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Question 1 of 15
1. Question
1 pointsConsider the following statements regarding the PM-Vidyalaxmi Scheme:
- The scheme offers collateral-free, guarantor-free loans to students for higher education in top-ranked domestic institutions.
- An interest subvention of 3% is provided for students with an annual family income of up to ₹8 lakh.
- The scheme is applicable only to students enrolled in Government Higher Education Institutions (HEIs).
How many of the above statements are correct?
Correct
Answer: (b)
Explanation
Statement I is correct:
The PM-Vidyalaxmi Scheme is designed to expand access to higher education by providing collateral-free and guarantor-free education loans. It specifically targets students who secure admission in meritorious and top-ranked institutions, typically identified through frameworks such as the National Institutional Ranking Framework (NIRF). The removal of collateral requirements aims to ensure that financial constraints do not hinder access to quality higher education.Statement II is correct:
The scheme incorporates an interest subvention component to enhance affordability. Under this provision, students belonging to families with an annual income of up to ₹8 lakh are eligible for a 3% interest subvention during the moratorium period (i.e., course duration plus a specified grace period). This feature reduces the effective interest burden and promotes equity in access to education financing.Statement III is incorrect:
The scope of the PM-Vidyalaxmi Scheme is not restricted solely to Government Higher Education Institutions (HEIs). Instead, it extends to both public and private institutions, provided they meet the prescribed quality benchmarks (such as NIRF rankings or equivalent standards). Therefore, limiting the scheme only to Government HEIs is factually incorrect.Incorrect
Answer: (b)
Explanation
Statement I is correct:
The PM-Vidyalaxmi Scheme is designed to expand access to higher education by providing collateral-free and guarantor-free education loans. It specifically targets students who secure admission in meritorious and top-ranked institutions, typically identified through frameworks such as the National Institutional Ranking Framework (NIRF). The removal of collateral requirements aims to ensure that financial constraints do not hinder access to quality higher education.Statement II is correct:
The scheme incorporates an interest subvention component to enhance affordability. Under this provision, students belonging to families with an annual income of up to ₹8 lakh are eligible for a 3% interest subvention during the moratorium period (i.e., course duration plus a specified grace period). This feature reduces the effective interest burden and promotes equity in access to education financing.Statement III is incorrect:
The scope of the PM-Vidyalaxmi Scheme is not restricted solely to Government Higher Education Institutions (HEIs). Instead, it extends to both public and private institutions, provided they meet the prescribed quality benchmarks (such as NIRF rankings or equivalent standards). Therefore, limiting the scheme only to Government HEIs is factually incorrect. -
Question 2 of 15
2. Question
1 pointsConsider the following statements regarding the Unified Pension Scheme (UPS):
- It guarantees a minimum pension of ₹10,000 per month on retirement after a minimum of 10 years of service.
- The government’s contribution to the pension fund has been increased to 18.5% of the basic salary.
- The scheme provides for inflation indexation through Dearness Relief (DR) based on the All India Consumer Price Index for Industrial Workers (AICPI-IW).
- In the event of the death of a pensioner, the family is entitled to 60% of the pension drawn by the employee.
How many of the above were parts of the Unified Pension Scheme?
Correct
Answer: (d)
Explanation
Statement I is correct:
The Unified Pension Scheme (UPS) provides for an assured minimum pension of ₹10,000 per month upon retirement, subject to a minimum qualifying service of 10 years. This provision ensures a baseline level of income security for employees, particularly those with shorter service spans.Statement II is correct:
Under UPS, the government’s contribution to the pension fund has been enhanced to 18.5% of basic pay plus dearness allowance (DA), compared to 14% under the earlier National Pension System (NPS) framework. This reflects a policy shift towards greater fiscal support for post-retirement security.Statement III is correct:
The scheme incorporates inflation indexation through Dearness Relief (DR), which is linked to the All India Consumer Price Index for Industrial Workers (AICPI-IW). This ensures that pension amounts are periodically adjusted to maintain real purchasing power and protect retirees from inflation.Statement IV is correct:
The UPS includes an Assured Family Pension provision. In the event of the death of a pensioner, the family is entitled to receive 60% of the pension that the employee was drawing immediately prior to death. This provision ensures continued financial support to dependents.Incorrect
Answer: (d)
Explanation
Statement I is correct:
The Unified Pension Scheme (UPS) provides for an assured minimum pension of ₹10,000 per month upon retirement, subject to a minimum qualifying service of 10 years. This provision ensures a baseline level of income security for employees, particularly those with shorter service spans.Statement II is correct:
Under UPS, the government’s contribution to the pension fund has been enhanced to 18.5% of basic pay plus dearness allowance (DA), compared to 14% under the earlier National Pension System (NPS) framework. This reflects a policy shift towards greater fiscal support for post-retirement security.Statement III is correct:
The scheme incorporates inflation indexation through Dearness Relief (DR), which is linked to the All India Consumer Price Index for Industrial Workers (AICPI-IW). This ensures that pension amounts are periodically adjusted to maintain real purchasing power and protect retirees from inflation.Statement IV is correct:
The UPS includes an Assured Family Pension provision. In the event of the death of a pensioner, the family is entitled to receive 60% of the pension that the employee was drawing immediately prior to death. This provision ensures continued financial support to dependents. -
Question 3 of 15
3. Question
1 pointsWhich of the following components are included under the “Pradhan Mantri Janjatiya Unnat Gram Abhiyan”?
- Provision of Pucca houses under PM-AWAS (Urban)
- Establishment of Tribal Multipurpose Marketing Centers (TMMC)
- Saturation of electricity and clean cooking fuel connections
- Digitization of land records in Scheduled Areas
- Setting up of Eklavya Model Residential Schools
Select the correct answer using the code given below:
Correct
Answer: (b)
Explanation
Statement I is incorrect.
The provision of pucca houses under PM-AWAS (Urban) is not a component of the Pradhan Mantri Janjatiya Unnat Gram Abhiyan. Housing support for tribal populations is typically linked to PMAY-G (Gramin) rather than the urban component, and even then, it is not a defining pillar of this specific programme.Statement II is correct.
The initiative includes strengthening tribal livelihoods and market linkages, including the establishment of Tribal Multipurpose Marketing Centres (TMMC) or similar infrastructure to support value addition and marketing of tribal products.Statement III is correct.
The programme follows a saturation approach in selected tribal villages, ensuring access to basic services such as electricity, clean cooking fuel (LPG), drinking water, and connectivity, in line with broader inclusive development goals.Statement IV is correct.
It also emphasizes governance and land-related reforms, including digitization of land records in Scheduled Areas, which is crucial for securing tribal land rights and improving administrative efficiency.Statement V is incorrect.
Eklavya Model Residential Schools (EMRS) are implemented under a separate central scheme for tribal education, and are not a core component of this Abhiyan.Incorrect
Answer: (b)
Explanation
Statement I is incorrect.
The provision of pucca houses under PM-AWAS (Urban) is not a component of the Pradhan Mantri Janjatiya Unnat Gram Abhiyan. Housing support for tribal populations is typically linked to PMAY-G (Gramin) rather than the urban component, and even then, it is not a defining pillar of this specific programme.Statement II is correct.
The initiative includes strengthening tribal livelihoods and market linkages, including the establishment of Tribal Multipurpose Marketing Centres (TMMC) or similar infrastructure to support value addition and marketing of tribal products.Statement III is correct.
The programme follows a saturation approach in selected tribal villages, ensuring access to basic services such as electricity, clean cooking fuel (LPG), drinking water, and connectivity, in line with broader inclusive development goals.Statement IV is correct.
It also emphasizes governance and land-related reforms, including digitization of land records in Scheduled Areas, which is crucial for securing tribal land rights and improving administrative efficiency.Statement V is incorrect.
Eklavya Model Residential Schools (EMRS) are implemented under a separate central scheme for tribal education, and are not a core component of this Abhiyan. -
Question 4 of 15
4. Question
1 pointsWith reference to the “Pradhan Mantri Annadata Aay Sanraksan Abhiyan” (PM-AASHA), consider the following statements:
- It integrates the Price Support Scheme (PSS) and the Price Deficiency Payment Scheme (PDPS).
- Under PDPS, the government directly purchases the physical stock of oilseeds from farmers.
- The Private Procurement & Stockist Scheme (PPPS) allows for the participation of private players in the procurement of oilseeds on a pilot basis.
Which of the statements given above are correct?
Correct
Answer: (c)
Explanation
Statement I is correct:
The Pradhan Mantri Annadata Aay Sanraksan Abhiyan (PM-AASHA) is an umbrella scheme aimed at ensuring remunerative prices to farmers, especially for pulses and oilseeds. It subsumes and integrates key price support mechanisms, notably the Price Support Scheme (PSS) and the Price Deficiency Payment Scheme (PDPS), thereby combining both procurement-based and deficiency payment approaches.Statement II is incorrect:
Under the Price Deficiency Payment Scheme (PDPS), the government does not procure physical stock. Instead, it compensates farmers by paying the difference between the Minimum Support Price (MSP) and the actual market price when the latter falls below MSP.Statement III is correct:
The Private Procurement & Stockist Scheme (PPPS) is a component of PM-AASHA that allows participation of private sector players in procurement operations, particularly for oilseeds. It is implemented on a pilot basis to augment procurement capacity and improve market efficiency.Incorrect
Answer: (c)
Explanation
Statement I is correct:
The Pradhan Mantri Annadata Aay Sanraksan Abhiyan (PM-AASHA) is an umbrella scheme aimed at ensuring remunerative prices to farmers, especially for pulses and oilseeds. It subsumes and integrates key price support mechanisms, notably the Price Support Scheme (PSS) and the Price Deficiency Payment Scheme (PDPS), thereby combining both procurement-based and deficiency payment approaches.Statement II is incorrect:
Under the Price Deficiency Payment Scheme (PDPS), the government does not procure physical stock. Instead, it compensates farmers by paying the difference between the Minimum Support Price (MSP) and the actual market price when the latter falls below MSP.Statement III is correct:
The Private Procurement & Stockist Scheme (PPPS) is a component of PM-AASHA that allows participation of private sector players in procurement operations, particularly for oilseeds. It is implemented on a pilot basis to augment procurement capacity and improve market efficiency. -
Question 5 of 15
5. Question
1 pointsIn the context of the “NAMASTE” Scheme (National Action for Mechanized Sanitation Ecosystem), consider the following objectives:
- Elimination of hazardous cleaning of sewers and septic tanks.
- Providing alternative livelihoods to sanitation workers.
- Direct financial assistance for the construction of individual household latrines.
- Digital profiling of all sanitation workers across Urban Local Bodies.
How many of the above usually form the core pillars of the NAMASTE scheme?
Correct
Answer: (c)
Explanation
Statement I is correct:
The NAMASTE Scheme aims at the elimination of hazardous manual cleaning of sewers and septic tanks by promoting mechanization and safe sanitation practices. This is its core objective, aligned with the broader goal of ending manual scavenging.Statement II is correct:
A key pillar of the scheme is to rehabilitate sanitation workers by providing skill development, capacity building, and alternative livelihood opportunities. This ensures a transition from unsafe occupations to dignified and sustainable employment.Statement III is incorrect:
The provision of direct financial assistance for the construction of individual household latrines is associated with schemes like the Swachh Bharat Mission (SBM), not NAMASTE. NAMASTE focuses on worker safety and mechanization, not toilet construction.Statement IV is correct:
The scheme includes digital profiling and database creation of sanitation workers across Urban Local Bodies (ULBs). This helps in targeted interventions, monitoring, and delivery of benefits, forming an important administrative pillar.Incorrect
Answer: (c)
Explanation
Statement I is correct:
The NAMASTE Scheme aims at the elimination of hazardous manual cleaning of sewers and septic tanks by promoting mechanization and safe sanitation practices. This is its core objective, aligned with the broader goal of ending manual scavenging.Statement II is correct:
A key pillar of the scheme is to rehabilitate sanitation workers by providing skill development, capacity building, and alternative livelihood opportunities. This ensures a transition from unsafe occupations to dignified and sustainable employment.Statement III is incorrect:
The provision of direct financial assistance for the construction of individual household latrines is associated with schemes like the Swachh Bharat Mission (SBM), not NAMASTE. NAMASTE focuses on worker safety and mechanization, not toilet construction.Statement IV is correct:
The scheme includes digital profiling and database creation of sanitation workers across Urban Local Bodies (ULBs). This helps in targeted interventions, monitoring, and delivery of benefits, forming an important administrative pillar. -
Question 6 of 15
6. Question
1 pointsConsider the following statements:
Statement I: The PM-DevINE (Prime Minister’s Development Initiative for North East Region) is a 100% Central Sector Scheme.
Statement II: It aims to fund infrastructure and social development projects based on the felt needs of the North-Eastern States rather than being a substitute for existing central or state schemes.
Statement III: The North Eastern Council (NEC) is the sole implementing agency for all projects sanctioned under this scheme.
Which one of the following is correct in respect of the above statements?
Correct
Answer: (c)
Explanation
Statement I is correct:
The PM-DevINE (Prime Minister’s Development Initiative for North East Region) is designed as a 100% Central Sector Scheme, meaning it is fully funded by the Central Government. This reflects the strategic importance of the North-Eastern Region and the need for focused, centrally supported interventions.Statement II is correct:
The scheme aims to support infrastructure and social development projects based on the felt needs of the North-Eastern States, rather than duplicating or substituting existing Central or State schemes. This gap-filling and need-based approach justifies why the Centre directly funds the scheme, thereby explaining Statement I.Statement III is incorrect:
The North Eastern Council (NEC) is not the sole implementing agency under PM-DevINE. While NEC plays an important role in coordination and project oversight, multiple implementing agencies (including Central Ministries, State Governments, and other bodies) may execute projects under the scheme. Hence, the statement is factually incorrect.Incorrect
Answer: (c)
Explanation
Statement I is correct:
The PM-DevINE (Prime Minister’s Development Initiative for North East Region) is designed as a 100% Central Sector Scheme, meaning it is fully funded by the Central Government. This reflects the strategic importance of the North-Eastern Region and the need for focused, centrally supported interventions.Statement II is correct:
The scheme aims to support infrastructure and social development projects based on the felt needs of the North-Eastern States, rather than duplicating or substituting existing Central or State schemes. This gap-filling and need-based approach justifies why the Centre directly funds the scheme, thereby explaining Statement I.Statement III is incorrect:
The North Eastern Council (NEC) is not the sole implementing agency under PM-DevINE. While NEC plays an important role in coordination and project oversight, multiple implementing agencies (including Central Ministries, State Governments, and other bodies) may execute projects under the scheme. Hence, the statement is factually incorrect. -
Question 7 of 15
7. Question
1 pointsConsider the following statements:
Statement I: The ‘Vibrant Villages Programme’ (VVP) aims to improve the quality of life of people living in identified border villages, primarily on the northern border.
Statement II: The scheme provides for the creation of livelihoods through the promotion of agriculture, horticulture, and tourism, thereby checking out-migration.
Which one of the following is correct in respect of the above statements?
Correct
Answer: (a)
Explanation
Statement I is correct:
The Vibrant Villages Programme (VVP) is a centrally sponsored initiative aimed at the comprehensive development of select villages along India’s northern land borders (particularly in states/UTs like Arunachal Pradesh, Sikkim, Uttarakhand, Himachal Pradesh, and Ladakh). Its core objective is to improve the quality of life of residents and ensure that border areas remain vibrant and strategically populated.Statement II is correct:
The programme emphasizes sustainable livelihood generation through the promotion of agriculture, horticulture, tourism, and allied activities. By strengthening economic opportunities locally, it seeks to reduce out-migration from these remote border villages.Incorrect
Answer: (a)
Explanation
Statement I is correct:
The Vibrant Villages Programme (VVP) is a centrally sponsored initiative aimed at the comprehensive development of select villages along India’s northern land borders (particularly in states/UTs like Arunachal Pradesh, Sikkim, Uttarakhand, Himachal Pradesh, and Ladakh). Its core objective is to improve the quality of life of residents and ensure that border areas remain vibrant and strategically populated.Statement II is correct:
The programme emphasizes sustainable livelihood generation through the promotion of agriculture, horticulture, tourism, and allied activities. By strengthening economic opportunities locally, it seeks to reduce out-migration from these remote border villages. -
Question 8 of 15
8. Question
1 pointsConsider the following pairs of Government Portals/Apps and their Functions:
Portal/App Function I. e-SAKSHI Tracking of MPLADS project fund flow II. SUGAM Licensing and regulation of medical devices III. UDGAM Searching for unclaimed deposits across banks IV. U-WIN Digital tracking of the Universal Immunization Program V. e-SARAS Marketing of products made by SHG women How many of the above pairs are incorrectly matched?
Correct
Answer: (d)
Explanation
Pair I is correct:
e-SAKSHI is a digital platform associated with the MPLADS (Members of Parliament Local Area Development Scheme). It enables tracking of project implementation and fund flow, enhancing transparency and monitoring.Pair II is correct:
SUGAM portal, operated by the Central Drugs Standard Control Organization (CDSCO), facilitates online licensing, registration, and regulation of drugs and medical devices. It is a key regulatory interface.Pair III is correct:
UDGAM (Unclaimed Deposits – Gateway to Access Information) is an initiative of the Reserve Bank of India (RBI) that allows users to search for unclaimed deposits across multiple banks through a centralized portal.Pair IV is correct:
U-WIN is a digital platform developed by the Ministry of Health and Family Welfare for tracking vaccination of pregnant women and children under the Universal Immunization Programme (UIP). It digitizes immunization records nationwide.Pair V is correct:
e-SARAS is an e-commerce platform launched under Deendayal Antyodaya Yojana – National Rural Livelihoods Mission (DAY-NRLM) for marketing products made by Self-Help Group (SHG) women, promoting rural entrepreneurship.Incorrect
Answer: (d)
Explanation
Pair I is correct:
e-SAKSHI is a digital platform associated with the MPLADS (Members of Parliament Local Area Development Scheme). It enables tracking of project implementation and fund flow, enhancing transparency and monitoring.Pair II is correct:
SUGAM portal, operated by the Central Drugs Standard Control Organization (CDSCO), facilitates online licensing, registration, and regulation of drugs and medical devices. It is a key regulatory interface.Pair III is correct:
UDGAM (Unclaimed Deposits – Gateway to Access Information) is an initiative of the Reserve Bank of India (RBI) that allows users to search for unclaimed deposits across multiple banks through a centralized portal.Pair IV is correct:
U-WIN is a digital platform developed by the Ministry of Health and Family Welfare for tracking vaccination of pregnant women and children under the Universal Immunization Programme (UIP). It digitizes immunization records nationwide.Pair V is correct:
e-SARAS is an e-commerce platform launched under Deendayal Antyodaya Yojana – National Rural Livelihoods Mission (DAY-NRLM) for marketing products made by Self-Help Group (SHG) women, promoting rural entrepreneurship. -
Question 9 of 15
9. Question
1 pointsConsider the following statements about the “Mission Shakti” of the Ministry of Women and Child Development:
- It is an umbrella scheme for safety, security, and empowerment of women consisting of two sub-schemes: ‘Sambal’ and ‘Samarthya’.
- ‘Sambal’ focuses on the safety and security of women, while ‘Samarthya’ focuses on the empowerment of women through schemes like Pradhan Mantri Matru Vandana Yojana (PMMVY).
Which of the statements given above is/are correct?
Correct
Answer: (c)
Explanation
Statement I is correct.
Mission Shakti is an umbrella scheme of the Ministry of Women and Child Development aimed at ensuring safety, security, and empowerment of women. It is structured into two sub-schemes, namely ‘Sambal’ and ‘Samarthya’, to provide an integrated framework for addressing different dimensions of women’s welfare.Statement II is correct.
The division of functions within the scheme is clearly demarcated. ‘Sambal’ focuses on safety and security through interventions such as One Stop Centres and Women Helplines. ‘Samarthya’, on the other hand, focuses on empowerment and welfare measures, including schemes like Pradhan Mantri Matru Vandana Yojana (PMMVY). This classification accurately reflects the design of Mission Shakti.Incorrect
Answer: (c)
Explanation
Statement I is correct.
Mission Shakti is an umbrella scheme of the Ministry of Women and Child Development aimed at ensuring safety, security, and empowerment of women. It is structured into two sub-schemes, namely ‘Sambal’ and ‘Samarthya’, to provide an integrated framework for addressing different dimensions of women’s welfare.Statement II is correct.
The division of functions within the scheme is clearly demarcated. ‘Sambal’ focuses on safety and security through interventions such as One Stop Centres and Women Helplines. ‘Samarthya’, on the other hand, focuses on empowerment and welfare measures, including schemes like Pradhan Mantri Matru Vandana Yojana (PMMVY). This classification accurately reflects the design of Mission Shakti. -
Question 10 of 15
10. Question
1 pointsConsider the following statements in respect of the “Deep Ocean Mission” (DOM):
- It is a multi-ministerial mission led by the Ministry of Earth Sciences (MoES) to explore the deep ocean for resources.
- One of the components involves the development of a manned submersible to carry three people to a depth of 6,000 meters.
- The mission includes a component for the desalination of seawater using offshore wind energy.
- India has been allocated a site in the Central Indian Ocean Basin by the International Seabed Authority (ISA) for the exploration of polymetallic nodules.
Which of the statements given above are correct?
Correct
Answer: (a)
Explanation
Statement I is correct.
The Deep Ocean Mission (DOM) is a flagship initiative led by the Ministry of Earth Sciences (MoES). It adopts a multi-ministerial approach, involving coordination with various scientific and technical agencies, with the objective of exploring deep ocean resources, developing technologies, and strengthening ocean research capabilities.Statement II is correct.
A key component of the mission is the development of a manned submersible (MATSYA-6000) designed to carry three persons to a depth of 6,000 meters. This capability is crucial for deep-sea exploration, resource assessment, and scientific research.Statement III is incorrect.
The mission does include components related to ocean energy and desalination, but it does not specifically involve desalination using offshore wind energy. The focus is more on low-temperature thermal desalination (LTTD) and ocean-based renewable energy systems, not wind-powered desalination. Hence, the statement is inaccurate.Statement IV is correct.
India has been allocated an exploration area in the Central Indian Ocean Basin (CIOB) by the International Seabed Authority (ISA) for the exploration of polymetallic nodules, which are rich in minerals such as nickel, cobalt, copper, and manganese. This forms a significant basis for India’s deep-sea mining ambitions under DOM.Incorrect
Answer: (a)
Explanation
Statement I is correct.
The Deep Ocean Mission (DOM) is a flagship initiative led by the Ministry of Earth Sciences (MoES). It adopts a multi-ministerial approach, involving coordination with various scientific and technical agencies, with the objective of exploring deep ocean resources, developing technologies, and strengthening ocean research capabilities.Statement II is correct.
A key component of the mission is the development of a manned submersible (MATSYA-6000) designed to carry three persons to a depth of 6,000 meters. This capability is crucial for deep-sea exploration, resource assessment, and scientific research.Statement III is incorrect.
The mission does include components related to ocean energy and desalination, but it does not specifically involve desalination using offshore wind energy. The focus is more on low-temperature thermal desalination (LTTD) and ocean-based renewable energy systems, not wind-powered desalination. Hence, the statement is inaccurate.Statement IV is correct.
India has been allocated an exploration area in the Central Indian Ocean Basin (CIOB) by the International Seabed Authority (ISA) for the exploration of polymetallic nodules, which are rich in minerals such as nickel, cobalt, copper, and manganese. This forms a significant basis for India’s deep-sea mining ambitions under DOM. -
Question 11 of 15
11. Question
1 pointsThree runners A, B, and C run around a circular track of 12 km. Their speeds are 3 kmph, 4 kmph, and 6 kmph respectively. If they start together from the same point, after how many hours will they meet again at the starting point?
Correct
Answer: b
Detailed Solution:
- Calculate the time taken by each runner for one lap:
- Time for A = 12 / 3 = 4 hours
- Time for B = 12 / 4 = 3 hours
- Time for C = 12 / 6 = 2 hours
- The runners meet at the starting point at the Least Common Multiple (LCM) of their lap times.
- LCM of (4, 3, 2) = 12.
- They meet again after 12 hours.
Incorrect
Answer: b
Detailed Solution:
- Calculate the time taken by each runner for one lap:
- Time for A = 12 / 3 = 4 hours
- Time for B = 12 / 4 = 3 hours
- Time for C = 12 / 6 = 2 hours
- The runners meet at the starting point at the Least Common Multiple (LCM) of their lap times.
- LCM of (4, 3, 2) = 12.
- They meet again after 12 hours.
-
Question 12 of 15
12. Question
1 pointsConsider two numbers X and Y. Their HCF is 15 and their product is 2700.
Statement-I: The LCM of X and Y is 180.
Statement-II: There are exactly two such pairs of numbers (X, Y) possible.
Which of the following is correct?
Correct
Answer: c
Detailed Solution:
Using the relation:
Product of two numbers = HCF × LCM2700 = 15 × LCM
LCM = 2700 ÷ 15 = 180Hence, Statement-I is correct.
Let the numbers be X = 15a and Y = 15b, where a and b are co-prime so that the HCF remains 15.
Then:
(15a)(15b) = 2700
225ab = 2700
ab = 12The co-prime factor pairs of 12 are (1, 12) and (3, 4).
This gives the numbers:
(15, 180) and (45, 60)These are the only two distinct (unordered) pairs satisfying the conditions.
Hence, Statement-II is also correct.
Incorrect
Answer: c
Detailed Solution:
Using the relation:
Product of two numbers = HCF × LCM2700 = 15 × LCM
LCM = 2700 ÷ 15 = 180Hence, Statement-I is correct.
Let the numbers be X = 15a and Y = 15b, where a and b are co-prime so that the HCF remains 15.
Then:
(15a)(15b) = 2700
225ab = 2700
ab = 12The co-prime factor pairs of 12 are (1, 12) and (3, 4).
This gives the numbers:
(15, 180) and (45, 60)These are the only two distinct (unordered) pairs satisfying the conditions.
Hence, Statement-II is also correct.
-
Question 13 of 15
13. Question
1 pointsA gardener has a certain number of plants. When he plants them in rows of 6, 8, 10, or 12, he is left with 5 plants every time. But when he plants them in rows of 13, nothing is left. What is the total number of plants?
Correct
Answer: a Detailed Solution:
- Find the LCM of 6, 8, 10, and 12: LCM = 120.
- Set the general form of the number: 120k + 5.
- Test values of k to satisfy divisibility by 13:
- If k = 1: 125 (No)
- If k = 7: 120(7) + 5 = 840 + 5 = 845.
- Check 845 / 13 = 65 (Rem = 0).
- Total plants = 845.
Incorrect
Answer: a Detailed Solution:
- Find the LCM of 6, 8, 10, and 12: LCM = 120.
- Set the general form of the number: 120k + 5.
- Test values of k to satisfy divisibility by 13:
- If k = 1: 125 (No)
- If k = 7: 120(7) + 5 = 840 + 5 = 845.
- Check 845 / 13 = 65 (Rem = 0).
- Total plants = 845.
-
Question 14 of 15
14. Question
1 pointsIf the LCM of two numbers is 48, which of the following cannot be their HCF?
Correct
Answer: d
Detailed Solution:
- Apply the rule: The HCF must always be a factor of the LCM.
- Check divisibility:
- 48 / 8 = 6 (Integer)
- 48 / 12 = 4 (Integer)
- 48 / 16 = 3 (Integer)
- 48 / 18 = 2.66 (Not an integer).
- Result: 18 cannot be the HCF.
Incorrect
Answer: d
Detailed Solution:
- Apply the rule: The HCF must always be a factor of the LCM.
- Check divisibility:
- 48 / 8 = 6 (Integer)
- 48 / 12 = 4 (Integer)
- 48 / 16 = 3 (Integer)
- 48 / 18 = 2.66 (Not an integer).
- Result: 18 cannot be the HCF.
-
Question 15 of 15
15. Question
1 pointsPassage:
“The shift towards ‘Electric Vehicles’ (EVs) is often touted as the panacea for urban air pollution. However, this transition is fraught with a ‘hidden’ carbon footprint. Most of the electricity used to charge these vehicles in developing nations still comes from coal-fired power plants. Furthermore, the mining of lithium and cobalt—essential for EV batteries—is an ecologically invasive process that often displaces indigenous communities and consumes vast quantities of water in arid regions. True sustainability requires not just a change in the fuel source, but a fundamental reduction in the dependency on private transport.”
Which of the following is the most critical and practical message conveyed by the passage?
Correct
Answer: c
Detailed Solution:
- Analyze the central argument: The author identifies problems with EV energy sources (coal) and raw material extraction (lithium/cobalt).
- Identify the concluding solution: The text explicitly states that a change in “fuel source” is not enough and calls for a “fundamental reduction” in private transport.
- Evaluate Option (c): This directly reflects the idea that swapping one technology for another (substitution) without changing consumption patterns (dependency) is insufficient.
- Discard other options: (a) is too broad, (b) is an extreme policy not in the text, and (d) introduces a political concept (nationalization) not discussed.
Incorrect
Answer: c
Detailed Solution:
- Analyze the central argument: The author identifies problems with EV energy sources (coal) and raw material extraction (lithium/cobalt).
- Identify the concluding solution: The text explicitly states that a change in “fuel source” is not enough and calls for a “fundamental reduction” in private transport.
- Evaluate Option (c): This directly reflects the idea that swapping one technology for another (substitution) without changing consumption patterns (dependency) is insufficient.
- Discard other options: (a) is too broad, (b) is an extreme policy not in the text, and (d) introduces a political concept (nationalization) not discussed.
Click Here to Download the Insta Test PDF – Question Paper Click Here to Download the Insta Test PDF – Synopsis
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