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Class 10th - Math Solution's NCERT 2020 Hindi on Windows Pc

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Last Updated: 2022-07-20

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Class 10th - Math Solution's NCERT 2020 Hindi for PC – Technical Specifications

Name	Class 10th - Math Solution's NCERT 2020 Hindi
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Here you will get UP Board class 10th Mathematics syllabus for the current academic session 2019-2020. This syllabus gives the details of the course structure and topics to be prepared throughout the session. With the updated Mathematics Syllabus of UP Board Class 10th, students can make the right study schedule and prepare accordingly to score well in the board examination 2020.
इकाई – 1 : संख्या पद्धित

(1) वास्तविक संख्याएँ

युक्लिड विभाजन प्रमेयिका, अंगणित का आवारभुत प्रमेय – उदाहरण सहित √2, √3, √5 अपरिमेय संख्याओं का सत्यापन, परिमेय संख्याओं का सांत/असांत आवर्ती दशमलव के पदों में निरूपण.

इकाई – 2 : बीजगणित

1. बहुपद- बहुपद के शुन्यांक. द्विघात बहुपदों के गुणांकों और शुन्यांको के मध्य सम्बन्ध. वास्तविक गुणांकों वाले बहुपदो के लिए विभाजन एल्गोरिथम का कथन तथा उस पर सामान्य प्रश्न.

2. दो चर वाले रैखिक समीकरण युग्म –

दो चरों में रैखिक समीकरण युग्म और रैखिक युग्म का ग्राफीय विधि से हल. एक रैखिक समीकरण युग्म को हल करने की बीजगणितीय विधि.

1. प्रतिस्थापन विधि

2. विलोपन विधि

3. वज्रगुणन विधि

दो चरों के रैखिक समीकरणों के युग्म में बदले जा सकने वाले समीकरण.

3. द्विघात समीकरण

मानक द्विघात समीकरण ax2+bx+c=0 (a≠0) द्विघात समीकरणों (केवल वास्तविक मूल) का द्विघात सूत्रों द्वारा, गुणनखण्ड द्वारा, पूर्ण वर्ग बनाकर हल निकालना. द्विघात समीकरण का विविवतकर और उनके मूलों की प्रकृति के बीच सम्बन्ध. द्विघात समीकरण के दिन-प्रतिदिन के अनप्रयोग तथा इन पर आधारित इबारती प्रश्न.

4. समान्तर श्रेणियाँ

समान्तर श्रेणी के nवें पद की व्यूत्पत्ति तथा समान्तर श्रेणी के प्रथम nपदों का योग. सामन्य जीवन पर आधारित प्रश्नों को हल करने के लिए इसका अनुप्रोयग.

इकाई – 3 : निर्देशांक ज्यामिति

1. रेखा (दिविमीय)-

निर्देशांक ज्यामिति की अवधारणा, रैखिक समीकरणों के ग्राफ, दुरी सूत्र, विभाजन सूत्र (आंतरिक विभाजन), त्रिभुज के क्षेत्रफल.

UP Board Exam 2019: Check Class 10th Mathematics Question Paper

इकाई – 4 : ज्यामिति

1. त्रिभुज –

समरूप त्रिभुज के परिभाषा, उदाहरण, प्रतिउदाहरण.

(क) त्रिभुज की एक भुजा के समान्तर खीची गयी रेखा त्रिभुज की शेष दो भुजाओं को समान अनुपात में विभाजित करती है.

(ख) त्रिभुज की दो भुजाओं को समान अनुपात में विभाजित करने वाली रेखा, तीसरी भुजा के समान्तर होती है.

(ग) यदि दो त्रिभुजों में संगत – भुजाओं का एक युग्म अनुपातिक हूर अंतरित कोण बराबर हो तो त्रिभुज समरूप होती है.

(घ) यदि दो त्रिभुजों में संगत कोणों का एक युग्म बराबर हो और उनकी संगत भुजाएँ अनुपातिक हो, तो त्रिभुज समरूप होते है.

(ड़) एक त्रिभुज का एक कोण, दुसरे त्रिभुज के संगत कोण के बराबर हो तथा उनकी संगत भुजाएँ अनुपातिक हो तो त्रिभुज समरूप होगा.

(च) यदि समकोण त्रिभुज के समकोण वाले शीर्ष से कर्ण पर लम्ब डाला गया हो, तो लम्ब रेखा के दोनों ओर के त्रिभुज परस्पर और मूल त्रिभुज के समरूप होते हैं.

(छ) समरूप त्रिभुजों के क्षेत्रफलों का अनुपात संगत भुजाओं के वर्गों के समानुपाती होता है.

(ज) एक समकोण त्रिभुज के कर्ण का वर्ग अन्य दो भुजाओं के वर्गों के योगफल के बराबर होता है.

(झ) किसी त्रिभुज में यदि एक भुजा का वर्ग अन्य दो भुजाओं के वर्गों के योगफल के बराबर हो, तो पहली भुजा के सामने का कोण समकोण होता है.

2. वृत्त – वृत्त की स्पर्श रेखा, स्पर्श बिन्दु

(क) वृत्त की स्पर्शरेखा, स्पर्श बिन्दु से होकर जाने वाली त्रिज्या पर लम्ब होती है.

(ख) किसी वाह्य बिन्दु से खिंची गई, दो स्पर्श रेखाओं की ल्म्बाइयां बराबर होती है.

3. रचनाएँ –

(क) दिए हुए रेखाखण्ड का दिये हुए अनुपात में विभाजित करना (आन्तरिक).

(ख) एक वृत्त के बाहर स्थित एक बिन्दु से उस पर स्पर्श रेखाओं की रचना करना.

(ग) एक दिए गये त्रिभुज के समरूप एक त्रिभुज की रचना करना.