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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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#River_India
PENISULAR RIVER SYSTEM
▪️ The Penisular rivers are much older than Himalayan Rivers.
▪️ Penisular Rivers are Non - Perennial Rivers.
▪️ Rivers have reached their Mature stage and have almost reached the Base level.
▪️ Characterised by Broad and shallow valleys.
▪️ Water divide in Penisular rivers forms by Western ghats.
▪️ Velocity and load carrying capacity is low due to Low gradient.
▪️ East flowing rivers make deltas at their mouth while West flowing rivers make Estuaries.
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📣 Recruitment Notification:
Himachal Pradesh Judicial Services Exam
▪️Total Posts - 17
▪️Apply by - 12th May
▪️Eligibility - LLB
▪️Pay Scale - Level J-1
(Basic - 77,840)
✅ Exam Dates
▪️Prelims - 9th July
▪️Mains - 19th August
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📣 EPFO EO/AO & APFC
Exam on 02nd July, 2023
▪️EO/AO - 9.30 to 11.30 AM
▪️APFC - 2 PM to 4 PM
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📣 BPSC Vacancy Notification : Assistant Divisional Fire Officer
✅ Total Post: 21
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ALL REPORTS & INDICES 2022&2023 - If you read this pdf compulsory you can score 4 marks in GS PRELIMS 2023. Meticulously made content for Prelims 2023 UPSC/TSPSC/APPSC.
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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
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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.
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ALL MINISTRY-WISE GOVT SCHEMES FROM 2019-2023, Source: Respective ministry websites. If you read this content-Your Govt schemes preparation is completed.
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• The work on the strategic 14.5 km long Zojila tunnel, an all-weather connection between the Kashmir valley and the Ladakh region - is going on at a rapid pace and over 40 per cent of the drilling has been completed,
• It will pass under the Zojila Pass in the Himalayas between Ganderbal in Kashmir and Drass town in Kargil district of Ladakh.
• Z-Morh Tunnel is a part of the Zojila tunnel project.
• Z-Morh tunnel, which connects Gagangir with Sonamarg and provides all-weather connectivity to the resort in the Ganderbal district of central Kashmir, will be inaugurated in October this year.
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Clean Plant program
✅With the demand for foreign planting materials of fruits like apples, avocados and blueberries rising over the years, the Central government plans to set up 10 ‘Clean Plant Centres’
✅Objective: To boost domestic production of the selected fruit crops
✅Services offered: disease diagnostic, therapeutics, multiplying of plants and generation of mother plants
✅Need for ‘Clean plant program’: Currently, it is difficult to get disease-free and genuine planting materials for horticultural crops in India.
✅Also, the process of importing plants is very cumbersome, as the imported plants must be kept in quarantine for two years.
✅Nodal Ministry: Ministry of Agriculture and Farmers Welfare
✅Implementing agency: National Horticulture Board (NHB)
✅Funding: 100% be Central government
✅It will be set up under the ‘Atmanirbhar Clean Plant Program’ (announced in Budget 2023-24)
