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Mathematics Optional
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📈 Analytical overview of Telegram channel Mathematics Optional
Channel Mathematics Optional (@mathematics_optional_notes) in the English language segment is an active participant. Currently, the community unites 10 347 subscribers, ranking 19 231 in the Education category and 38 757 in the India region.
📊 Audience metrics and dynamics
Since its creation on невідомо, the project has demonstrated rapid growth, gathering an audience of 10 347 subscribers.
According to the latest data from 30 June, 2026, the channel demonstrates stable activity. Although there has been a change in the number of participants by -122 over the last 30 days and by -9 over the last 24 hours, overall reach remains high.
- Verification status: Not verified
- Engagement rate (ER): The average audience engagement rate is 2.96%. Within the first 24 hours after publication, content typically collects N/A% reactions from the total number of subscribers.
- Post reach: On average, each post receives 0 views. Within the first day, a publication typically gains 0 views.
- Reactions and interaction: The audience actively supports content: the average number of reactions per post is 0.
- Thematic interests: Content is focused on key topics such as upsc, mathematics, kataria, mathematic, ज्वाइन.
📝 Description and content policy
Channel description not provided.
Thanks to the high frequency of updates (latest data received on 01 July, 2026), the channel maintains relevance and a high level of publication reach. Analytics show that the audience actively interacts with content, making it an important point of influence in the Education category.
10 347
Subscribers
-924 hours
-457 days
-12230 days
Posts Archive
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#Food_Preservatives are substances added to food to prevent or slow down spoilage and maintain natural colours and flavours.
Two reasons for food spoilage
• Microbial contamination
• Fats reacting with oxygen (oxidation)
Preservative criteria
• Non-toxic
• Functional
• Flavourless
• Economical
Sorbic acid - It is a food preservative which protects many food varieties from yeast and mold spoilage. It is an organic compound, with naturally strong antimicrobial capabilities.
Sodium benzoate - It is a food preservative commonly used in fruit pies, jams, beverages, salads, foods with acidic pH.
It is used in processed foods to prevent the growth of bacteria or fungus that could spoil the food.
Citric Acid - Its acidic pH makes it useful as a food preservative and preserves the color of the food since it significantly slows the oxidation.
Monosodium glutamate (MSG) is not a food preservative.
It is a food additive, which is used as a flavour enhancer commonly added to Chinese food, canned vegetables, soups and processed meats.
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Basai Wetland
• Located in Gurugram district in Haryana, is a flora and fauna rich water body.
• Recognised as one of India's Important Bird and Biodiversity Areas.
• Basai wetland is recognised globally as an Important Bird Area (IBA) by the BirdLife International.
• Species: White ramped vulture, red head vulture present in the wetland were listed as Critically Endangered in the IUCN red list. @CivilservicesBaba
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Circular Economy A circular economy is an economic system of closed loops in which raw materials, components and products lose their value as little as possible, renewable energy sources are used and systems thinking is at the core. In this article we will explain this definition in more detail. @CivilservicesBaba Often focus on the use of raw materials or on system change. Definitions that focus on resource use often follow the 3-R approach:
Reduce (minimum use of raw materials)
Reuse (maximum reuse of products and components)
Recycle (high quality reuse of raw materials) @CivilservicesBaba
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🔴 What is a Central Bank Digital Currency (CBDC) ?
👉CBDC is a legal tender issued by a central bank in a digital form.
👉 It is similar to a fiat currency issued in paper and is interchangeable with any other fiat currency
🔴 What is the need for CBDC?
👉 the goal is to provide users with convenience and security of digital as well as the regulated, reserve-backed circulation of the traditional banking system.
🔴 What does this change for citizens?
👉 There are several models proposed by technology experts and evangelists on how the Digital Rupee could be transacted but a formal announcement by the Reserve Bank of India will likely detail how the Digital Rupee will be transacted by citizens.
♦️One chief difference will be that a Digital Rupee transaction will be instantaneous as opposed to the current digital payment experience.
@UPSCMainsZone
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Green Bonds : is a debt security issued by an organization for the purpose of financing or refinancing projects that contribute positively to the environment and/or climate. A green bond is alternatively known as a climate bond @civilservicesBaba
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Carbon neutral means that any CO2 released into the atmosphere from a company’s activities is balanced by an equivalent amount being removed. @civilservicesBaba
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Cryptocurrency: A digital currency that is secured by cryptography and used as a medium of exchange within a peer-to-peer (P2P) digital economic system. Cryptographic techniques ensures that these systems are completely immune to fraud and counterfeiting.
The first cryptocurrency to be ever created was Bitcoin, introduced by pseudonymous developer Satoshi Nakamoto, in 2009
@civilservicesBaba
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Digital Rupee :Digital currency will also lead to a more efficient and cheaper currency management system @UPSCPRELIMSZONE
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River Rejuvenation is the result of a sudden fall in sea level or a sudden uplift in land surface due to tectonic movements.
This disturbance enables a rise in river’s potential energy (energy stored in river due to newly created height difference from base level).
This energy results in increased river bed erosion. Vertical erosion or downcutting is associated with river rejuvenation as seen in Chambal Ravines.
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🌀Forest Report (IFSR) 2021
▪️Key pointer about India :
▫️Total Forest Cover = 21.71%
▫️Total Forest & Tree Cover = 24.62%
▪️Largest Forest Cover ( Area wise):-
1. MP
2.Arunachal Pradesh
3.Chhattisgarh
4.Odisha
5.Maharashtra
▪️Total Forest Cover ( %age of total GA) : Top five States are
▫️Mizoram (84.53%)
▫️Arunachal Pradesh (79.33%)
▫️Meghalaya (76.00%)
▫️Manipur (74.34%)
▫️Nagaland(73.90%)
▪️Total mangrove cover- 4,992 sq km.
Join @UPSCPrelimszone
@civilservicesBaba
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✅ APEC का मतलब एशिया-पैसिफिक इकोनॉमिक कोऑपरेशन है और यह एक रीजनल इकोनॉमिक फोरम है, जिसे साल 1989 में स्थापित किया गया था। इसका मुख्य उद्देश्य बढ़ती निर्भरता का लाभ प्रदान करना है। @civilservicesBaba
✅ APEC का उद्देश्य समावेशी, टिकाऊ, अभिनव और सुरक्षित विकास को बढ़ावा देने की मदद से अधिक से अधिक समृद्धि बनाना है।
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Bonn Convention: The Convention on the Conservation of Migratory Species of Wild Animals, also known as the Convention on Migratory Species (CMS) or the Bonn Convention, is an international agreement that aims to conserve migratory species within their migratory ranges. India is a signatory to this Convention.
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Arrange the following in chronological order:
1. Warren Hastings
2. Clive
3. Lord Cornwallis
4. Lord Wellesley
(A) 4, 3, 2, 1
(B) 1, 2, 3, 4
(C) 3, 1, 4, 2
(D) 2, 1, 3, 4
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The Tropic of Cancer passes through how many states of India?
(A) 6
(B) 7
(C) 8
(D) 9
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What's Alpha- Cex?
Alpha - Cex is the first exchange with a DAO mechanism as its underlying mechanism worldwide.
We are committed to building an inclusive financial ecosystem with consensus, joint construction, and sharing of global retail investors.
Users offer liquidity and trading depth for the platform, and the platform gives shares to users and shares the revenue with users. The platform and users are equal, 90% of equities are held by users, and 10% are by teams & contributors.
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