जब चार संख्याएँसमानुपात में होती हैं, तो इसका अर्थ है कि पहले दो संख्याओं का अनुपात अंतिम दो संख्याओं के अनुपात के बराबर होता है। इसे निम्नलिखित रूप में व्यक्त किया जा सकता है:

दिए गए मान:

समानुपात स्थापित करना:

समानुपात के सूत्र का उपयोग करते हुए, हम लिख सकते हैं:

क्रॉस-मल्टिप्लाई करना:

यह समीकरण सिम्प्लिफाई करने पर प्राप्त होता है:

के लिए हल करना:
ज्ञात करने के लिए, हम दोनों पक्षों का वर्गमूल लेंगे:

इस प्रकार, हमें प्राप्त होता है:

निष्कर्ष:

>का मानहै।

प्रासंगिकता:

समानुपातों का ज्ञान विभिन्न क्षेत्रों में महत्वपूर्ण है, जैसेअर्थशास्त्रऔरडेटा विश्लेषण। हाल ही मेंभारत में आर्थिक असमानताके अध्ययन में, विभिन्न आय समूहों के बीच अनुपात का उपयोग किया गया है ताकि यह समझा जा सके कि कैसे संसाधनों का वितरण होता है। इसके अलावा,गणितीय मॉडलिंग<औरसांख्यिकीय विश्लेषणमें समानुपात का उपयोग भविष्यवाणियों और चर के बीच संबंधों को समझने में किया जाता है।

To find the Mean when given the Median and Mode, we can use the relationship between these three measures of central tendency. The formula is:

Mean = Mode + (Median – Mode) × 3/2

Given:

• Median = 25
• Mode = 24

Step-by-Step Calculation:

1. Calculate the Difference:
   Mode=25 24 1 Median Mode 25 24 1

2. Multiply the Difference by 3/2:
   (

Median−Mode)3 2 1 3 2 1.5 Median 2 3 1 2 3 1.5

3. Calculate the Mean:
   Mean= Median− Mode) 3 2 Mean Mode+ Median− Mode 2 3
   $Mean=24+1.5=25.5$24 1.5 25.5

Conclusion:

Thus, theMean is 25.5.

This relationship highlights the interconnectedness of statistical measures and can be useful in various analytical contexts, such as in economic data analysis sociological studies, where understanding distributions is crucial. For example, recent studies on income distribution may show how these measures can reflect economic disparities and inform policy decisions.

Photochemical Smog: Formation, Effects, and Mitigation

**1. Formation of Photochemical Smog:

• Photochemical smog forms when sunlight reacts with nitrogen oxides (NOx) and volatile organic compounds (VOCs) in the atmosphere. This reaction produces ozone (O3) and other harmful substances. For example, automobile emissions and industrial discharges are major sources of NOx and VOCs, leading to smog formation in cities like Delhi and Los Angeles.

**2. Effects of Photochemical Smog:

• Health Impacts: Smog can cause respiratory problems, aggravate asthma, and lead to lung diseases. Recent studies indicate an increase in respiratory ailments and hospital admissions in cities with high smog levels.
• Environmental Damage: It can damage vegetation, reduce crop yields, and harm urban infrastructure by degrading building materials.

**3. Mitigation Strategies:

• Regulating Emissions: Implementing emission standards for vehicles and industries, such as those enforced in California and European countries, can reduce NOx and VOC levels.
• Promoting Clean Energy: Transitioning to renewable energy sources and electric vehicles helps decrease pollution. For instance, India’s FAME Scheme promotes electric mobility to tackle urban air pollution.

1999 Gothenburg Protocol

**1. Overview:

• The 1999 Gothenburg Protocol is an international agreement aimed at reducing acidification, eutrophication, and ground-level ozone. It establishes emission reduction targets for sulfur dioxide (SO2), nitrogen oxides (NOx), and VOC.

**2. Objectives and Impact:

• Emission Reduction Targets: Countries agreed to limit their emissions of key pollutants, which helps reduce smog and improve air quality.
• Implementation: The protocol has led to significant improvements in air quality in Europe and has been a model for similar agreements in other regions.

The Gothenburg Protocol and other mitigation strategies are crucial in managing photochemical smog and protecting both human health and the environment.

Natural Processes of Cellulose Decomposition

**1. Decomposition by Microorganisms:

• Cellulose Decomposition begins with microorganisms such as bacteria and fungi breaking down plant material in the soil. For example, in forest ecosystems, fungi like white rot fungi decompose cellulose, converting it into simpler compounds.

**2. Formation of Humus:

• As microorganisms decompose cellulose, it forms humus, a dark, organic material in soil. Humus improves soil fertility and structure, while its breakdown process continues to release carbon dioxide (CO2) and water into the atmosphere.

**3. Cellulose Fermentation:

• In anaerobic conditions, such as in wetlands or the digestive systems of ruminants (e.g., cattle), cellulose fermentation by microbes produces methane (CH4) in addition to CO2 and water. For example, the rumen of cattle hosts microbes that ferment cellulose from ingested plant material.

**4. Carbon Sequestration and Release:

• Over time, some cellulose-derived carbon is sequestered in peatlands or sedimentary layers before being released as CO2 through natural processes like soil respiration or biological decay.

Recent Example:

• In 2023, studies of Amazon rainforest soil showed how high moisture levels enhance microbial activity, accelerating cellulose decomposition and impacting carbon cycling in tropical ecosystems.

These natural processes ensure that cellulose is efficiently converted into carbon dioxide, water, and other end products, contributing to the global carbon cycle and soil health.

Increase in Life Expectancy and New Health Challenges

**1. Emergence of Chronic Diseases:

• Chronic illnesses such as cardiovascular diseases, diabetes, and cancer have become more prevalent as the population ages. For example, the incidence of Type 2 diabetes has increased significantly in India, affecting millions.

**2. Geriatric Care:

• An aging population has intensified the need for geriatric care and long-term care facilities. Many elderly individuals face issues like dementia and arthritis, requiring specialized medical attention.

**3. Mental Health Issues:

• Mental health disorders, including depression and anxiety, are on the rise among older adults. The recent National Mental Health Survey 2023 highlighted the growing burden of mental health conditions among the elderly.

**4. Healthcare System Strain:

• The increase in life expectancy has placed a strain on healthcare infrastructure and resources, necessitating improvements in medical services and public health policies.

Steps to Address the Challenges

**1. Strengthening Preventive Healthcare:

• Promote preventive measures and regular screenings for chronic diseases to enable early detection and management. Programs like National Health Mission (NHM) are working towards improving preventive healthcare.

**2. Enhancing Geriatric Care:

• Invest in geriatric care services and long-term care facilities. The Elderly Care Program launched in 2023 aims to address these needs by improving care facilities and support systems.

**3. Improving Mental Health Support:

• Expand mental health services and integrate them into primary healthcare. The Mental Health Support Scheme introduced in 2023 focuses on providing counseling and therapy services.

**4. Upgrading Healthcare Infrastructure:

• Enhance healthcare infrastructure and training for healthcare professionals to better manage the needs of an aging population. The Ayushman Bharat Scheme aims to provide affordable and comprehensive healthcare services.

Addressing these challenges through targeted strategies will be crucial for adapting to the changing health dynamics associated with increased life expectancy.