Solution (b) 

Explanation:  

• The Parliament can legislate on matters from the State List in India under certain  conditions. According to Article 249 of the Indian Constitution, the Parliament is  empowered to make laws on subjects listed in the State List if the Rajya Sabha (the  upper house of Parliament) passes a resolution to that effect with a two-thirds  majority present and voting. This provision allows the Parliament to legislate on state  subjects, typically for a limited period, in the national interest, and subject to certain  conditions. Hence option b is correct. 

Solution (c) 

Explanation: 

• The President and not the Governor can suspend or dissolve the state legislative  assembly during President’s rule. Under Article 356 of the Constitution of India, when  President’s rule is imposed in a state, the state legislature is suspended, and the  President appoints an Administrator to administer the state. Hence option a is  incorrect.

IASBABA’S DAY 37-60 DAYS PLAN 

• The governor does not recommend the appointment of the Advocate General of the  State. Rather he himself appoints the Advocate General of the State under Article 165  of the Indian Constitution on the recommendation of the State government. Hence  option b is incorrect. 
• The Governor of a state can reserve a bill passed by the state legislature for the assent  of the President under Article 200 of the Indian Constitution. If the Governor reserves  a bill for the assent of the President, the President may assent to the bill, withhold  assent to the bill, or return the bill to the state legislature for reconsideration. If the  President returns the bill to the state legislature, the legislature may pass the bill again  with or without amendments. If the legislature passes the bill again, the President  cannot withhold assent to the bill. Hence option c is correct. 

• The Governor of a state cannot remove the Chairperson of the State Public Service  Commission (SPSC). The Chairperson of the SPSC can only be removed by the President  of India. This is because the SPSC is an independent body that is responsible for  recruiting civil servants for the state government. The independence of the SPSC is  essential to ensure that the recruitment process is fair and impartial. Hence option d  is incorrect.

Solution (d) 

Explanation: 

• A feature that can be said to be constant throughout all polities characterised as  Federal, is that there is a division of power across various tiers (levels of government)  – such as Centre, Regional/ State, Local, etc. Federalism is a system of government in  which power is divided between a central authority and various constituent units of  the country. A federation has minimum two levels of government. All these levels of  governments enjoy their power somewhat independent of the other. Hence Option d  is correct.

Solution (a) 

Explanation: 

• The Indian Constitution has three lists – the Union List, the State List and the  Concurrent List, which demarcate the subjects on which the Union Legislature alone,  the State Legislature alone, and both Union and State Legislatures can make laws  respectively. 
• The Union List includes subjects like Defence, Foreign Affairs, Railways, and Post and  Telegraph. Hence Pair 1 is correctly matched. 
• The Concurrent List includes subjects like Education, Transfer of Property other than  Agricultural land, Forests, Trade Unions, Adulteration, Adoption and Succession. Both  Union and State Legislature alone can make laws on these matters. Hence Pair 2 is  incorrectly matched. 

• State List includes subjects like Agriculture, Police, Prison, Local Government, Public  Heath, Land, Liquor, Trade and Commerce, Livestock and Animal Husbandry, State  Public Services etc. Normally only the State Legislature can make laws on these  matters. Hence Pair 3 is incorrectly matched.

Solution (d) 

Explanation: 

• Article 74 states that there shall be a Council of Ministers with the Prime Minister at  the head to aid and advise the President who shall in the exercise of his functions, act  in accordance with such advice. By the Forty-Fourth Amendment Act,1978, it was  decided that the President can ask the Council of Ministers to reconsider its advice  but, has to accept the reconsidered advice of the Council of Ministers. Hence  statement 1 is incorrect. 
• If after an election, no leader has a clear majority in the Lok Sabha, then the President  has to use his own discretion to appoint a person as the Prime Minister (may not  necessarily be the leader with maximum seats) in judging who really may have the  support of the majority or who can actually form and run the government. Hence  statement 2 is incorrect. 

• The President can be removed from office by a process of impeachment for ‘violation  of the Constitution’. The impeachment charges can be initiated by either House of  Parliament. These charges should be signed by one-fourth members of the House (that  framed the charges), and a 14 days’ notice should be given to the President. However,  the Constitution does not define the meaning of the phrase ‘violation of the  Constitution’. Hence statement 3 is incorrect.

Solution (b) 

Explanation: 

• The following features describe Indian system as federal form of government: o Dual government 

o Written constitution 

o Division of powers between centre and states 

o Supremacy of the constitution 

o Rigid constitution 

o Independent Judiciary 

o Lok Sabha and Rajya Sabha 

• Appointment of CAG, All India Services, reservation of bill passed by state legislature  for the President and integrated judiciary are all features characterizing Unitary form  of government.

Solution (a) 

Explanation: 

• Under Advisory Jurisdiction of the Supreme Court, the Supreme Court of India  possesses advisory jurisdiction also. This means that the President of India can refer  any matter that is of public importance or that which involves interpretation of  Constitution to Supreme Court for advice. However, the Supreme Court is not bound  to give advice on such matters and the President is not bound to accept such an advice.  Hence, option a is the correct answer.

Solution (c) 

Explanation: 

• The Finance Commission (FC) is a constitutional body as it is established under the  Article 280. It provides for the scheme of distribution of net tax proceeds collected by  the Union government between the Centre and the States. Hence, statement 1 is not  correct. 
• The Finance Commission is constituted every five years and is a body that is exclusively  constituted by the Union Government. It consists of a chairman and four other  members who are appointed by the President. The Finance Commission  (Miscellaneous Provisions) Act, 1951, has specified the qualifications for chairman and  other members of the commission. Hence, statement 2 is correct. 

• The share of States from the divisible pool (vertical devolution) stands at 41% as per  the recommendation of the 15th Finance Commission. The Union government has  notified the constitution of the 16th Finance Commission under the chairmanship of  Dr. Arvind Panagariya for making its recommendations for the period of 2026-31.  Hence, statement 3 is correct.

Solution (d) 

Explanation: 

• Any question regarding disqualification arising out of defection is to be decided by the  presiding officer of the House. Originally, the act provided that the decision of the  presiding officer is final and cannot be questioned in any court. However, in Kihoto 

Hollohan case (1993), the Supreme Court declared this provision as unconstitutional  on the ground that it seeks to take away the jurisdiction of the Supreme Court and the  high courts. Hence, option d is the correct answer.

Solution (c) 

Explanation: 

• An independent member of a House (elected without being set up as a candidate by  any political party) becomes disqualified to remain a member of the House if he joins  any political party after such election. Hence, statement 1 is INCORRECT. 

• A nominated member of a House becomes disqualified for being a member of the  House if he joins any political party after the expiry of six months from the date on  which he takes his seat in the House. This means that he may join any political party  within six months of taking his seat in the House without inviting this disqualification.  Hence, statement 2 is INCORRECT.

Solution (b) 

Explanation: 

• According to the Article 244(2), the provisions of the Sixth Schedule shall apply to the  administration of the tribal areas in the States of Assam, Meghalaya, Tripura, and  Mizoram. The tribal areas in these four states are to be administered as Autonomous  Districts. And the Governor is empowered to organize and reorganize the autonomous  districts. Hence, option b is the correct answer.

Solution (d) 

Explanation: 

• Active Euthanasia is an intentional act to deliberately kill a terminally ill patient using  various means whereas passive euthanasia happens when medical treatment is  removed purposefully resulting in a person’s death to relieve him from unending pain.  Hence, statement 1 is not correct. 
• The Aruna Shanbaug case triggered debate of Euthanasia in India. Supreme court in  2011 recognised passive euthanasia in this case by which it had permitted withdrawal  of life-sustaining treatment from patients not in a position to make an informed  decision. Subsequent to this, in a landmark judgment (2018), the Supreme Court  recognised passive euthanasia and living will. Hence, statement 2 is not correct. 

• Passive Euthanasia is also known as mercy killing because it intends to end a life in  order to relieve pain and suffering, and the motive is good here (to ensure painless  death). Hence, statement 3 is not correct.

Solution (b) 

Explanation: 

• The 69th Constitutional Amendment Act of 1991 provided a special status to the Union  Territory of Delhi, and redesignated it the National Capital Territory of Delhi and  designated the administrator of Delhi as the lieutenant governor. Hence, statement 1  is correct. 
• The Act created a legislative assembly and a council of ministers for Delhi. The  elections are conducted by the election commission of India. The assembly can make  laws on all the matters of the State List and the Concurrent List except the three  matters of the State List, that is, public order, police, and land. Hence, statement 2 is  not correct. 

• The chief minister of Delhi is appointed by the President (not by the Lt. Governor). The  other ministers are appointed by the president on the advice of the chief minister. The  ministers hold office during the pleasure of the president. The council of ministers is  collectively responsible to the assembly. Hence, statement 3 is correct.

Solution (c) 

Explanation: 

• The Delimitation Commission is appointed by the President of India and works in  collaboration with the Election Commission of India (ECI). The Delimitation  Commission in India is a high-power body whose orders have the force of law and  cannot be called in question before any court. Hence, statement 1 is INCORRECT. 

• The Delimitation Commission Act was enacted in 1952. And till now, the Delimitation  Commissions have been set up four times — 1952, 1963, 1973 and 2002 under the  Acts of 1952, 1962, 1972 and 2002. Hence, statement 2 is INCORRECT.

Solution (b) 

Explanation: 

The President of India is not elected directly by the people but by members of the Electoral  College. The following members form part of the Electoral College: 

• The elected members of the legislative assemblies of the states 
• The elected members of both the Houses of Parliament 
• The elected members of the legislative assemblies of the Union Territories of Delhi and  Puducherry 

Hence, option b is correct.

Solution (a) 

Explanation: 

• The President of India is an integral part of the Parliament. Hence, Statement 1 is  correct. 
• The President of India is not a member of either House of Parliament and does not sit  in the Parliament to attend its meetings. 
• A bill passed by both the Houses of Parliament cannot become law without the  President’s assent. Hence, Statement 2 is correct. 
• The President summons and pro-rogues both House, dissolves the Lok Sabha,  addresses both Houses, and so on. 

Solution (c) 

Explanation: 

• Zonal Councils are statutory bodies as they are established by an act of the Parliament. Hence, Statement 1 is incorrect. 
• They are aimed at promoting cooperation between states, union territories, and the  centre. 
• The five zonal councils were set up under the States Re-organisation Act, of 1956. They  are: 

o The Northern Zonal Council 

o The Central Zonal Council  

o The Eastern Zonal Council 

o The Western Zonal Council  

o The Southern Zonal Council 

• Each zonal council consists of the home minister of the central government, chief  ministers of all states in that zone, two other ministers from each state in that zone,  and the administrator of each territory in the zone. Hence, Statement 2 is correct. 
• The Union Home Minister is the Chairman of each of these Councils. • The Chief Ministers of the States included in each zone act as Vice-Chairman of the  Zonal Council for that zone by rotation, each holding office for a period of one year at  a time. 
• They are only deliberative and advisory bodies that make recommendations regarding  economic and social planning. Hence, Statement 3 is correct. 

• They may advise the central government and the government of each state concerned  upon the action to be taken on any such matter.

Solution (b) 

Explanation: 

• The President can resign from his/her office by addressing the resignation letter to the  Vice-President of India. Hence, Statement 1 is correct. 
• He/She can also be removed from the office before completion of his term by the  process of impeachment by the Parliament. 
• The Constitution explicitly stipulates a tenure of five years for the President.  • Article 56 of the Indian Constitution states that the President shall hold office for a  term of live years from the date on which he/she enters upon his/her office. Hence,  Statement 2 is correct. 

• The President of India can hold office beyond his/her term of five years until his/her  successor assumes charge to avoid any ‘interregnum’. Hence, Statement 3 is incorrect. • The President is also eligible for re-election and may be elected for any number of  terms

Solution (b) 

Explanation: 

The Vice-President, like the president, is elected indirectly. The Vice-President of India is  elected by an electoral college consisting of all the members of both houses of Parliament.  This includes both Nominated members of Parliament and elected members of Parliament.  Hence, option b is correct.

Solution (a) 

Explanation: 

• The Governor is the chief executive head of the state. But, like the President, he is a  nominal executive head. He is appointed by the President by warrant under his hand  and seal. Hence Statement 1 is correct. 

• The Supreme Court in 1979 held that the office of governor of a state is not an  employment under the Central government. It is an independent constitutional office  and is not under the control of or subordinate to the Central government. Hence  Statement 2 is incorrect.

Solution (c) 

Context: 

• Nanopore technology represents humanity’s latest weapon in the ongoing battle  against diseases. In this context, it becomes important from the perspective of UPSC. 

Explanation: 

• Nanopore technology refers to nano-scale holes embedded in a thin membrane  structure to detect the pote ntial change when charged biological molecules smaller  than nanopores pass through the hole. It is a cutting-edge method for sequencing DNA  and RNA by detecting changes in electrical conductivity as molecules pass through a  nanopore. Hence, statement 1 is correct. 

• It has the potential to sense and analyse single-molecule amino acids, DNA, RNA, etc.  In contrast to other sequencing technologies, nanopore-based sequencing is cheaper,  very easy to use, does not require much computational and lab infrastructure, and only needs a small amount of DNA in a test sample. Hence, statement 2 is correct.

Solution (a) 

Context: 

• Researchers at the Centre for Peninsular Aquatic Genetic Resources, Kochi, of the  National Bureau for Fish Genetic Resources (NBFGR) claimed to have developed a  captive breeding protocol for black-collared yellow catfish. In this context, a question  can be asked by UPSC about it.

IASBABA’S DAY 37-60 DAYS PLAN 

Explanation: 

• Black-collared yellow catfish is endemic to the Chalakudy river in Kerala. It is  characterized by its greenish-brown mottled coloration, shorter barbels, and distinct  genetic traits, the species coexists with the endangered Horabagrus Nigricollaris.  Hence, statement 1 is correct. 

• It has been classified as endangered in the International Union for Conservation of  Nature (IUCN) Red List. The captive breeding programme of the fish began in 2020,  and the first-generation stock was successfully bred by the researchers. The  development of the breeding technique will help in the conservation of the species.  Hence, statement 2 is not correct.

Solution (c) 

Context: 

• The Telangana government has decided to rope in experts from the Indian Institute of  Technology, Hyderabad (IIT-H), to study the impact of the construction of the  Polavaram project on the Godavari River. In this context, a question can be asked by  UPSC about the project. 

Explanation: 

• Polavaram Project is a multi-purpose irrigation project built on the Godavari River in  West Godavari district and East Godavari district in Andhra Pradesh. It involves the  construction of a dam to address water scarcity, boost agricultural productivity, and  generate power. Designed to withstand massive floods that could occur once in 1000  years, the Polavaram Spillway is set to have the highest discharge capacity in the world.  It has been accorded national project status by the central government. Hence, option  c is the correct answer.

Solution (d) 

Context: 

• Union Minister for Road Transport and Highways recently announced the completion  of a 4-lane, 2.35 km Banihal Bypass on NH-44. In this context, a question about the  location of the pass can be asked by UPSC. 

Explanation: 

• Banihal Bypass is a four-lane, 2.35 km bypass to Banihal town in Jammu & Kashmir, a  section that was riddled with chronic traffic snarl-ups. It was built at a cost of Rs 224.44  crore. Strategically located on the Ramban–Banihal section of NH-44, the bypass  features 4 viaducts spanning 1,513 meters and 3 culverts, effectively addressing the  persistent bottleneck caused by roadside markets and shops. Hence, option d is the  correct answer.

Solution (a) 

Context: 

• ISRO recently said the cowpea seeds it had sent to space onboard the PSLV-C60 POEM 4 platform have germinated under microgravity conditions within four days of the  launch of the mission. In this context, a question can be asked about cowpea. 

Explanation: 

• Cowpea (Vigna unguiculata) is an annual plant within the pea family (Fabaceae). It is a  leguminous crop having long trailing vines producing seeds of black, white, or red  colour used widely in various food preparations. It is also known as a black-eyed pea,  southern pea, etc. Hence, statements 1 and 2 are correct. 
• It originated and was domesticated in Southern Africa and was later moved to East and  West Africa and Asia. The plant tolerates drought, performs well in a wide variety of  soils, and, being a legume replenishes low-fertility soils when the roots are left to  decay. Hence, statement 3 is not correct. 

• The world’s largest production and consumption of cowpea is in West Africa, which  accounts for more than 87% of world production and use. Nigeria, the largest producer  and consumer, accounts for 46% of production worldwide. Hence, statement 4 is not  correct.

Solution (a) 

Context: 

• Lok Sabha Speaker is set to inaugurate ‘Panchayat Se Parliament 2.0’ at the Central Hall  of Samvidhan Sadan. In this context, a question can be asked by UPSC about it. 

Explanation: 

• Panchayat Se Parliament 2.0 is organised by the National Commission for Women  (NCW), in collaboration with the Lok Sabha Secretariat and the Ministry of Tribal  Affairs. The programme is being organised in commemoration of the 150th birth  anniversary ofBhagwan Birsa Munda, the revered tribal leader and freedom fighter. It  will bring together 502 elected women representatives from Scheduled Tribes across  22 states and Union Territories. Its primary focus is to empower these women  representatives from Panchayati Raj institutions by enhancing their understanding of  constitutional provisions, parliamentary procedures, and governance. Hence, options  1, 2 and 3 are correct and option 4 is not correct.

Solution (b) 

Context: 

• As per a recent report ‘rabbit fever’ has witnessed more than 50 per cent rise in the  US in recent years. In this context, a question can be asked by UPSC about this disease.

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Explanation: 

• Rabbit Fever is also commonly known as Tularemia. It is a rare and sometimes deadly  infectious disease that is seen in children between the 5-9 years age group, older men,  and American Indians or Alaska Natives. Hence, statements 1 and 3 are correct. 

• It is caused by the bacterium Francisella tularensis and can infect animals and people.  Rabbits, hares and rodents are more likely to get the disease. The illness can be mild  or severe and high-grade fever is a common symptom in all kinds of illnesses. The signs  and symptoms of tularemia can depend on how the bacteria has entered the body.  Hence, statement 2 is not correct.

Solution (d) 

Context: 

• A “groundbreaking” atomic clock built at a top-secret UK lab will make military  operations more secure through experimental quantum technology over the years. In  this context, a question can be asked by UPSC about the atomic clock. 

Explanation: 

• Atomic Clock is a device that measures time using the vibrations of atoms. Atomic  clocks work by using a type of atom called a “cesium atom”. Cesium atoms are very  stable and have a very specific frequency at which their electrons vibrate. This  frequency is used as the basis for the atomic clock’s timekeeping. Hence, statement 1  is correct.

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• It specifically uses the oscillations of the electrons in atoms to keep time. To measure  time using cesium atoms, an atomic clock uses a device called a “microwave cavity”.  The microwave cavity is a chamber that is filled with cesium vapor. Hence, statement  2 is correct. 

• It is the most accurate time-keeping device available, with a margin of error of just a  few billionths of a second per day. It is far more precise than conventional clocks  because atomic oscillations have a much higher frequency and are much more stable.  Hence, statement 3 is correct.

Solution (b) 

Context: 

• Scientists are deploying two telescopes which are part of the Cubic Kilometre Neutrino  Telescope or KM3NeT to detect high-energy neutrinos, also known as ghost particles,  under the Mediterranean Sea. In this context, a question can be asked indirectly about  IceCube Neutrino Observatory. 

Explanation: 

• IceCube Neutrino Observatory is a device located at the Earth’s South Pole that detects  subatomic particles called neutrinos. Built and maintained by the IceCube  Collaboration, it consists of approximately 350 physicists from 58 institutions across  14 countries, led by the University of Wisconsin–Madison. Hence, statement 1 is not  correct.

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• IceCube collaborators address several big questions in physics, like the nature of dark  matter and the properties of the neutrino itself. Neutrinos are tiny subatomic particles,  often called ‘ghost particles’ because they barely interact with anything else. Neutrinos  are, however, the most common particle in the universe. Hence, statement 2 is  correct.

Solution (a) 

Context: 

• Amid rising tensions in India-Bangladesh relations, Dhaka is reportedly mulling to  purchase the Abdali Short Range Ballistic Missiles (SRBMs) aka the Hatf 2 missiles, from  Pakistan. In this context, a question can be asked by UPSC about the missile. 

Explanation: 

• Abdali (Hatf 2) is a short-range, road-mobile, solid propellant ballistic missile. It  measures 6.5 m in length, 0.56 m in diameter, and weighs 1,750 kg at launch. It can  range 180-200 km while carrying a variable 250-450 kg warhead. It is equipped with  an inertial guidance system and has a CEP of 150 m. Hence, statement 1 is correct. 

• Developed by Pakistan’s Space Research Commission (SUPARCO), the Abdali missile  system is designed for quick-reaction battlefield scenarios. Its relatively small warhead  limits its destructive capability, but its accuracy is sufficient to target military bases and  airfields or critical infrastructure such as power plants and industrial facilities. Hence,  statement 2 is not correct.

Solution (b)  

Explanation 

Option (a) is incorrect: The passage mentions that there are concerns about the threat to  privacy posed by new digital technologies as seen in the lines, “In recent years, there has been  growing concern about the threat to privacy posed by new technologies, such as big data and  artificial intelligence.” This does not mean that merely deploying such technologies violates  the right to privacy as mentioned in this option. If these technologies are misused, then one  can say that a violation has happened. However, the given option is not correct because mere  deployment is not a violation. Hence, this is not the most rational inference.  

Option (b) is correct: The given passage is about the threat to privacy from the misuse of  digital technologies deployed by corporations. When privacy is respected, an individual  expresses him/herself freely as seen in the lines “Corporations can use these technologies to 

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collect and analyse vast amounts of personal information, which can then be used to target  individuals with …. When individuals have their privacy respected, they are free to make  their own choices about their lives and to pursue their interests without fear of government  or corporations.”  

Option (c) is incorrect: Though government has been mentioned in the last line, the main  theme of the passage is how digital technologies can be misused by corporations to violate  the right to privacy. Hence, this option is not the most rational inference.  

Option (d) is incorrect: The given option mentions the growth of digital technologies and  states that individual privacy acts as a hindrance to it. However, the passage is about how  digital technologies can be misused by corporations to extract personal data. Also, the context  of the growth of digital economy and issues inherent in it have not been discussed in the  passage. Moreover, this option statement is rather pessimistic in tone, while the passage is  not. Hence, this option is not correct. 

Solution (b)  

Explanation 

Option (a) is incorrect: The statement is based on the lines “Renewable energy technologies,  such as solar and wind power, have become more efficient and cost-effective, reducing our  reliance on fossil fuels.” These lines mean that new technologies have reduced dependence  on fossil fuels as they are more cost-efficient. However, the statement mentions efficiency and  cost-effectiveness as the reasons for reliance on technologies for climate change mitigation,  which is not what is mentioned in the passage. So, this option is not the most rational  inference.  

Option (b) is correct: The passage is about how technology causes climate change acting as  an evil as visible in the lines, “Energy-intensive processes, transportation, and deforestation,  often enabled by technology, have contributed to rising carbon dioxide levels”, and now how  technology is a necessity to combat climate change as seen in the lines, “Conversely,  technology offers vital tools to combat climate change. Renewable energy technologies, such  as solar and wind power, have become more efficient and cost-effective, reducing our reliance  on fossil fuels. Innovations in energy storage, electric vehicles, and sustainable agriculture  offer pathways to a lower-carbon future” So, in the context of climate change, technology  can be considered as a necessary evil. Therefore, this option is the most rational inference. Option (c) is incorrect: The main theme of the passage is how technology aided climate  change, and how it will help in addressing the impact of climate change in the future. However,  the option is very narrow in context as it is based on the line, “Furthermore, technology aids  in climate monitoring and data collection, providing valuable insights into climate patterns  and trends.” It only mentions climate monitoring and data collection as helpful tools in  understanding climate patterns, which is not the central theme of the passage. So, this is not  the most rational inference.  

Option (d) is incorrect: The given option seems to be correct, but it is not, because it only  partially covers the main theme of the passage. It only mentions technologies for the future 

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(which have been mentioned just as examples to showcase the good side of technology) and  misses how technology contributes to climate change. The context of the lines, “The industrial  and technological advancements of the past century have been a significant driver of  greenhouse gas emissions. Energy-intensive processes, transportation, and deforestation,  often enabled by technology, have contributed to rising carbon dioxide levels” is missing in  the option. Hence, this option is not the most rational inference. 

Solution (b)  

Explanation 

Let present ages of Shikha and Rudra be x and y respectively.  

So, x + y = 62  

Or x = 62 – y  

6 years ago, the age of Shikha = x – 6  

6 years ago, the age of Rudra = y – 6  

6 years ago, the age of Shikha was 4 times that of Rudra.  

So, x – 6 = 4(y – 6)  

Or x – 6 = 4y – 24  

Or 4y – x = 18  

Or 4y – (62 – y) = 18 (since, x = 62 – y)  

Or 5y – 62 = 18  

Or 5y = 80  

Or y = 80/5 = 16  

Now, x = 62 – y = 62 – 16 = 46 

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Difference between the present ages of Shikha and Rudra = 46 – 16 = 30 years So, option (b) is  the right answer. 

Solution (d)  

Explanation 

As discussed above, the maximum marks that can be obtained in this condition is 130. For a  single wrong answer, marks will get reduced by 5.  

No student obtained negative marks. So, the marks obtained may be 0, 5, 10, …., 130; i.e. 27  possible marks.  

So, 27 students can appear for the exam and each of them may get a different score. Hence,  option (d) is the right answer. 

Solution (c)  

Explanation 

Let the distributed t-shirts be a-3d, a-d, a+d and a+3d  

Sum of the number of distributed t-shirts = a – 3d + a – d + a + d + a + 3d = 148  

4a = 148  

a = 37  

According to the question,  

(a – d) (a + d) = (a – 3d) (a + 3d) + 8 

a2 – d2 = a2 – 9d2 + 8  

8d2 = 8  

d2 = 1  

d = ± 1  

For d = 1,  

T-shirts distributed to the third orphanage = a + d = 37 + 1 = 38  For d = -1  

T-shirts distributed to the third orphanage = 37 – 1 = 36  

Hence, option (c) is the right answer.