es
Feedback
Mathematics Optional

Mathematics Optional

Ir al canal en Telegram

📈 Análisis del canal de Telegram Mathematics Optional

El canal Mathematics Optional (@mathematics_optional_notes) en el segmento lingüístico de Inglés es un actor destacado. Actualmente la comunidad reúne a 10 347 suscriptores, ocupando la posición 19 231 en la categoría Educación y el puesto 38 757 en la región India.

📊 Métricas de audiencia y dinámica

Desde su creación el невідомо, el proyecto ha mostrado un crecimiento acelerado, reuniendo a 10 347 suscriptores.

Según los últimos datos del 30 junio, 2026, el canal mantiene una actividad estable. En los últimos 30 días la variación de miembros fue de -122, y en las últimas 24 horas de -9, conservando un alto alcance.

  • Estado de verificación: No verificado
  • Tasa de interacción (ER): El promedio de interacción de la audiencia es 2.96%. Durante las primeras 24 horas tras publicar, el contenido suele obtener N/A% de reacciones respecto al total de suscriptores.
  • Alcance de las publicaciones: Cada publicación recibe en promedio 0 visualizaciones. En el primer día suele acumular 0 visualizaciones.
  • Reacciones e interacción: La audiencia responde de forma activa: el promedio de reacciones por publicación es 0.
  • Intereses temáticos: El contenido se centra en temas clave como upsc, mathematics, kataria, mathematic, ज्वाइन.

📝 Descripción y política de contenido

No se ha proporcionado la descripción del canal.

Gracias a la alta frecuencia de actualizaciones (últimos datos recibidos el 01 julio, 2026), el canal mantiene la vigencia y un amplio alcance. La analítica demuestra que la audiencia interactúa activamente con el contenido, lo que lo convierte en un punto de referencia dentro de la categoría Educación.

10 347
Suscriptores
-924 horas
-457 días
-12230 días
Archivo de publicaciones
सीमा रेखाएं - प्रमुख अंतर्राष्ट्रीय सीमाएँ 🌀 ------------------- √√ रेखा का नाम – डूरंड रेखा (Durand Line) ● किसके बीच – पाकिस्तान तथा अफगानिस्तान ● 1886 में सर मार्टिमर डूरंड द्वारा निर्धारित। ----------------------- √√ रेखा का नाम – मैकमोहन रेखा (Macmahon Line) ● किसके बीच – भारत तथा चीन ● 1120 किमी. लंबी यह रेखा सर हेनरी मैकमोहन द्वारा निर्धारित की गई थी। लेकिन चीन इसे स्वीकार नहीं करता। ----------------------- √√ रेखा का नाम – रेडक्लिफ रेखा (Radcliffe Line) ● किसके बीच – भारत तथा पाकिस्तान ● 1947 में भारत-पाकिस्तान सीमा आयोग के अध्यक्ष सर सायरिल रेडक्लिफ द्वारा निर्धारित। ------------------------ √√ रेखा का नाम – 17 वीं समानांतर रेखा (17th Parallel) ● किसके बीच – उत्तरी वियतनाम तथा द. वियतनाम ● वियतनाम के एकीकरण के पहले यह देश को दो भागों में बांटती थी। ----------------------- √√ रेखा का नाम – 24 वीं समानांतर रेखा (24th Parallel) ● किसके बीच – भारत तथा पाकिस्तान ● पाकिस्तान के अनुसार कच्छ क्षेत्र का यह रेखा सही निर्धारण करती है लेकिन भारत इस रेखा को स्वीकार नहीं करता है। ----------------------- √√ रेखा का नाम – 38 वीं समानांतर रेखा (38th Parallel) ● किसके बीच – उत्तर कोरिया तथा दक्षिण कोरिया ● कोरिया को दो भागों में बांटती है। ------------------------ √√ रेखा का नाम – 49 वीं समानांतर रेखा (49th Parallel) ● किसके बीच – अमेरिका तथा कनाडा ● अमेरिका तथा कनाडा को दो भागों में बांटती है। ----------------------- √√ रेखा का नाम – हिंडनबर्ग रेखा (Hindenburg Line) ● किसके बीच – जर्मनी तथा पोलैंड ● प्रथम विश्व युद्ध में जर्मनी की सेना यहीं से वापस लौटी थी। ------------------------ √√ रेखा का नाम – ओडरनास रेखा (Order-Neisse Line) ● किसके बीच – जर्मनी तथा पोलैंड ● द्वितीय विश्व युद्ध के बाद निर्धारित की गई। ----------------------- √√ रेखा का नाम – मैगिनाट रेखा (Maginot Line) ● किसके बीच – जर्मनी तथा फ्रांस ● जर्मनी के आक्रमण से बचाव के लिए फ्रांस ने यह रेखा बनाई थी। ------------------------ √√ रेखा का नाम – सीजफ्राइड रेखा (Seigfrid Line) ● किसके बीच – जर्मनी तथा फ्रांस ● जर्मनी ने यह रेखा बनाई थी। Join @UPSCMainsGuidance

Emailing ECO MCQ 550 VIVEK SINGH.pdf

🔆Directive Principles Of State policy DPSP ✅ The constitution of India aims to establish not only political democracy but also socioeconomic justice to the people to establish a welfare state. ✅These provisions are given in Part IV of Indian Constitution. ✅ Directive Principles of state policy are in the form of instructions to the governments at the centre as well as states. ✅Though these principles are non justiciable, they are fundamental in the governance of the country. ✅ The idea of the Directive Principles of State Policy has been taken from the Irish Republic . ✅The Directive Principles of State policy were incorporated in our constitution in order to provide economic justice and to avoid concentration of wealth in the hands of few people. ✅ The constitution covers from Article 36 to 51 as Directive Principles of State Policy. ✅They are unique blend of socialistic, liberal, democratic and Gandhian Principles. ✅ They describe as the ‘conscience of the constitution’. ✅ In the “State of Tamil Nadu etc. Vs L.Abu Kavur Bai” case in 1984 , the Supreme court held that although directive principles of State Policy are not enforceable, yet the court should not avoid them

List of countries by length of coastline 1) Canada's coastline is world's longest, measuring 202,080 km (includes the mainland coast and the coasts of offshore islands) 2) Indonesia (99,083 km) 3) Norway (58,133 km) 4) Greenland* (44,087 km) 5) Russia (37,653 km) 6) Philippines (36,289 km) 7) Japan (29,751 km) 8) Australia (25,760 km) 9) United States (19,924 km) 10) Antarctica* (17,968 km) 11) New Zealand (15, 134 km) 12) China (14,500 km) 13) Greece (13,676 km) 14) United Kingdom (12,429 km) 15) Mexico (9330 km) 16) Italy (7782 km) 17) India (7516km)

#SargassoSea is a region of the Atlantic Ocean bounded by 4 ocean currents forming an ocean gyre. 1) Gulf Stream on the west 2) North Atlantic Drift on the north 3) Canary Current on the east 4) North Atlantic Equatorial Current on the south Unlike all other seas, it has no land boundaries. It is the only sea in the world which has no coast. It is distinguished from other parts of the Atlantic Ocean by its characteristic brown seaweed called Sargassum and often calm blue water. Sargasso Sea is famous for its floating seaweed that covers large swathes of ocean. But it also boasts an astounding wealth of biodiversity that has earned it the nickname "The Floating Rainforest of the Sea." The four ocean currents together forming a clockwise-circulating system of ocean currents termed the North Atlantic Gyre. Bermuda is near the western fringes of the sea. The four ocean currents deposit the marine plants and refuse which they are carrying into this sea, yet the ocean water in the Sargasso Sea is distinctive for its deep blue color and exceptional clarity, with underwater visibility of up to 61m

Coal Gasification is one of the clean coal technologies and involves the process of converting coal into synthesis gas/ syngas. • Syngas is a mixture of hydrogen (H2), carbon monoxide (CO) and carbon dioxide (CO2). • The by-products of coal gasification include coke, coal tar, sulfur, ammonia and fly ash, all having their own potential uses. • CO2 and ammonia are further reacted to produce urea. • Syngas can also be used in a variety of other applications such as in the production of electricity, fuel for IC engines, making plastics, cement etc

Environmental Impact Assessment or EIA is the process or study which ▪️predicts the effect of a proposed industrial/infrastructural project on the environment. ▪️prevents the proposed activity/project from being approved without proper oversight or taking adverse consequences into account. ▪️compares various alternatives for a project and seeks to identify the one which represents the best combination of economic and environmental costs and benefits.

There are 4 types of genetic diseases 1⃣ Single Gene - Disorders caused by abnormality or mutation in the sequence of one gene. 2⃣ Multifactorial - Caused by a combination of environmental factors as well as mutations in multiple genes. 3⃣ Chromosomal - Abnormalities in chromosome structure such has missing or extra copies 4⃣ Mitochondrial - Caused by a mutation in non-chromosomal DNA of mitochondria

42nd Amendment Act of 1976 added four new Directive Principles to the original list. Those DPSPs are: 1⃣ Article 39 - To secure opportunities for healthy development of children. 2⃣ Article 39A - To promote equal justice and to provide free legal aid to the poor. 3⃣ Article 43A - To take steps to secure the participation of workers in the management of industries 4⃣ Article 48A - To protect and improve the environment and to safeguard forests and wild life.

Hotspot volcanism is a type of volcanism that occurs at the interior of the lithospheric plates rather than plate margins. Well known hotspots include- 1) Hawaiian Hotspot 2) Yellowstone Hotspot 3) Reunion Hotspot Hotspot volcanism occurs due to abnormally hot centres in the mantle known as "mantle plumes". Most of the mantle plumes lie far from tectonic plate boundaries (e.g. Hawaiian Hotspot), but there are some exceptions which are located near plate boundaries (e.g. Iceland Hotspot, Afar Hotspot).

Washington Convention on International Trade in Endangered Species of Wild Fauna and Flora or CITES, aims at regulating the international trade of specimens of endangered animals and plants. India has ratified this Convention in 1976

Kigali Amendment to the Montreal Protocol on Substances that Deplete the Ozone Layers. it will help reduce the production and consumption of hydrofluorocarbons (HFCs), potent greenhouse gases (GHGs), and thus to avoid global warming by up to 0.4°C this century

#Shell_companies are corporate entities which do not have any active business or significant assets in their possession. These companies remain legally registered (but merely on paper), without actually producing goods and services. They are mainly set up for the purposes of tax evasion and money laundering.

Global Internet Forum to Counter Terrorism is an initiative of Facebook, Microsoft, Twitter and YouTube with the objective of disrupting terrorist abuse on their respective platforms by dedicated technology, counterterrorism and operations teams.

Private Member's Bills : A Member of Parliament (MP) who is not a Minister in the Union Cabinet is called a Private Member. Bills introduced by such members are called Private Member's Bills. Private Member Bill (PMB) is same as that of a Government Bill. These bills can deal with any issue and can also be a Constitutional Amendment Bill. It can be introduced in either the Lok Sabha or Rajya Sabha

Dark Net, Deep Web and Surface Web ✅"Dark net" is commonly confused with "deep web." The deep web refers to unindexed sites which are unsearchable; in most cases, this is because those sites are protected by passwords. ✅Part of the WWW (World Wide Web) which is not indexed by a search engine like Google is Deep Web and it about 500-600 times larger than the surface web. ✅Surface Web -Also called the Visible Web, Indexed Web, Indexable Web or Lightnet -is that portion of the World Wide Web that is readily available to the general public and searchable with standard web search engines. It is the opposite of the deep web. It only constitutes 4-6% of the whole web. @civilservicesBaba

Scope of application of nanotechnology in the development process of the country: Agriculture: Nanotechnology can be used in agriculture and food production in the form of Nano sensors for monitoring crop growth and pest control by early identification of plant diseases. These Nano sensors can help enhance production and improve food safety. With inputs related to water use, fertiliser and pesticides delivered in nanoscale productivity and yield can be increased. Medical applications: Development of newer drug delivery systems based on nanotechnology methods is being tried for conditions like cancer, diabetes, fungal infections, and viral infections and in gene therapy. Nanotechnology has also found its use in diagnostic medicine as contrast agents, fluorescent dyes and magnetic nanoparticles. Electronics: The semiconductor industry has been able to improve the performance of electronic systems for more than four decades by downscaling silicon-based devices. Carbon nanomaterials such as one dimensional (1D) carbon nanotubes and two dimensional (2D) graphene have emerged as promising options due to their superior electrical properties which allow for fabrication of faster and more power-efficient electronics. Textiles and Clothing: Nanotechnology has shown a huge potential in the textile and clothing industry which is normally very traditional. Coating is a common technique used to apply Nano-particles onto textiles. The success of nanotechnology in textile applications lies in areas of durability, flexibility, wash ability and softness. The use of nanotechnology allows textiles to become multifunctional and produce fabrics with special functions, including antibacterial, UV-protection, easy clean, water & stain repellent and anti-odour. Energy equipment: Nanoscales and nanoporous membranes are being used to facilitate production of biomass fuel. Energy transmission could potentially be made much more efficient by using engineered nanomaterials. Throughout the renewable-energy sector, nanotechnology has the potential to increase process efficiencies and process yields, decrease costs and enable energy processes that would not be attainable any other way. @civilservicesBaba

Nanotechnology ✅Nanotechnology is the term given to those areas of science and engineering where phenomena that take place at dimensions in the nanometre scale are utilised in the design, characterisation, production and application of materials, structures, devices and systems. ✅Nanotechnology primarily refers to the use and creation of particles that are smaller than 100 nanometre.  ✅The American physicist and Nobel Prize laureate Richard Feynman introduce the concept of nanotechnology in 1959 @civilservicesBaba

Blood Groups: ABO ✅ABO grouping is based on the presence or absence of two surface antigens (chemicals that can induce immune response) on the RBCs namely A and B. ✅Similarly, the plasma of different individuals contain two natural antibodies (proteins produced in response to antigens). ✅ABO blood groups are controlled by the gene I. The plasma membrane of the red blood cells has sugar polymers that protrude from its surface and the kind of sugar is controlled by the gene. The gene (I) has three alleles IA, IB and i. ✅The alleles IA and IB produce a slightly different form of the sugar while allele i does not produce any sugar. ✅Because humans are diploid organisms, each person possesses any two of the three I gene alleles. ✅IA and IB are completely dominant over i, in other words when IA and i are present only IA expresses (because i does not produce any sugar), and when IB and i are present IB expresses. ✅But when IA and IB are present together they both express their own types of sugars: this is because of co-dominance. Hence red blood cells have both A and B types of sugars.@civilservicesBaba

📌 AT-1 bonds (Additional tier 1 bonds) are : 🔸️ Perpetual bonds [ No fixed maturity tenure ] have fixed Interest rate (But interest rate is usually set high, because AT-1 bonds are very risky) 🔸️ Unsecured bonds : Not backed by any mortgage/physical asset or source of revenue are listed on exchange Issued to fulfil (capital adequacy Ratiol under basel 3 Norms. @UPSCPRELIMSZONE 🔸️ AT-1 bonds can be written down, if common Equity tier-1 capital of bank falls below 5.5% of Risk weighted assets