• Solution: (c)

Statement Analysis: 

• Both species benefit from mutualism in their interactions with each other. For instance, plants need the help of animals for pollinating their flowers and dispersing their seeds. In return for the service provided by animals, plants offer rewards or fees in the form of pollen and nectar for pollinators and juicy and nutritious fruits for seed dispersers. Hence, Statement 1 is correct.

• In Amensalism on the other hand one species is harmed whereas the other is unaffected. Hence, statement 2 is incorrect.

• The interaction where one species is benefitted and the other is neither benefited or harmed is called commensalism. For instance, an orchid growing as an epiphyte on a mango branch, and barnacles growing on the back of a whale benefit while neither the mango tree nor the whale derives any apparent benefit. Hence, statement 3 is correct.

Parasitism is a kind of relationship between two species, where the parasite gains benefits that come at the expense of the host member. In parasitism, only one species benefits, that is, parasites and the interaction is detrimental to the other species, that is, the host. Hence, statement 4 is correct.

Solution: (c)

Statement Analysis: 

Statement 1 is incorrect: More than 70 per cent of all the species recorded on the earth are animals, while plants (including algae, fungi, bryophytes, gymnosperms and angiosperms) comprise not more than 22 per cent of the total. Among animals, insects are the most species-rich taxonomic group, making up more than 70 per cent of the total.

Statement 2 is correct: The number of fungi species in the world is  more  than  the combined total of the species of fishes, amphibians, reptiles and mammals.

Statement 3 is incorrect: The diversity at the species level of the Western Ghats is more than the Eastern Ghats.

Solution: (a)

Statement Analysis: 

Loss of biodiversity refers to the disappearance or decline of the biological diversity on the planet. It is accelerated by a variety of factors. However, the accelerated rates of species extinctions that the world is facing nowadays are largely due to human activities. Four major  causes have  been  identified  for  the same, which are referred to as The Evil Quartet. It includes – Habitat loss and fragmentation, over-exploitation, invasive alien species and co-extinctions. Hence, option (a) is correct.

Invasive alien species are usually animals, plants or organisms which are introduced to a place outside of their native range.

Species richness is the number of species within a defined region.

Ecosystem diversity is the study of different ecosystems like deserts, lakes, ponds, temperate, tropical etc in a certain location and its effects on environment and humans.

Solution: (b)

Statement Analysis: 

• Statement 1 is incorrect: Primary production is defined as the amount of biomass or organic matter produced per unit area over a time period by plants during photosynthesis.
• The rate of biomass production is called productivity.
• Gross primary productivity of an ecosystem is the rate of production of organic matter during photosynthesis.
• Statement 2 is correct: A considerable amount of Gross primary productivity (GPP) is utilised by plants in respiration. Gross primary productivity minus respiration losses (R), is the net primary productivity (NPP).
• GPP – R = NPP GPP = NPP + R

Net primary productivity is the available biomass for the consumption of heterotrophs.

Solution: (c)

Statement Analysis: 

Statement 2 and 4 are correct: Ex situ Conservation– In this approach, threatened animals and plants are taken out from their natural habitat and placed in special settings where they can be protected and given special care. Zoological parks, botanical gardens and wildlife safari parks serve this purpose. There are many animals that have become extinct in the wild but continue to be maintained in zoological parks.

Solution: (b)

Statement Analysis: 

• Tundra ecosystem is the ecosystem that is devoid of trees and covered with snow for most of the year. They are found in cold climates and in regions with limited or scarce rainfall.
• Statement 1 is incorrect: There are two types of tundra: arctic and alpine. Arctic tundra occurs below the polar ice cap. It occupies the northern fringe of Canada, Alaska, European Russia, Siberia and the island group of the Arctic Ocean. Alpine tundra occurs at high mountains at all latitudes.
• Statement 2 is correct: Typical vegetation of arctic tundra is cotton grass, sedges, dwarf heath, willows, birches and lichens. Animals of tundra are reindeer, musk ox, arctic hare, caribou, lemmings and squirrels.

Statement 3 is correct: Organisms in Tundra have evolved to withstand extreme environments. Mammals of the tundra region have large body size, small tail and small ear to avoid the loss of heat from the surface.

Solution: (a)

Statement Analysis: 

• A food chain represents the sequential transfer of matter and energy in the form of food from one organism to another. It consistently begins with producers and concludes with the apex predator. Two primary types of food chains exist: The Grazing Food Chain and the Detritus Food Chain.

• Statement 1 is correct- The Grazing Food Chain starts with living producers (plants). However, the Detritus food chain begins with the decomposition of dead organic matter by microorganisms, including bacteria and fungi.
• Statement 2 is incorrect- In aquatic ecosystems, the Grazing Food Chain serves as the primary pathway for energy flow. In contrast, in terrestrial ecosystems, a significantly greater proportion of energy flows through the detritus food chain compared to the Grazing Food Chain.

Solution: (a)

Statement Analysis: 

• Succession is when one community of plants and animals replaces another in an ecosystem. During succession some species colonise an area and their population become more numerous whereas populations of other species decline and even disappear. The entire sequence of communities that successively change in a given area are called sere(s).
• Statement 1 is correct. The pioneer species are those species which initiate the development of an ecological community in an area with currently no life form’s existence. In primary succession on rocks these are usually lichens which are able to secrete acids to dissolve rock, helping in weathering and soil formation.
• Statement 2 is correct. Pioneer species can tolerate and trade through most of the prevailing harsh environmental conditions.
• Statement 3 is incorrect. In a climax community (not in pioneer community), the plants and animals are in balance with each other and their environment. A climax community refers to a stable ecosystem in its final stage of ecological succession. The climax community remains stable as long as the environment remains unchanged

Solution: (b)

Statement Analysis: 

• • Adaptation is any attribute of the organism (morphological, physiological, and behavioural) that enables the organism to survive and reproduce in its habitat. Many adaptations have evolved over a long evolutionary time and are genetically fixed.
  • Statement 1 is incorrect: Eurythermal organisms can tolerate and thrive in a wide range of temperatures. Stenothermal organisms are restricted to a narrow range of temperatures.

• Statement 2 is correct: Hydrophytes are plants that are adapted to live in water or moist environments. 

• Adaptations include:

1. In submerged forms, the stem is long, thin, porous, and bendable.
2. Either the cuticle is completely absent or, if present, it is narrow and poorly formed.
3. Hydrophytes are able to survive in anaerobic environments.
4. They have specialized aerating organs.

• Statement 3 is correct: Epiphytes are plants that grow by perching on other plants. They solely use the supporting plants for shelter and not for water or food. These epiphytes can be found in tropical rainforests. Orchids and Hanging Mosses are examples. Adaptations include:

1. Aerial roots (for respiration) and clinging roots (which hold the epiphytes firmly to the surfaces of the supporting structures).
2. In some, the stems are succulent (they store water) and produce pseudo-bulbs or tubers.
3. The occurrence of a thick cuticle and depressed stomata slows transpiration significantly.

Solution: (d)

Statement Analysis: 

• The standing crop of an ecosystem includes all living organisms, regardless of their position in the food chain. Standing crops can be measured for different levels of organization within an ecosystem, from individual organisms to populations, communities, and entire ecosystems.
• In ecology, standing crop refers to the total amount of living biomass present in a given area at a specific moment in time. This includes all organisms, from producers like plants and algae to consumers like animals and bacteria. Standing crop is an important metric for understanding the productivity and functioning of an ecosystem. It can be used to assess the carrying capacity of an environment, track changes over time, and compare different ecosystems. The biomass of a species is expressed in terms of fresh or dry weight.

Solution: (c)

Statement Analysis: 

• • Statement 1 is correct: The shola forests are characterized as ‘Southern Montane Wet Temperate Forest’ by various experts like Harry George Champion and SK Seth. These forests are found in valleys with sufficient moisture and proper drainage, generally at an altitude of more than 1500 meters. The top regions of these forests are covered with grasslands, known as Shola grasslands.

• Statement 2 is correct: Shola forests are distributed across various parts of the Western Ghats. Shola forests are found in the Nilgiris, located in the states of Tamil Nadu and Kerala. These forests are also found in the Anamalais, Palni hills, Kalakadu, Mundanthurai and Kanyakumari in the states of Tamil Nadu and Kerala.

Solution: (b)

Statement Analysis: 

• Statement 1 is correct: Banni grasslands lie in the Kutch district of Gujarat, India. It forms a transitional zone between the Thar Desert to the north and the Arabian Sea to the south, creating a mosaic of arid and semi-arid ecosystems. The Banni grassland in Gujarat‟s Kachchh district is one of the largest grasslands in the Indian subcontinent with an area of over 2500 sq.km
• Statement 2 is correct: Banni grasslands cover 2,497 square kilometers and account for over 45% of Gujarat’s pastures. Bannis is classified as a Dichanthium-Cenchrus-Lasiurus grass cover because it combines two ecosystems: wetlands and grasslands. These grasslands support a diverse range of flora and wildlife, including plants, birds, animals, reptiles, and amphibians. A huge freshwater lake locally known as Chhari-Dhand (Dhand means a shallow lake) is a prominent feature of the Banni grassland.
• Statement 3 is incorrect: Maldharis tribe breed cattle, camels and smaller ruminants like goats and sheep. They are concentrated mainly in the eastern Kutch as well as in western Kutch which includes Banni, Asia’s largest grassland. Maldharis dominates the banni grassland.

Statement 4 is correct: The Central government has approved a proposal to set up a cheetah conservation breeding center in Kutch district. Banni grassland used to be the habitat of cheetahs, which became extinct over time.

Solution: (c)

Statement Analysis: 

• • A bio-geo-chemical cycle denotes the route through which a chemical substance travels across the biotic and abiotic components of the Earth. It is divided into three parts: Nutrient Cycle, Gaseous Cycle, and Sedimentary Cycle. The Phosphorus cycle and Sulphur cycle fall under the classification of sedimentary cycles.

• Statement 1 is correct- The phosphorus cycle is a sedimentary biogeochemical process that illustrates the transfer of phosphorus across the lithosphere, hydrosphere, and biosphere. The cycle encompasses the flow of phosphorus through rocks, water, soil, sediments, and organisms.

• Statement 2 is correct- Phosphorus primarily circulates in its solid forms (phosphates) and doesn’t readily enter the atmosphere through respiration like carbon dioxide does.

• Statement 3 is correct: Phosphorus is naturally stored in rock as phosphates. Weathering rocks release small amounts of phosphates into the soil, which plants take through roots. Herbivores and other animals acquire phosphorus from plants. Phosphate-solubilizing bacteria decompose waste products and deceased organisms, releasing phosphorus into the environment.

Solution (b)

Explanation:

• Ecological diversity refers to the variety of ecosystems in a given region, including both terrestrial (land) and aquatic (water) ecosystems. It encompasses the different habitats, ecological processes, and species interactions within these environments. (Statement 1 is correct)
• Ecological diversity operates on a broader scale compared to genetic and species diversity. It encompasses different ecosystems and their complex interactions across landscapes and regions, making it the largest scale of biodiversity. (Statement 2 is correct)

Ecological diversity does not exclude human-altered ecosystems. In fact, it includes the variation in all ecosystems, including those modified by human activities, such as agricultural and urban landscapes. These systems are considered part of ecological diversity as they host distinct ecological processes and species interactions. (Statement 3 is incorrect)

Solution (a)

Explanation:

• Stenothermal organisms are the types of animals which are capable of living only at a certain temperature or within a very narrow range of temperatures. Unlike eurythermal organisms, which can tolerate a broad range of temperatures, stenothermal organisms have limited thermal tolerance. This means they are highly sensitive to changes in temperature, making them vulnerable to temperature fluctuations in their environment. (Statement 1 is correct)
• The temperature range that stenothermal organisms are adapted to varies significantly across different species. For example, some stenothermal organisms thrive in cold environments (like polar regions), while others are adapted to warmer tropical conditions. Therefore, the temperature tolerance is species-specific and not uniform across all stenothermal organisms. (Statement 2 is incorrect)

Solution (a)

Explanation:

• A flagship species is often chosen to represent an environmental cause, campaign, or habitat. These species are charismatic and have strong public appeal, making them ideal ambassadors for conservation efforts. They symbolize the ecological health of their habitat and play a crucial role in raising awareness for conservation initiatives. (Statement 1 is correct)
• he protection of flagship species often results in broader conservation efforts that benefit the entire ecosystem. By preserving the habitat of a flagship species, other species, including those that are vulnerable or less well-known, also receive protection. This creates a cascading effect of conservation for multiple species sharing the same habitat. (Statement 2 is correct)

Since the protection of a flagship species often leads to broader conservation efforts benefiting the entire ecosystem, Statement-II is the correct explanation for Statement-I

Solution (c)

Explanation:

• Wetlands play a critical role in water purification by filtering pollutants, sediments, and nutrients from the water before it reaches rivers, lakes, or oceans. Wetland plants and microorganisms break down contaminants, improving water quality. The Ramsar Convention on Wetlands recognizes wetlands’ role in water purification and maintaining water quality. (Statement 1 is correct)
• Wetlands act as natural buffers against flooding by absorbing excess water during heavy rainfall or storm surges. Their ability to store and slowly release water helps reduce the severity of floods and protects surrounding areas. (Statement 2 is correct)
• Wetlands are significant carbon sinks, particularly peatlands, which store large amounts of carbon in the form of organic matter. By sequestering carbon, wetlands help mitigate climate change by reducing the amount of carbon dioxide in the atmosphere. (Statement 3 is correct)

Wetlands are not typically associated with tidal energy generation. While tidal energy is a renewable resource harnessed from ocean tides, it requires specific coastal infrastructures like tidal turbines. Wetlands, though vital for other ecosystem services, do not directly contribute to energy generation. (Statement 4 is incorrect)

Solution (d)

Explanation:

• Stoneflies are sensitive to changes in water quality, particularly oxygen levels. They are bioindicators of clean, well-oxygenated water, as they require high dissolved oxygen concentrations to survive. Their presence or absence can indicate the ecological health of river systems. (Option a is correct)
• Butterflies are excellent bioindicators of habitat health and the quality of plant life. They are sensitive to environmental changes and plant health, which affects their population and reproduction. Their presence often indicates a well-functioning ecosystem with healthy vegetation. (Option b is correct)
• Salmon populations are often used as indicators of ecosystem health. Changes in their populations can reflect the presence of diseases, water pollution, and other environmental stressors that affect aquatic ecosystems. (Option c is correct)

Grizzly Bears (Ursus arctos horribilis) are not native to tropical regions. Grizzly bears are typically found in temperate regions of North America, particularly in the western United States, Canada, and Alaska. They inhabit forests, mountain ranges, and meadows but are absent from tropical ecosystems such as rainforests or tropical savannas. Grizzly bears play a significant role as keystone species in temperate ecosystems, but their presence does not serve as an indicator of biodiversity or ecosystem health in tropical regions. (Option d is incorrect)

Solution (b)

Explanation:

• Keystone species do not necessarily have a high population density. In fact, many keystone species have relatively low population numbers but exert a disproportionate influence on their ecosystem. The impact of keystone species comes from the critical role they play in maintaining the structure and function of an ecosystem, not from their abundance. E.g.: Gray wolf in Yellowstone National Park (Statement 1 is incorrect)
• Keystone species can be found across all types of organisms, from animals and plants to microorganisms like bacteria and fungi. Their critical ecological roles can range from top predators that regulate prey populations to plants that provide essential resources for other species. E.g.: Sea otters, Beavers and certain Mangrove plants. (Statement 2 is correct)

The role of a keystone species is not the same across different ecosystems. A species’ role is specific to the ecosystem it inhabits. In one ecosystem, a species may function as a predator, while in another, it may be an ecosystem engineer or primary producer. Keystone species’ roles vary based on the structure and needs of the ecosystem they support. (Statement 3 is incorrect)

Solution (d)

Explanation:

• Allopatric speciation occurs when populations of the same species are geographically isolated, leading to the evolution of distinct species. The physical separation of populations prevents gene flow, causing genetic differences to accumulate over time, eventually resulting in speciation. The formation of new species on islands or in geographically separated regions. Darwin’s finches on the Galapagos Islands are a classic example of allopatric speciation. (Statement 1 is correct)
• Peripatric speciation is a subtype of allopatric speciation where a small, isolated population at the edge of a larger population undergoes speciation due to geographic isolation. It is characterized by the smaller population size, which accelerates genetic drift and the accumulation of unique traits. Speciation in isolated island populations or small groups at the edges of the species’ main range. (Statement 2 is correct)

While sympatric speciation does not require geographic separation, it is still classified as a geographic mode of speciation because it occurs within the same geographic area. It happens when new species evolve from a single ancestral species while inhabiting the same geographic region. This speciation process often involves changes in behavior, niche differentiation, or genetic mutations that reduce gene flow between subpopulations. (Statement 3 is correct)

Solution (c)

Statement Analysis:

The Disaster Management Act of 2005 defines a disaster as a catastrophe, mishap, calamity, or grave occurrence arising from natural or man-made causes that result in substantial loss of life, destruction of property, or damage to the environment. The following 12 disasters are included as Notified Disasters in India:

• Cyclone
• Avalanche
• Pest Attack and Frost
• Cold Wave
• Drought
• Earthquake
• Fire
• Flood
• Tsunami
• Hailstorm
• Landslide 
• Cloud Burst

Heat Wave is not included in it. Hence, option c is correct.

The 15th Finance Commission has also declined to include heat waves on the list of notified disasters. However, the commission does allow states to use up to 10% of their State Disaster Response Fund (SDRF) funds for “local disasters” like heat waves, which states can notify on their own

Note: Presently the notified list of disasters eligible for National Disaster Response Fund/State Disaster Response Fund (SDRF) assistance.

Solution (a)

Statement Analysis:

• Tell Umm Amer Heritage Site is situated on the coastal dunes of the Nuseirat Municipality, just 10 km south of the Gaza city of Palestine. Hence, Statement 1 is incorrect.
• It was founded in the fourth century.
• It is an ancient Christian monastery founded by Hilarion the Great. Hence, Statement 2 is correct.
• It was the first monastic community in the Holy Land, laying the groundwork for the spread of monastic practices in the region.
• The monastery occupied a strategic position at the crossroads of major trade and communication routes between Asia and Africa.

It is also known as the ‘Monastery of Saint Hilarion’. Hence, Statement 3 is correct.

Solution (d)

Statement Analysis:

Recently India signed a ‘Cultural Property Agreement’ to prevent and curb the illicit trafficking of antiquities from India with the United States of America. It is aligned with the 1970 UNESCO Convention on the Means of Prohibiting and Preventing the Illicit Import, Export, and Transfer of Ownership of Cultural Property, to which both countries are state parties. It restricts the importation into the United States of certain archaeological material ranging in date from 1.7 million years ago through 1770 CE and certain ethnological material, which may include categories of civic, religious, and royal architectural material, religious material and ceremonial items, and manuscripts ranging in date from 2nd century BCE to 1947 CE. Hence, option d is correct.

Solution (c)

Statement Analysis:

• The Right to Shelter in India is recognised as a fundamental right under the broader ambit of the Right to Life guaranteed by Article 21 of the Indian Constitution. Hence, option c is correct.
• This right ensures that every citizen has access to adequate housing, which is considered essential for living a life with dignity.
• It implies not just a roof over one’s head but also includes adequate privacy, space, security, lighting, ventilation, basic infrastructure, and proximity to workplaces and social amenities.

Solution (b)

Statement Analysis:

• U-WIN is aimed at digitising India’s Universal Immunisation Programme (UIP). Hence, option b is correct.
• The platform will be used to register and vaccinate every pregnant woman, record her delivery outcome, register every newborn delivery, administer birth doses, and all vaccination events thereafter.
• The U-WIN is going to be the single source of information for immunisation services, updating vaccination status, delivery outcome, and reports like antigen-wise coverage, etc.

Solution (c)

Statement Analysis:

• The Oparin-Haldane Hypothesis, Miller-Urey Experiment, and Panspermia Hypothesis are related to the Evolution of Life. Hence, option c is correct.
• In 1924 and 1929, Oparin and Haldane respectively suggested the first molecules making up the earliest life forms gradually self-organised from a “primordial soup” in a young earth’s tempestuous, prebiotic environment. This idea is today called the Oparin-Haldane hypothesis.
• Miller-Urey Experiment showed that in the right conditions, inorganic compounds could give rise to complex organic compounds. Under it methane, ammonia, and water were mixed and applied an electric current to produce amino acids, the building blocks of proteins.
• The Panspermia Hypothesis suggests that meteorites could have brought life’s building blocks to Earth, supported by discoveries of extraterrestrial organic material and amino acids on asteroids.

Solution (a)

Statement Analysis:

• Amaravati School of Sculpture was developed in Southern India and was patronaged by Satavahanas. Hence, Statement 1 is incorrect.
• It was developed in the Krishna-Godavari lower valley, in and around Amravati, Nagarjunakonda, Goli, Ghantasala, and Vengi.
• It was developed indigenously during the 3rd century BCE to 250 CE. Hence, Statement 2 is incorrect.
• It was mainly influenced by Buddhist imagery.

Its sculptures are made of white marble and represent Buddha’s life and the lives of Buddha in both human and animal forms. Hence, Statement 3 is correct.

Solution (c)

Statement Analysis:

• Namo Drone Didi Scheme aims to provide drones to 15,000 selected women SHGs for offering rental services to farmers. Hence, Statement 1 is correct.
• Rs 500 crore has been earmarked for this initiative under the Union budget 2024-25. 
• This scheme will empower women in rural areas by integrating them into the technological advancements in agriculture, thus fostering entrepreneurship. 

Its implementation period spans from 2023-24 to 2025-26. Hence, Statement 2 is correct.

Solution (a)

Statement Analysis:

• The Remission of Duties and Taxes on Exported Products (RoDTEP) Scheme is a flagship export promotion scheme of the Ministry of Commerce, India. Hence, Statement 1 is incorrect.
• It aims to boost domestic exports and replace the export incentive scheme,

Merchandise Exports from India (MEIS) scheme. 

• It aims to refund to the exporters the embedded central, state, and local duties and taxes paid on inputs that have so far not been refunded or rebated. Hence, Statement 2 is correct.
• It covers physical exports as well as outbound shipments of services from India. Service providers can also claim refunds on applicable hidden levies.
• It will be implemented by Customs through a simplified IT System. 
• It is open to both manufacturers and merchant exporters, without any threshold of turnover. Hence, Statement 3 is correct.
• The most important condition is that such goods should have been directly exported by such a person.

Solution (c)

Statement Analysis:

• The Green Climate Fund is the world’s largest dedicated climate fund which was set up at COP 16 held in Cancun. Hence, Statement 1 is correct.
• It accelerates transformative climate action in developing countries through a country-owned partnership approach and use of flexible financing solutions and climate investment expertise.
• The GCF is a legally independent institution with a fully independent secretariat headed by an Executive Secretary.
• The Secretariat, located in Songdo South Korea, began its work in December 2013. 

It is an operating entity of the financial mechanism of the United Nations Framework Convention on Climate Change (UNFCCC). Hence, Statement 2 is correct.

Solution (a)

Explanation:

We can factor the given equation as:

(a – b)^2 = 25

Taking the square root of both sides, we get:

a – b = ±5

Since a and b are positive integers, we can’t have a – b = -5. Therefore:

a – b = 5

Now, we can express b as:

b = a – 5

Substituting this value of b into the original equation, we get:

a^2 – 2a(a – 5) + (a – 5)^2 = 25

Simplifying this equation, we get:

a^2 – 2a^2 + 10a + a^2 – 10a + 25 = 25

Combine like terms:

0 = 0

This equation is true for all values of a. However, since a and b are positive integers, we can try different values of a to find a corresponding value of b.

If a = 5, then b = 0 (not a positive integer).

If a = 6, then b = 1 (a positive integer).

Therefore, a = 6 and b = 1.

The value of a + b is: a) 7

Solution (a)

Explanation:

We can factor the given equation as:

(x + y + z)(x^2 + y^2 + z^2 – xy – yz – zx) = 50

Since x, y, and z are integers, we can try different values of x + y + z to find a corresponding value of x^2 + y^2 + z^2 – xy – yz – zx.

If x + y + z = 5, then we can find values of x, y, and z that satisfy the equation.

Therefore, the value of x + y + z is: a) 5

Solution (d)

Explanation:

We can calculate the number of ways to form the committee as follows:

– Total number of ways to form a 5-member committee from 12 people (8 men + 4 women): 12C5 = 792.

– Number of ways to form a 5-member committee with 0 women (all men): 8C5 = 56.

– Number of ways to form a 5-member committee with 1 woman: 8C4 * 4C1 = 70 * 4 = 280.

– Number of ways to form a 5-member committee with at least 2 women: 792 – 56 – 280 = 456.

However, this answer is not among the options. Let’s re-evaluate the problem:

– Number of ways to form a 5-member committee with exactly 2 women: 8C3 * 4C2

= 56 * 6 = 336.

– Number of ways to form a 5-member committee with exactly 3 women: 8C2 * 4C3 = 28 * 4 = 112.

– Number of ways to form a 5-member committee with exactly 4 women: 8C1 * 4C4 = 8 * 1 = 8.

Adding these up, we get:

336 + 112 + 8 = 456

However, we missed the case where all 5 members are women:

4C5 = 0 (since we can’t choose 5 women from only 4)

So, the correct answer remains:

None of the above (correct answer is 456)

Solution (d)

Explanation:

We can calculate the number of ways to invite the friends as follows:

– Number of ways to invite exactly 2 relatives: 4C2 * 4C3 = 6 * 4 = 24.

– Number of ways to invite exactly 3 relatives: 4C3 * 4C2 = 4 * 6 = 24.

– Number of ways to invite exactly 4 relatives: 4C4 * 4C1 = 1 * 4 = 4.

Adding these up, we get:

24 + 24 + 4 = 52

However, this answer is not among the options. Let’s re-evaluate the problem:

– Total number of ways to invite 5 friends from 8 friends: 8C5 = 56.

– Number of ways to invite 5 friends with 0 relatives: 4C5 = 0 (since we can’t choose 5 non-relatives from only 4).

– Number of ways to invite 5 friends with 1 relative: 4C1 * 4C4 = 4 * 1 = 4.

So, the number of ways to invite 5 friends with at least 2 relatives is:

56 – 0 – 4 = 52

However, we missed the case where all 5 friends are relatives:

4C5 = 0 (since we can’t choose 5 relatives from only 4)

So, the correct answer remains:

(correct answer is 52)

Solution (c)

Statement Analysis:

Option (a) is not correct: According to the passage, the protein rhodopsin is responsible for vision in humans and microalgae use it in place of chlorophyll to survive in the oceans. The same phenomenon is not taking place in both ecosystems, even though the same biochemical is used. It can be assumed that the biochemical rhodopsin is being utilised by humans and microalgae differently and hence as far as the information in the passage is concerned, it is not the ‘same’ phenomenon that is occurring on land and water. Even if it was, we could not have generalized it based on just one example. Hence, option (a) is not correct. 

Option (b) is not correct: The passage mentions the adaptation of the microalgae to the changing environment and how it has adapted to the effects of global warming. The passage does not talk about climate mitigation, or whether biochemical like rhodopsin may prove helpful in such a cause.  

Option (c) is correct: Consider the line, “As climate change reduces the availability of nutrients in the sea, marine microalgae or eukaryotic phytoplankton fire up a protein called rhodopsin”. This implies that microalgae are adopting to changing external environment. It is further mentioned in the passage, “Estimates suggested they may absorb as much light as chlorophyll-based photosynthesis in the sea, which also captures light to generate energy and food”. These lines imply that rhodopsin replaces chlorophyll in microalgae to facilitate food production. This way, the passage revolves around the theme of adaptability to changing external conditions. Hence, option (c) is correct. 

Option (d) is not correct:  The passage revolves around the theme of adaptability by taking the case of microalgae and discussing the process of their survival in the absence of chlorophyll. The passage does not mention the effects of adaptability on productivity. The passage only narrates how adaptability can help in survival in a changing environment. Hence, option (d) is not correct.