विचारांवर केंद्रित असल्यामुळे या उताऱ्यासाठी 'पसायदान : श्रेष्ठ प्रार्थना' हे शीर्षक अत्यंत समर्पक आणि योग्य ठरते.

Explanation

उताऱ्यातील संदर्भानुसार अहंकाराचे चार स्तर आणि त्यांची वैशिष्ट्ये पुढीलप्रमाणे स्पष्ट होतात:

अज्ञानजन्य अहंकार हा ज्याला आपल्या व्यक्तिमत्त्वाचा परिचय नाही अशा व्यक्तींचा असतो, म्हणून (a) ची योग्य जोडी (iv) व्यक्तिमत्त्वाचा परिचय नसणे ही आहे.

व्यक्तिगत अहंकार हा ज्यांना स्वतःची ओळख पटायला लागली आहे अशा व्यक्तींशी संबंधित आहे, म्हणून (b) ची योग्य जोडी (iii) स्वतःची ओळख पटविणे ही आहे.

व्यापक अहंकार हा ज्यांना व्यापक किंवा विशाल दृष्टी प्राप्त झाली आहे अशा लोकांमध्ये असतो, म्हणून (c) ची योग्य जोडी (ii) दृष्टीकोन विशाल करणे ही आहे.

ज्ञानजन्य निरहंकार हा आत्मतत्त्व प्राप्त झालेल्या व्यक्तींना स्वानंद सुखाची ठेव मिळवून देतो, म्हणून (d) ची योग्य जोडी (i) स्वानंद सुखाची ठेव ही आहे.

Explanation

उताऱ्यामध्ये स्पष्टपणे नमूद केले आहे की, त्याग हा सर्व व्यक्तिमत्त्वाचा पाया आहे. या त्यागाचे लेणे, त्याचे मोठेपण, त्याची सूक्ष्म भूमिका आणि त्यागाचे जीवनमूल्य आपल्याला आई-वडिलांच्या सहवासामध्ये आणि कुटुंब संस्थेमध्ये प्राप्त होते. म्हणूनच सर्वोच्च त्यागाचे जीवनमूल्य मिळण्याचे स्थान आई-वडिलांचा सहवास हेच आहे.

Explanation

Based on the provided passage, the items in the list match as follows:

Pair (a) matches with (iv) because the text states that the nature of all human beings should gradually turn towards culture.

Pair (b) matches with (i) because the author mentions that Pasayadan is requested for public welfare so that people can find a good path.

Pair (c) matches with (ii) because the passage highlights walking on the path of righteousness and self-welfare.

Pair (d) matches with (iii) because the text expresses the desire for our deeds and actions to be done for the welfare of others.

Explanation

The second paragraph of the passage states that great books transcend the provincial limits of their origin. To transcend means to go beyond, surpass, or rise above. Therefore, great books rise above provincial limits, which allows them to remain as world literature with a universal and enduring appeal across all times and places.

Explanation

According to the passage, passing the test of time refers to the enduring interest in a book over centuries and ages. A great book transcends its era of origin, appealing to people across different generations. Therefore, passing the test of time means that the book continues to be recognized and valued as great over a long period. This is perfectly aligned with statement (b).

Explanation

According to the second paragraph of the passage, the interest in many good books is limited to a definite period of history, whereas great books transcend local limits, exhibit universal appeal, and deal with the fundamental questions confronting humans across all times and places. This directly supports statement (c).

According to the third paragraph, great books must pass the test of time, as an enduring interest over the centuries confirms their greatness, whereas good books often have their interest limited to a specific era. This directly supports statement (d).

Explanation

Statement (a) is correct because the passage explicitly mentions that great books require thought, which is why people often shy away from reading them.

Statement (e) is correct because the text highlights that great books must pass the test of time, asserting that an enduring, long-lasting interest in a book confirms its greatness.

Explanation

The first sentence of the passage states that the richness of great books shows itself in the many levels of meaning they contain. In this context, the verb contain means to possess or hold within, making have the most appropriate and direct synonym to complete the sentence.

Explanation

Since G and H are selected for Team 1, and A and H cannot work together, A must be assigned to Team 2.

Because C and A must work together, C is also assigned to Team 2.

Since B and F cannot work with C, and C is in Team 2, both B and F must be in Team 1.

This places four members (G, H, B, and F) in Team 1. Since the total number of students is eight, and each team must have at least four members, both teams must contain exactly four members.

Thus, the remaining four students, A, C, D, and E, must form Team 2. This assignment also satisfies the final condition because E is in Team 2 while G is in Team 1.

Explanation

Let the number of family members who take only coffee be C, those who take only tea be T, and those who take both coffee and tea be B.

The total number of members who take tea is T + B, and the total number of members who take coffee is C + B.

According to the given conditions: C = ½ (T + B) which simplifies to 2C = T + B T = ½ (C + B) which simplifies to 2T = C + B

Subtracting the second equation from the first: 2C - 2T = T - C 3C = 3T C = T

Let C = T = x. Substituting this back into the first equation: 2x = x + B B = x

Thus, C = T = B = x.

Evaluating Statement (a): The total number of persons who take either coffee or tea or both is: C + T + B = x + x + x = 3x The number of persons who take only coffee or only tea is x. Thrice this value is 3x, which validates Statement (a).

Evaluating Statement (b): The total number of persons who take only coffee and those who take only tea is: C + T = x + x = 2x The number of persons who take both is B = x. Twice this value is 2x, which validates Statement (b).

Explanation

Each person must make exactly one true statement and one false statement. Under the scenario where S is guilty, S is the only culprit, while R, T, and P are innocent.

Under this scenario, R's first statement (S did not do it) is false, and R's second statement (I did not do it) is true.

S's first statement (I did not do it) is false, and S's second statement (P did not do it) is true.

T's first statement (I did not do it) is true, and T's second statement (I did not know who did it) is false, which implies T knew that S was the culprit.

This scenario satisfies all the conditions of the puzzle perfectly.

Explanation

Let N be the total number of steps on the escalator, and r be the speed of the escalator in steps per second.

When Vini runs 8 steps, she takes 21.0 seconds to reach the top. During this time, the escalator moves 21.0 × r steps. The sum of these steps equals the total steps of the escalator: N = 8 + 21.0 × r

When Vini runs 13 steps, she takes 13.5 seconds. During this time, the escalator moves 13.5 × r steps: N = 13 + 13.5 × r

Equating both expressions for N: 8 + 21.0 × r = 13 + 13.5 × r 7.5 × r = 5 r = 2/3 steps per second

Substituting the value of r back to find the total steps N: N = 8 + 21.0 × (2/3) = 8 + 14 = 22 steps

If Vini decides not to run any steps, she stands stationary on the escalator. The time t required for her to reach the top is: t = N / r = 22 / (2/3) = 33 seconds

Explanation

Let the radius of the circle be R. For an equilateral triangle of side length a inscribed in this circle, the relationship between the circumradius R and the side length a is given by the formula: R = a / √3 a = R √3

The area of the equilateral triangle is: Area_triangle = (√3 / 4) a² = (√3 / 4) (R √3)² = (3 √3 / 4) R²

The area of the circle is: Area_circle = π R²

To find how many times the area of the circle is with respect to the area of the triangle, we divide the area of the circle by the area of the triangle: Ratio = Area_circle / Area_triangle = (π R²) / ((3 √3 / 4) R²) = 4π / (3 √3)

Explanation

To find the book that is a new law book with a blue cover, we look for the common book across the three specified categories. The books with blue covers are M, P, N, and Q. The new volumes are L, M, and Q. The law books are L, M, and N. Taking the intersection of these three groups, book M is the only book that satisfies all three criteria of having a blue cover, being a new volume, and being a law book.

Explanation

In deductive logic and the square of opposition, contraries are defined as two propositions that cannot both be true at the same time, but can both be false. This relationship typically exists between universal affirmative and universal negative propositions.

Statement (a) is a universal negative proposition, asserting that no citizen of smart city X wastes water. Statement (c) is a universal affirmative proposition, asserting that every citizen of smart city X uses water carelessly.

These two statements cannot be true simultaneously because a population cannot consist entirely of people who do not waste water and simultaneously consist entirely of people who waste water. However, both statements can be false at the same time. This occurs when the population is mixed, meaning some citizens use water carefully while other citizens use water carelessly. In this scenario, both universal claims (a) and (c) are false.

Explanation

The performance relationships derived from the given information are: Dharm > Karim > Beena Ashu > Beena Ashu > Mike

To determine the rank of Beena when the five students are arranged in descending order, we must consider the possible positions of Mike. Since there is no information comparing Mike with Dharm, Karim, or Beena, and no comparative link between Ashu and Dharm or Karim, multiple orderings are possible.

If the performance order is Dharm > Karim > Ashu > Mike > Beena, Beena ranks fifth. If the performance order is Dharm > Karim > Ashu > Beena > Mike, Beena ranks fourth.

Since Beena's position depends entirely on the relative performance of Mike, she does not certainly rank fourth in the descending order. Therefore, the statement is incorrect.

Explanation

The premises establish that only members of farmer families can appear for the exam. This means appearing candidates are a subset of farmer families, but it does not mean every farmer family has a candidate appearing. Furthermore, while all girl candidates receive free coaching, this does not imply that the coaching is exclusive to girls, nor that all exam candidates receive it. Because no such logical deductions can be made from the premises, the conclusion stating that none of the statements is relevant to the information is correct.

Explanation

Let the four natural numbers written by Zina be a, b, c, and d.

Choosing three numbers at a time and summing them gives four distinct equations: a + b + c = 186 a + b + d = 194 a + c + d = 206 b + c + d = 215

Adding these four equations together yields: 3 × (a + b + c + d) = 186 + 194 + 206 + 215 3 × (a + b + c + d) = 801

Dividing by 3, we find the sum of all four numbers: a + b + c + d = 267

To find the largest individual number, we subtract the smallest sum of three numbers from the total sum of all four numbers: Largest number = 267 - 186 = 81

Explanation

In the early morning, the Sun rises in the East, which means shadows are cast towards the West. Since the shadow of E's house falls on D's house, D's house must be located to the West of E's house. It is also given that E's house is located to the West of C's house, and A's house is located to the East of C's house, which means C's house is to the West of A's house. Combining these horizontal relationships from West to East gives the sequence: D is to the West of E, E is to the West of C, and C is to the West of A. This puts the houses in the direct West-to-East order of D, E, C, and A. Because E lies further to the West and A lies further to the East in this arrangement, A's house is definitely located to the East of E's house.

Explanation

The given condition states that when a natural number P is multiplied by 11 and 33 is added, the resulting sum is divisible by 9. This can be represented mathematically as:

11P + 33 ≡ 0 (mod 9)

By reducing the coefficients modulo 9, we get: 11 ≡ 2 (mod 9) 33 ≡ 6 (mod 9)

Substituting these values into the congruence relation: 2P + 6 ≡ 0 (mod 9) 2P ≡ -6 (mod 9) 2P ≡ 3 (mod 9)

To solve for P, we multiply both sides of the congruence by 5, which is the modular inverse of 2 modulo 9: P ≡ 15 (mod 9) P ≡ 6 (mod 9)

The smallest natural number P that satisfies this congruence is 6. For P = 6, the expression becomes 11 × 6 + 33 = 99, which is perfectly divisible by 9 with a remainder of zero.

Explanation

The argument concludes that abolishing the law forbidding the sale of kidneys in India would result in a greater number of successful kidney transplants. For this causal relationship to hold true, there must be a supply of kidneys available for purchase once the law is changed. If no individuals were willing to sell their kidneys, legalizing the practice would not lead to any increase in transplants. Therefore, the argument directly depends on the assumption that some people in India are willing to sell a kidney.

Explanation

Based on the given relationships:

B is the father of C. Since C is not B's son, C must be B's daughter (female).

P is the brother of C (male).

Q is the daughter of C (female).

Since C is the mother of Q and P is the brother of C, P is the maternal uncle (uncle from mother's side) of Q. Consequently, Q is the niece of P. Therefore, the pair representing the maternal uncle and his niece is P and Q.

Explanation

From the statement that some cars are days, there is a guaranteed overlap between the set of cars and the set of days. The statement that all days are nights means the entire set of days is contained within the set of nights. Since the overlapping region of cars and days lies entirely within the set of days, it must also lie within the set of nights. Therefore, there is a guaranteed overlap between nights and cars, making the conclusion that some nights are cars logically true.

Explanation

Distance covered by a wheel is given by the formula: Distance = Circumference × Number of revolutions = π × Diameter × Number of revolutions

Since both the bigger and smaller wheels of the tractor cover the exact same distance, the relationship is: π × D₁ × N₁ = π × D₂ × N₂

Simplifying the equation by canceling π on both sides: D₁ × N₁ = D₂ × N₂

Substituting the given values: 50 × 21 = 35 × N₂

Solving for N₂: N₂ = (50 × 21) / 35 N₂ = 1050 / 35 N₂ = 30

Explanation

The treasure hunter argues that ancient shipwrecks must be salvaged because they are in danger of becoming extinct in salty ocean waters, implying that natural oceanic conditions threaten their preservation. The archaeologist directly contradicts this by stating that the shipwrecks have stabilized over centuries and face no natural danger of disappearing, with the only real threat being human looting. Therefore, the core point of disagreement is whether, or in what sense, an ancient shipwreck can be considered on the verge of extinction or destruction.

Explanation

Profit share in a partnership is directly proportional to the product of the investment and the time period. Let the initial investments of Sanjay, Ashok, and Ketan be 2, 6, and 10 units respectively to avoid fractional calculations.

For the first 4 months, the investments are: Sanjay = 2 units Ashok = 6 units Ketan = 10 units

For the remaining 8 months: Sanjay doubles his investment, making it 2 + 2 = 4 units. Ashok withdraws half, leaving 6 - 3 = 3 units. Ketan withdraws half, leaving 10 - 5 = 5 units.

The total profit share ratio is calculated as: Sanjay = (2 × 4) + (4 × 8) = 8 + 32 = 40 Ashok = (6 × 4) + (3 × 8) = 24 + 24 = 48 Ketan = (10 × 4) + (5 × 8) = 40 + 40 = 80

Simplifying the ratio of profit shares: Sanjay : Ashok : Ketan = 40 : 48 : 80 = 5 : 6 : 10

Explanation

The selection is made using the combination formula ⁿCᵣ = n! / (r! × (n - r)!).

To form a committee of 10 members from 15 men and 7 women such that there are at least 6 women, there are two mutually exclusive cases: selecting 6 women and 4 men, or selecting 7 women and 3 men.

Case 1: Choosing 6 women from 7, and 4 men from 15. Number of ways = ⁷C₆ × ¹⁵C₄ ⁷C₆ = 7 ¹⁵C₄ = (15 × 14 × 13 × 12) / (4 × 3 × 2 × 1) = 1365 Number of ways = 7 × 1365 = 9555

Case 2: Choosing 7 women from 7, and 3 men from 15. Number of ways = ⁷C₇ × ¹⁵C₃ ⁷C₇ = 1 ¹⁵C₃ = (15 × 14 × 13) / (3 × 2 × 1) = 455 Number of ways = 1 × 455 = 455

Total number of ways = 9555 + 455 = 10010

Explanation

Based on the provided text, laboratory studies have shown that triclosan has the potential to adversely affect bone density in animals. In public health and consumer safety, the precautionary principle dictates that when a chemical widely used in everyday human products like soaps, toothpastes, and sanitizers demonstrates potential toxicity or adverse health effects in animal models, proactive measures should be taken. Since humans are continuously exposed to these products, demonstrating this potential harm in animal models provides a valid scientific basis to ban or restrict its use in consumer goods to prevent potential harm to human bone health before definitive damage is widespread.

Explanation

To find the original number of shells S had, we can work backward from the number of shells received by R.

Let Q be the number of shells that Q had. R received one third of Q's shells plus 1 more: (1/3) × Q + 1 = 14 (1/3) × Q = 13 Q = 39

Let P be the number of shells that P had. Q received one third of P's shells plus 11 more: (1/3) × P + 11 = 39 (1/3) × P = 28 P = 84

Let S be the original number of shells S had. P received one third of S's shells plus 14 more: (1/3) × S + 14 = 84 (1/3) × S = 70 S = 210

Explanation

Deposition before an inquiry committee demands absolute honesty, integrity, and transparency. Giving a fair and truthful account of the situation ensures that the organization can accurately identify the root cause of the product failure. Simultaneously, taking responsibility as a team and assuring the committee that subordinates will proactively and constructively assert their critical views on crucial decisions in the future demonstrates a high degree of accountability, professional maturity, and a forward-looking, problem-solving attitude to prevent future losses while maintaining the collaborative framework of the organization.

Explanation

The critical issue at hand is the frequent loss of lives due to asphyxiation and accidents while performing manual scavenging inside sewers. The most direct, effective, and immediate solution to prevent these fatalities is to eliminate human contact with hazardous sewage by substituting manual labor with mechanical alternatives. Prioritizing the collection of funds and collaborating with innovators to develop technological gadgets and automated systems ensures a practical and immediate reduction in human risk. This technological intervention directly addresses the core physical hazard, thereby safeguarding human lives from the most dangerous aspects of scavenging work.

Explanation

As a senior civil officer, the primary responsibility is to implement sustainable, structural, and long-term solutions that empower marginalized populations like the tribal community.

While tribal groups are often deprived of access to local natural resources, temporary administrative orders or emotional appeals for sympathy from private entities do not resolve the systemic issues.

Collaborating with academic institutions, particularly college teachers and students of humanities and sociology, brings practical expertise to understand local socio-economic dynamics. Designing and executing an empowerment plan with their assistance ensures that the tribal community becomes aware of their rights and develops sustainable livelihoods. Securing corporate social responsibility funds provides the necessary financial capital to support these developmental initiatives. This comprehensive approach builds community-led self-reliance and guarantees long-term welfare.

Explanation

As the head of an environmental NGO, maintaining scientific accuracy and institutional credibility is the highest priority when dealing with public interest disclosures. When government officials attempt to tarnish the credibility of the report by pressurizing state laboratories, obtaining verification from an independent, external laboratory specializing in similar environmental audits ensures that the findings are scientifically robust and indisputable. This triangulation of data shields the NGO from allegations of bias or misinformation, neutralizing pressure tactics. Disclosing the findings to the public only after such rigorous validation ensures that the advocacy is backed by unassailable evidence, thereby preserving the NGO's integrity, protecting its registration through solid truth, and effectively holding the violating power generation units accountable.

Explanation

As an administrative leader heading a department for industrial promotion, it is essential to adapt regulatory frameworks to the evolving business landscape. Thoroughly studying the new proposals and taking the initiative to develop flexible selection criteria ensures that the administration transitions from obsolete, rigid methods to modern, knowledge-driven practices. This proactive approach allows the department to responsibly manage public funds while actively fostering innovation, support modern entrepreneurship, and meet the dynamic needs of the contemporary economy.