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Question 1 of 15
1. Question
1 pointsThe Atomic Energy Regulatory Board (AERB) regulates the safety of which of the following facilities/activities?
- Nuclear Power Plants (NPPs)
- Medical X-ray installations and radiotherapy units
- Transportation of radioactive materials
- Industrial radiography and food irradiation plants
Select the correct answer using the code given below:
Correct
Answer: (D)
Explanation:
The Atomic Energy Regulatory Board (AERB) has a comprehensive mandate to ensure that the use of ionizing radiation and nuclear energy in India does not cause undue risk to health and the environment. Its regulatory jurisdiction spans across various sectors:
Scope of AERB Regulation:
- Nuclear Power Projects and Operating Plants: From the site selection and construction phase to the final decommissioning of Nuclear Power Plants (NPPs).
- Medical Applications: This includes the regulation of Diagnostic X-ray equipment, Radiotherapy units used in cancer treatment, and Nuclear Medicine facilities.
- Industrial Applications: It covers Industrial Radiography (used for non-destructive testing), Food Irradiation plants (used for preservation), and the use of ionizing radiation in research.
- Nuclear Fuel Cycle Facilities: Regulation of uranium mines, ore processing plants, fuel fabrication facilities, and heavy water plants.
- Transport and Waste: It strictly regulates the transportation of radioactive materials across the country and the management of radioactive waste to ensure public safety.
Key Regulatory Functions:
- Consents and Licensing: Issuing licenses for the operation of any facility that handles radioactive substances.
- Safety Surveillance: Conducting periodic inspections to ensure compliance with safety standards.
- Standard Setting: Developing Safety Codes, Guides, and Manuals for nuclear and radiation safety.
Incorrect
Answer: (D)
Explanation:
The Atomic Energy Regulatory Board (AERB) has a comprehensive mandate to ensure that the use of ionizing radiation and nuclear energy in India does not cause undue risk to health and the environment. Its regulatory jurisdiction spans across various sectors:
Scope of AERB Regulation:
- Nuclear Power Projects and Operating Plants: From the site selection and construction phase to the final decommissioning of Nuclear Power Plants (NPPs).
- Medical Applications: This includes the regulation of Diagnostic X-ray equipment, Radiotherapy units used in cancer treatment, and Nuclear Medicine facilities.
- Industrial Applications: It covers Industrial Radiography (used for non-destructive testing), Food Irradiation plants (used for preservation), and the use of ionizing radiation in research.
- Nuclear Fuel Cycle Facilities: Regulation of uranium mines, ore processing plants, fuel fabrication facilities, and heavy water plants.
- Transport and Waste: It strictly regulates the transportation of radioactive materials across the country and the management of radioactive waste to ensure public safety.
Key Regulatory Functions:
- Consents and Licensing: Issuing licenses for the operation of any facility that handles radioactive substances.
- Safety Surveillance: Conducting periodic inspections to ensure compliance with safety standards.
- Standard Setting: Developing Safety Codes, Guides, and Manuals for nuclear and radiation safety.
-
Question 2 of 15
2. Question
1 pointsWith reference to the ‘Samriddh Gram’ initiative, consider the following statements:
- It is a phygital service delivery model designed by the Ministry of Rural Development.
- It leverages the BharatNet infrastructure to provide integrated social and economic services.
- The initiative has been nominated for the WSIS Prizes 2026 under the ‘Enabling Environment’ category.
Which of the statements given above are correct?
Correct
Answer: (B)
Explanation:
- Statement 1 is Incorrect: Although the initiative targets rural development, it is designed and implemented by the Department of Telecommunications (DoT) under the Ministry of Communications, not the Ministry of Rural Development.
- Statement 2 is Correct: A core pillar of the initiative is utilizing the high-speed broadband backbone of BharatNet. It transforms this connectivity from just internet access into a functional platform for delivering healthcare, education, and governance.
- Statement 3 is Correct: The Samriddh Gram initiative has indeed gained international recognition by being nominated for the WSIS (World Summit on the Information Society) Prizes 2026 in the Enabling Environment category.
Incorrect
Answer: (B)
Explanation:
- Statement 1 is Incorrect: Although the initiative targets rural development, it is designed and implemented by the Department of Telecommunications (DoT) under the Ministry of Communications, not the Ministry of Rural Development.
- Statement 2 is Correct: A core pillar of the initiative is utilizing the high-speed broadband backbone of BharatNet. It transforms this connectivity from just internet access into a functional platform for delivering healthcare, education, and governance.
- Statement 3 is Correct: The Samriddh Gram initiative has indeed gained international recognition by being nominated for the WSIS (World Summit on the Information Society) Prizes 2026 in the Enabling Environment category.
-
Question 3 of 15
3. Question
1 pointsHow does the Atal Pension Yojana (APY) differ from the National Pension System (NPS)?
Correct
Answer: (A)
Explanation:
Feature Atal Pension Yojana (APY) National Pension System (NPS) Returns/Pension Guaranteed. The government guarantees a minimum monthly pension of ₹1,000 to ₹5,000. Market-Linked. Returns depend on the performance of the funds (Equity, Corporate Bonds, Govt Securities). Eligibility (Age) Restricted to 18–40 years. Open to 18–70 years. Target Audience Primarily the unorganized sector. Open to all citizens (including Govt, Corporate, and Self-employed). Withdrawal Very restrictive before age 60; usually only in cases of death or terminal illness. Allows partial withdrawals (up to 25%) for specific reasons like education, marriage, or illness. Investment Choice No choice; the investment pattern is fixed by the government. Subscribers can choose their Pension Fund Manager and Asset Allocation (Active or Auto Choice). Incorrect
Answer: (A)
Explanation:
Feature Atal Pension Yojana (APY) National Pension System (NPS) Returns/Pension Guaranteed. The government guarantees a minimum monthly pension of ₹1,000 to ₹5,000. Market-Linked. Returns depend on the performance of the funds (Equity, Corporate Bonds, Govt Securities). Eligibility (Age) Restricted to 18–40 years. Open to 18–70 years. Target Audience Primarily the unorganized sector. Open to all citizens (including Govt, Corporate, and Self-employed). Withdrawal Very restrictive before age 60; usually only in cases of death or terminal illness. Allows partial withdrawals (up to 25%) for specific reasons like education, marriage, or illness. Investment Choice No choice; the investment pattern is fixed by the government. Subscribers can choose their Pension Fund Manager and Asset Allocation (Active or Auto Choice). -
Question 4 of 15
4. Question
1 pointsWith reference to the Bombay Natural History Society (BNHS), consider the following statements:
- It is a statutory body under the Ministry of Environment, Forest and Climate Change.
- It was founded in 1883 and is one of the largest non-governmental organizations in India engaged in conservation and biodiversity research.
- The society’s logo is the Great Indian Bustard, an endangered bird found in the grasslands of India.
Which of the statements given above is/are correct?
Correct
Answer: (B)
Explanation:
- Statement 1 is Incorrect: The Bombay Natural History Society (BNHS) is a non-governmental organization (NGO). It is not a statutory body (which would be created by an Act of Parliament) nor is it a government department. It is an autonomous research organization that often partners with the government.
- Statement 2 is Correct: It was founded on September 15, 1883, by eight residents of Mumbai (six Brits and two Indians). Today, it is one of the premier institutions in the Indian subcontinent for research in natural history, conservation, and biodiversity.
- Statement 3 is Incorrect: The logo of the BNHS is the Great Hornbill (specifically the Great Pied Hornbill), inspired by William, a Great Hornbill that lived on the society’s premises from 1894 to 1920. The Great Indian Bustard is a different critically endangered bird, but it is not the society’s logo.
Incorrect
Answer: (B)
Explanation:
- Statement 1 is Incorrect: The Bombay Natural History Society (BNHS) is a non-governmental organization (NGO). It is not a statutory body (which would be created by an Act of Parliament) nor is it a government department. It is an autonomous research organization that often partners with the government.
- Statement 2 is Correct: It was founded on September 15, 1883, by eight residents of Mumbai (six Brits and two Indians). Today, it is one of the premier institutions in the Indian subcontinent for research in natural history, conservation, and biodiversity.
- Statement 3 is Incorrect: The logo of the BNHS is the Great Hornbill (specifically the Great Pied Hornbill), inspired by William, a Great Hornbill that lived on the society’s premises from 1894 to 1920. The Great Indian Bustard is a different critically endangered bird, but it is not the society’s logo.
-
Question 5 of 15
5. Question
1 pointsWith reference to the Defence Research and Development Organisation (DRDO), consider the following statements:
- It is a statutory body established under the Defence Research and Development Act of 1958.
- The Secretary of the Department of Defence R&D serves as the ex-officio Chairman of the DRDO.
- The K. VijayRaghavan Committee was recently constituted to suggest reforms for overhauling the DRDO’s functioning and structure.
Which of the statements given above is/are correct?
Correct
Answer: (B)
Explanation:
- Statement 1 is Incorrect: The DRDO was formed in 1958 by the amalgamation of the Technical Development Establishment (TDEs) of the Indian Army and the Directorate of Technical Development & Production (DTDP) with the Defence Science Organisation (DSO). However, it is not a statutory body (created by an Act of Parliament). It functions as an attached office under the Ministry of Defence.
- Statement 2 is Correct: The administrative structure of the DRDO is headed by the Secretary, Department of Defence Research and Development, who also acts as the ex-officio Chairman of the DRDO. This ensures direct coordination between research activities and the Ministry of Defence.
- Statement 3 is Correct: In late 2023, the government appointed a high-powered committee led by K. VijayRaghavan (former Principal Scientific Adviser) to review the functioning of the DRDO. The goal was to make the organization more results-oriented and to encourage greater participation from the private sector and academia in defence R&D.
Incorrect
Answer: (B)
Explanation:
- Statement 1 is Incorrect: The DRDO was formed in 1958 by the amalgamation of the Technical Development Establishment (TDEs) of the Indian Army and the Directorate of Technical Development & Production (DTDP) with the Defence Science Organisation (DSO). However, it is not a statutory body (created by an Act of Parliament). It functions as an attached office under the Ministry of Defence.
- Statement 2 is Correct: The administrative structure of the DRDO is headed by the Secretary, Department of Defence Research and Development, who also acts as the ex-officio Chairman of the DRDO. This ensures direct coordination between research activities and the Ministry of Defence.
- Statement 3 is Correct: In late 2023, the government appointed a high-powered committee led by K. VijayRaghavan (former Principal Scientific Adviser) to review the functioning of the DRDO. The goal was to make the organization more results-oriented and to encourage greater participation from the private sector and academia in defence R&D.
-
Question 6 of 15
6. Question
1 pointsWith reference to the PM-Surya Ghar: Muft Bijli Yojana, consider the following statements:
- It provides up to 300 units of free electricity every month to one crore households.
- The scheme offers a subsidy covering up to 40% of the cost for solar plant installations.
- It is voluntary for beneficiaries to have a net-metering connection.
How many of the statements given above are correct?
Correct
Answer: (B)
Explanation:
- Statement 1 is Correct: Launched in early 2024, the scheme aims to provide up to 300 units of free electricity every month to one crore (10 million) households across India by encouraging the installation of rooftop solar systems.
- Statement 2 is Correct: The scheme provides a substantial subsidy to make solar adoption affordable. For a typical 3 kW system, the subsidy covers roughly 40% of the benchmark cost. Specifically, it offers ₹30,000 per kW for the first 2 kW and ₹18,000 for the additional kW, totaling ₹78,000 for a 3 kW system.
- Statement 3 is Incorrect: To avail of the benefits of free electricity, beneficiaries must have a net-metering connection. This allows the solar power generated to be fed back into the grid when not in use, and the 300 units free benefit is essentially realized through the offset of the export against the import from the DISCOM (Distribution Company).
Incorrect
Answer: (B)
Explanation:
- Statement 1 is Correct: Launched in early 2024, the scheme aims to provide up to 300 units of free electricity every month to one crore (10 million) households across India by encouraging the installation of rooftop solar systems.
- Statement 2 is Correct: The scheme provides a substantial subsidy to make solar adoption affordable. For a typical 3 kW system, the subsidy covers roughly 40% of the benchmark cost. Specifically, it offers ₹30,000 per kW for the first 2 kW and ₹18,000 for the additional kW, totaling ₹78,000 for a 3 kW system.
- Statement 3 is Incorrect: To avail of the benefits of free electricity, beneficiaries must have a net-metering connection. This allows the solar power generated to be fed back into the grid when not in use, and the 300 units free benefit is essentially realized through the offset of the export against the import from the DISCOM (Distribution Company).
-
Question 7 of 15
7. Question
1 pointsWith reference to the Green Credit Programme (GCP) under Mission LiFE, consider the following statements:
- It is an innovative market-based mechanism to incentivize voluntary environmental actions.
- In its initial phase, the programme focuses primarily on water conservation and afforestation.
- Green Credits generated can be traded on a dedicated domestic exchange platform.
How many of the statements given above are correct?
Correct
Answer: (C)
Explanation:
- Statement 1 is Correct: The Green Credit Programme (GCP) was launched as part of the Mission LiFE (Lifestyle for Environment) It is a market-based mechanism that incentivizes individuals, communities, and private sector industries to undertake voluntary environmental actions by issuing Green Credits.
- Statement 2 is Correct: While the programme has identified eight sectors (including waste management, air pollution reduction, and sustainable building), the initial focus and the first set of detailed rules released by the Ministry of Environment, Forest and Climate Change (MoEFCC) centered primarily on Water Conservation and Afforestation (Tree Plantation).
Statement 3 is Correct: Unlike traditional carbon credits, Green Credits are independent. The rules provide for the establishment of a dedicated domestic exchange platform where these credits can be traded, allowing entities to meet their environmental obligations or corporate social responsibility (CSR) goals.
Incorrect
Answer: (C)
Explanation:
- Statement 1 is Correct: The Green Credit Programme (GCP) was launched as part of the Mission LiFE (Lifestyle for Environment) It is a market-based mechanism that incentivizes individuals, communities, and private sector industries to undertake voluntary environmental actions by issuing Green Credits.
- Statement 2 is Correct: While the programme has identified eight sectors (including waste management, air pollution reduction, and sustainable building), the initial focus and the first set of detailed rules released by the Ministry of Environment, Forest and Climate Change (MoEFCC) centered primarily on Water Conservation and Afforestation (Tree Plantation).
Statement 3 is Correct: Unlike traditional carbon credits, Green Credits are independent. The rules provide for the establishment of a dedicated domestic exchange platform where these credits can be traded, allowing entities to meet their environmental obligations or corporate social responsibility (CSR) goals.
-
Question 8 of 15
8. Question
1 pointsThe term AI Tokens, frequently appearing in news regarding Large Language Models (LLMs), is best described as:
Correct
Answer: (B)
Explanation:
While humans perceive language as words and sentences, Large Language Models (LLMs) like Gemini or GPT do not read in the same way. They break down text into smaller, manageable chunks called Tokens.
- Granularity: A token can be a whole word (e.g., apple), a part of a word (e.g., ing in running), or even a single punctuation mark or character.
- Numerical Transformation: Each token is assigned a unique numerical ID. The model performs complex mathematical calculations on these numbers to predict which token should logically come next in a sequence.
- The Cost of Language: In the AI economy, Tokenomics refers to the cost of these units. Because different languages are tokenized differently (complex scripts like Devanagari often require more tokens per word than English), the efficiency of a Tokenizer directly affects the speed and cost of the AI.
Incorrect
Answer: (B)
Explanation:
While humans perceive language as words and sentences, Large Language Models (LLMs) like Gemini or GPT do not read in the same way. They break down text into smaller, manageable chunks called Tokens.
- Granularity: A token can be a whole word (e.g., apple), a part of a word (e.g., ing in running), or even a single punctuation mark or character.
- Numerical Transformation: Each token is assigned a unique numerical ID. The model performs complex mathematical calculations on these numbers to predict which token should logically come next in a sequence.
- The Cost of Language: In the AI economy, Tokenomics refers to the cost of these units. Because different languages are tokenized differently (complex scripts like Devanagari often require more tokens per word than English), the efficiency of a Tokenizer directly affects the speed and cost of the AI.
-
Question 9 of 15
9. Question
1 pointsConsider the following statements regarding the Western Tragopan:
- It is the state bird of Himachal Pradesh.
- It is locally referred to as Jujurana, meaning the King of Birds.
- The male of the species is known for raising two fleshy blue horns during the breeding season.
- It is currently categorized as ‘Critically Endangered’ on the IUCN Red List.
How many of the statements given above are correct?
Correct
Answer: (C)
Explanation:
- Statement 1 is Correct: The Western Tragopan (Tragopan melanocephalus) is officially the state bird of Himachal Pradesh. It replaced the Monal in this capacity in 2007 to draw more attention to its conservation.
- Statement 2 is Correct: In local folklore, it is called ‘Jujurana’, which translates to King of Birds. According to legend, the bird was created by the Great Creator using the most beautiful feathers of every other bird in the forest.
- Statement 3 is Correct: During the courtship display in the breeding season, the male Western Tragopan inflates two fleshy blue lappets (horns) on its head and expands a colorful throat patch to attract females. This unique feature gives it the name horned pheasant.
- Statement 4 is Incorrect: The Western Tragopan is categorized as Vulnerable on the IUCN Red List, not Critically Endangered. While its population is small and fragmented (estimated between 2,500 and 3,500 individuals), it does not yet meet the criteria for the Critically Endangered category.
Incorrect
Answer: (C)
Explanation:
- Statement 1 is Correct: The Western Tragopan (Tragopan melanocephalus) is officially the state bird of Himachal Pradesh. It replaced the Monal in this capacity in 2007 to draw more attention to its conservation.
- Statement 2 is Correct: In local folklore, it is called ‘Jujurana’, which translates to King of Birds. According to legend, the bird was created by the Great Creator using the most beautiful feathers of every other bird in the forest.
- Statement 3 is Correct: During the courtship display in the breeding season, the male Western Tragopan inflates two fleshy blue lappets (horns) on its head and expands a colorful throat patch to attract females. This unique feature gives it the name horned pheasant.
- Statement 4 is Incorrect: The Western Tragopan is categorized as Vulnerable on the IUCN Red List, not Critically Endangered. While its population is small and fragmented (estimated between 2,500 and 3,500 individuals), it does not yet meet the criteria for the Critically Endangered category.
-
Question 10 of 15
10. Question
1 pointsArrange the following events related to the Third Battle of Panipat in the correct chronological order:
- Maratha capture of Delhi.
- Restoration of Maratha dominance under Peshwa Madhavrao.
- Crossing of the Yamuna by Ahmad Shah Abdali to cut off Maratha supplies.
- Maratha victory at Kunjpura.
Select the correct answer using the code given below:
Correct
Answer: (A)
Explanation:
- Maratha capture of Delhi (August 1760): Under the leadership of Sadashivrao Bhau, the Maratha forces captured Delhi from the Afghan agents. This was a significant strategic victory that boosted Maratha morale before the final confrontation.
- Maratha victory at Kunjpura (October 1760): After taking Delhi, the Marathas moved north and stormed the Afghan garrison at Kunjpura (on the banks of the Yamuna). They slaughtered the Afghan forces there and seized a large stash of food and money.
- Crossing of the Yamuna by Ahmad Shah Abdali (October 1760): Infuriated by the loss at Kunjpura, Abdali took a massive risk and crossed the flooded Yamuna at Baghpat. This brilliant tactical move allowed him to get behind the Maratha army, effectively cutting off their supply lines and communications with Delhi.
- Restoration of Maratha dominance under Peshwa Madhavrao (1771): Following the devastating defeat on January 14, 1761, the Marathas retreated to the Deccan. However, under the young and capable Peshwa Madhavrao, they rebuilt their strength and returned to North India a decade later to re-establish their authority.
Incorrect
Answer: (A)
Explanation:
- Maratha capture of Delhi (August 1760): Under the leadership of Sadashivrao Bhau, the Maratha forces captured Delhi from the Afghan agents. This was a significant strategic victory that boosted Maratha morale before the final confrontation.
- Maratha victory at Kunjpura (October 1760): After taking Delhi, the Marathas moved north and stormed the Afghan garrison at Kunjpura (on the banks of the Yamuna). They slaughtered the Afghan forces there and seized a large stash of food and money.
- Crossing of the Yamuna by Ahmad Shah Abdali (October 1760): Infuriated by the loss at Kunjpura, Abdali took a massive risk and crossed the flooded Yamuna at Baghpat. This brilliant tactical move allowed him to get behind the Maratha army, effectively cutting off their supply lines and communications with Delhi.
- Restoration of Maratha dominance under Peshwa Madhavrao (1771): Following the devastating defeat on January 14, 1761, the Marathas retreated to the Deccan. However, under the young and capable Peshwa Madhavrao, they rebuilt their strength and returned to North India a decade later to re-establish their authority.
-
Question 11 of 15
11. Question
1 pointsEach of seven persons—A, B, C, D, E, F, and G—is sitting in a row facing North.
Statement 1: B sits third to the right of A. E sits second to the left of B. Only two persons sit between E and G.
Statement 2: F sits second to the right of G. C sits to the immediate left of B. D is an immediate neighbor of E.
Who sits at the extreme left end of the row?
Correct
Correct Answer: (c)
Detailed Solution:
From Statement 1: B is 3rd to the right of A (A _ _ B). E is 2nd to the left of B, which places E immediately to the right of A (A E _ B). Now, two people are between E and G. Case 1.1 (G is left of E): Following the relative string (G _ _ E), we get: G _ A E _ B. (6 positions). Case 1.2 (G is right of E): Following the relative string (E _ _ G), we get: A E _ B _ G. (6 positions). In both cases, we have only 6 positions defined. The 7th person could be at either the extreme left or extreme right. Thus, Statement 1 alone is insufficient.
From Statement 2: We have fragments: G _ F, C B, and D is next to E. Without the primary framework from Statement 1, we cannot determine the unique positions of all 7 people. Insufficient.
Combining Statements:
We apply the fragments from Statement 2 to the cases in Statement 1. In Case 1.1 (G _ A E _ B): F is 2nd to the right of G, filling the gap: G F A E _ B. C is immediate left of B: G F A E C B. D is a neighbor of E. The only available spot for D is to the right of B: G F A E C B D.
This uses all 7 people and places G at the extreme left. In Case 1.2 (A E _ B _ G): F is 2nd to the right of G. This would require an 8th position (A E _ B _ G _ F), which exceeds the 7-person limit. Conclusion: Both statements together provide a unique and valid arrangement.
Incorrect
Correct Answer: (c)
Detailed Solution:
From Statement 1: B is 3rd to the right of A (A _ _ B). E is 2nd to the left of B, which places E immediately to the right of A (A E _ B). Now, two people are between E and G. Case 1.1 (G is left of E): Following the relative string (G _ _ E), we get: G _ A E _ B. (6 positions). Case 1.2 (G is right of E): Following the relative string (E _ _ G), we get: A E _ B _ G. (6 positions). In both cases, we have only 6 positions defined. The 7th person could be at either the extreme left or extreme right. Thus, Statement 1 alone is insufficient.
From Statement 2: We have fragments: G _ F, C B, and D is next to E. Without the primary framework from Statement 1, we cannot determine the unique positions of all 7 people. Insufficient.
Combining Statements:
We apply the fragments from Statement 2 to the cases in Statement 1. In Case 1.1 (G _ A E _ B): F is 2nd to the right of G, filling the gap: G F A E _ B. C is immediate left of B: G F A E C B. D is a neighbor of E. The only available spot for D is to the right of B: G F A E C B D.
This uses all 7 people and places G at the extreme left. In Case 1.2 (A E _ B _ G): F is 2nd to the right of G. This would require an 8th position (A E _ B _ G _ F), which exceeds the 7-person limit. Conclusion: Both statements together provide a unique and valid arrangement.
-
Question 12 of 15
12. Question
1 pointsIs the integer X divisible by 36?
Statement 1: X is divisible by 9.
Statement 2: X/4 is an even integer.
Correct
Correct Answer: (c)
Detailed Solution:
To determine if X is divisible by 36, it must be divisible by 4 and 9 (as 4 and 9 are co-prime).
Statement 1: X is a multiple of 9. This does not confirm divisibility by 4. (e.g., if X = 18, No; if X = 36, Yes). Insufficient.
Statement 2: X/4 is even, so X/4 = 2k. This means X = 8k. Since X is a multiple of 8, it is necessarily divisible by 4. However, it does not confirm divisibility by 9. (e.g., if X = 8, No; if X = 72, Yes). Insufficient.
Combining Statements: X is divisible by 9 (from S1) and X is divisible by 8 (from S2). Since 8 and 9 are co-prime, X must be divisible by their LCM, which is 72. If X is a multiple of 72, it is fundamentally a multiple of 36 (since 72 = 36 * 2). Conclusion: We reach a definitive YES conclusion. Both statements together are sufficient.
Incorrect
Correct Answer: (c)
Detailed Solution:
To determine if X is divisible by 36, it must be divisible by 4 and 9 (as 4 and 9 are co-prime).
Statement 1: X is a multiple of 9. This does not confirm divisibility by 4. (e.g., if X = 18, No; if X = 36, Yes). Insufficient.
Statement 2: X/4 is even, so X/4 = 2k. This means X = 8k. Since X is a multiple of 8, it is necessarily divisible by 4. However, it does not confirm divisibility by 9. (e.g., if X = 8, No; if X = 72, Yes). Insufficient.
Combining Statements: X is divisible by 9 (from S1) and X is divisible by 8 (from S2). Since 8 and 9 are co-prime, X must be divisible by their LCM, which is 72. If X is a multiple of 72, it is fundamentally a multiple of 36 (since 72 = 36 * 2). Conclusion: We reach a definitive YES conclusion. Both statements together are sufficient.
-
Question 13 of 15
13. Question
1 pointsA person starts from point P and walks 10 meters North to reach point Q. From Q, he turns 135 degrees clockwise and walks 10 times the square root of 2 meters to reach point R. From point R, he turns 225 degrees anticlockwise and walks 10 meters to reach point S. What is the shortest distance between point P and point S?
Correct
Correct Answer: (d)
Detailed Solution:
- Let point P be the origin (0, 0). Walking 10m North to Q puts Q at (0, 10).
- At Q, the person is facing North. A 135-degree clockwise turn faces him toward the South-East (45 degrees below the positive x-axis).
- Displacement Q to R: The distance is 10 * sqrt(2) m. Since the direction is South-East (45 degrees): x-displacement = 10 * sqrt(2) * cos 45° = 10 m (East) y-displacement = 10 * sqrt(2) * sin 45° = 10 m (South) New coordinates R = (0 + 10, 10 – 10) = (10, 0).
- Turn at R: The person was facing South-East (135° CW from North). He turns 225° anticlockwise. New facing = 135° – 225° = -90°. A -90° bearing from North is exactly West.
- R to S: He walks 10m West from (10, 0). New coordinates S = (10 – 10, 0) = (0, 0).
- Shortest distance: Point S is exactly at Point P (0, 0). The distance is 0.
Incorrect
Correct Answer: (d)
Detailed Solution:
- Let point P be the origin (0, 0). Walking 10m North to Q puts Q at (0, 10).
- At Q, the person is facing North. A 135-degree clockwise turn faces him toward the South-East (45 degrees below the positive x-axis).
- Displacement Q to R: The distance is 10 * sqrt(2) m. Since the direction is South-East (45 degrees): x-displacement = 10 * sqrt(2) * cos 45° = 10 m (East) y-displacement = 10 * sqrt(2) * sin 45° = 10 m (South) New coordinates R = (0 + 10, 10 – 10) = (10, 0).
- Turn at R: The person was facing South-East (135° CW from North). He turns 225° anticlockwise. New facing = 135° – 225° = -90°. A -90° bearing from North is exactly West.
- R to S: He walks 10m West from (10, 0). New coordinates S = (10 – 10, 0) = (0, 0).
- Shortest distance: Point S is exactly at Point P (0, 0). The distance is 0.
-
Question 14 of 15
14. Question
1 pointsPoint A is 8m West of point B. Point C is 4m South of point B. Point D is 4m East of point C. Point E is 7m North of point D. Point F is 12m West of point E. What is the direction of point F with respect to point A?
Correct
Correct Answer: (a)
Detailed Solution:
Let B be (0, 0).
- A is 8m West of B: A = (-8, 0).
- C is 4m South of B: C = (0, -4).
- D is 4m East of C: D = (4, -4).
- E is 7m North of D: E = (4, 3).
- F is 12m West of E: F = (4 – 12, 3) = (-8, 3).
Final Position: A = (-8, 0) F = (-8, 3) Point F has the same x-coordinate as A but a higher y-coordinate. Thus, F is exactly 3 meters North of A.
Incorrect
Correct Answer: (a)
Detailed Solution:
Let B be (0, 0).
- A is 8m West of B: A = (-8, 0).
- C is 4m South of B: C = (0, -4).
- D is 4m East of C: D = (4, -4).
- E is 7m North of D: E = (4, 3).
- F is 12m West of E: F = (4 – 12, 3) = (-8, 3).
Final Position: A = (-8, 0) F = (-8, 3) Point F has the same x-coordinate as A but a higher y-coordinate. Thus, F is exactly 3 meters North of A.
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Question 15 of 15
15. Question
1 pointsPassage:
The quest for absolute certainty is often a roadblock to progress in both science and public policy. In science, the refusal to accept a theory because it is not ‘proven’ ignores the fact that science works on the principle of falsifiability and degrees of evidence, not absolute truth. In policy, waiting for 100% consensus on the impact of a regulation can lead to ‘paralysis by analysis,’ where the cost of inaction far exceeds the risks of acting on the best available data. A society that demands total certainty before addressing systemic risks is a society that will inevitably be overtaken by them.
Which of the following is the most logical and critical inference that can be made from the passage?
Correct
Correct Answer: (c)
Detailed Solution:
Option (a) is a correct scientific principle mentioned in the text, but it is too narrow to be the primary inference of the whole passage, which also discusses policy.
Option (b) is incorrect because the passage argues that seeking total consensus (certainty) is a roadblock that leads to systemic risk, rather than preventing it.
Option (d) is an overgeneralization. The text states the cost of inaction can exceed risks in certain contexts, but using always makes it logically unsound.
Option (c) is the most comprehensive and critical inference. It bridges both the scientific and policy examples to conclude that waiting for perfect information (certainty/consensus) is not necessary for progress or effective decision-making.
Incorrect
Correct Answer: (c)
Detailed Solution:
Option (a) is a correct scientific principle mentioned in the text, but it is too narrow to be the primary inference of the whole passage, which also discusses policy.
Option (b) is incorrect because the passage argues that seeking total consensus (certainty) is a roadblock that leads to systemic risk, rather than preventing it.
Option (d) is an overgeneralization. The text states the cost of inaction can exceed risks in certain contexts, but using always makes it logically unsound.
Option (c) is the most comprehensive and critical inference. It bridges both the scientific and policy examples to conclude that waiting for perfect information (certainty/consensus) is not necessary for progress or effective decision-making.
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