Taxonomy for Mathematics Articles-12th Class: Difference between revisions
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!Chapters | !Chapters | ||
!Topics | !Topics | ||
!'''Article Creator Name''' | |||
!'''अध्याय''' | !'''अध्याय''' | ||
!विषय | !विषय | ||
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|'''''PART-I''''' | |'''''PART-I''''' | ||
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|Relations and Functions | |Relations and Functions | ||
|Types of Relations | |Types of Relations | ||
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|संबंध और फलन | |संबंध और फलन | ||
|[[संबंधों के प्रकार]] | |[[संबंधों के प्रकार]] | ||
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|Types of Functions | |Types of Functions | ||
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|[[फलनों के प्रकार]] | |[[फलनों के प्रकार]] | ||
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|Composition of Functions and Invertible Function | |Composition of Functions and Invertible Function | ||
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|[[फलनों का संयोजन तथा व्युत्क्रमणीय फलन]] | |[[फलनों का संयोजन तथा व्युत्क्रमणीय फलन]] | ||
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|Binary Operations | |Binary Operations | ||
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|[[द्वि-आधारी संक्रियाएँ]] | |[[द्वि-आधारी संक्रियाएँ]] | ||
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|Relations | |Relations | ||
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|[[संबंध]] | |[[संबंध]] | ||
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|Functions | |Functions | ||
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|[[फलन]] | |[[फलन]] | ||
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|Inverse Trignometric Functions | |Inverse Trignometric Functions | ||
|Basic Concepts | |Basic Concepts | ||
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|प्रतिलोम त्रिकोणमितीय फलन | |प्रतिलोम त्रिकोणमितीय फलन | ||
|[[आधारभूत संकल्पनाएँ]] | |[[आधारभूत संकल्पनाएँ]] | ||
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|Properties of Inverse Trigonometric Functions | |Properties of Inverse Trigonometric Functions | ||
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|[[प्रतिलोम त्रिकोणमितीय फलनों के गुणधर्म]] | |[[प्रतिलोम त्रिकोणमितीय फलनों के गुणधर्म]] | ||
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|Inverse of a function | |Inverse of a function | ||
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|[[फलन का प्रतिलोम]] | |[[फलन का प्रतिलोम]] | ||
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|Matrices | |Matrices | ||
|Matrix | |Matrix | ||
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|आव्यूह | |आव्यूह | ||
|[[आव्यूह]] | |[[आव्यूह]] | ||
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|Types of Matrices | |Types of Matrices | ||
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|[[आव्यूहों के प्रकार]] | |[[आव्यूहों के प्रकार]] | ||
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|Operations on Matrices | |Operations on Matrices | ||
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|[[आव्यूहों पर संक्रियाएँ]] | |[[आव्यूहों पर संक्रियाएँ]] | ||
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|Transpose of a Matrix | |Transpose of a Matrix | ||
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|[[आव्यूह का परिवर्त]] | |[[आव्यूह का परिवर्त]] | ||
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|Symmetric and Skew Symmetric Matrices | |Symmetric and Skew Symmetric Matrices | ||
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|[[सममित तथा विषम सममित आव्यूह]] | |[[सममित तथा विषम सममित आव्यूह]] | ||
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|Elementary Operation(Transformation) of a Matrix | |Elementary Operation(Transformation) of a Matrix | ||
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|[[आव्यूह पर प्रारंभिक संक्रिया(आव्यूह रूपांतरण)]] | |[[आव्यूह पर प्रारंभिक संक्रिया(आव्यूह रूपांतरण)]] | ||
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|Invertible Matrices | |Invertible Matrices | ||
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|[[व्युत्क्रमणीय आव्यूह]] | |[[व्युत्क्रमणीय आव्यूह]] | ||
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|Order of a matrix | |Order of a matrix | ||
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|[[आव्यूह की कोटि]] | |[[आव्यूह की कोटि]] | ||
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|Column matrix | |Column matrix | ||
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|[[स्तंभ आव्यूह]] | |[[स्तंभ आव्यूह]] | ||
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|Row matrix | |Row matrix | ||
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|[[पंक्ति आव्यूह]] | |[[पंक्ति आव्यूह]] | ||
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|Square matrix | |Square matrix | ||
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|[[वर्ग आव्यूह]] | |[[वर्ग आव्यूह]] | ||
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|Diagonal Matrix | |Diagonal Matrix | ||
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|[[विकर्ण आव्यूह]] | |[[विकर्ण आव्यूह]] | ||
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|Scalar matrix | |Scalar matrix | ||
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|[[अदिश आव्यूह]] | |[[अदिश आव्यूह]] | ||
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|Identity matrix | |Identity matrix | ||
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|[[तत्समक आव्यूह]] | |[[तत्समक आव्यूह]] | ||
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|zero matrix | |zero matrix | ||
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|[[शून्य आव्यूह]] | |[[शून्य आव्यूह]] | ||
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|Negative of a matrix | |Negative of a matrix | ||
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|[[आव्यूह का ऋण आव्यूह]] | |[[आव्यूह का ऋण आव्यूह]] | ||
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|Difference of matrices | |Difference of matrices | ||
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|[[आव्यूहों का अंतर]] | |[[आव्यूहों का अंतर]] | ||
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|Inverse matrix | |Inverse matrix | ||
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|[[आव्यूह का व्युत्क्रम]] | |[[आव्यूह का व्युत्क्रम]] | ||
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|Determinants | |Determinants | ||
|Determinant | |Determinant | ||
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|सारणिक | |सारणिक | ||
|[[सारणिक]] | |[[सारणिक]] | ||
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|Properties of Determinants | |Properties of Determinants | ||
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|[[सारणिकों के गुणधर्म]] | |[[सारणिकों के गुणधर्म]] | ||
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|Area of a Triangle | |Area of a Triangle | ||
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|[[त्रिभुज का क्षेत्रफल]] | |[[त्रिभुज का क्षेत्रफल]] | ||
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|Minors and Cofactors | |Minors and Cofactors | ||
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|[[उपसारणिक और सहखंड]] | |[[उपसारणिक और सहखंड]] | ||
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|Adjoint and Inverse of a Matrix | |Adjoint and Inverse of a Matrix | ||
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|[[आव्यूह के सहखंडज और व्युत्क्रम]] | |[[आव्यूह के सहखंडज और व्युत्क्रम]] | ||
| Line 207: | Line 241: | ||
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|Application of Determinants and Matrices | |Application of Determinants and Matrices | ||
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|[[सारणिकों और आव्यूहों के अनुप्रयोग]] | |[[सारणिकों और आव्यूहों के अनुप्रयोग]] | ||
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|Consistent system | |Consistent system | ||
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|[[संगत निकाय]] | |[[संगत निकाय]] | ||
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|Inconsistent system | |Inconsistent system | ||
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|[[असंगत निकाय]] | |[[असंगत निकाय]] | ||
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|Continuity and Differentiablity | |Continuity and Differentiablity | ||
|Continuity | |Continuity | ||
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|सांतत्य तथा अवकलनीयता | |सांतत्य तथा अवकलनीयता | ||
|[[सांतत्य]] | |[[सांतत्य]] | ||
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|Differentiability | |Differentiability | ||
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|[[अवकलनीयता]] | |[[अवकलनीयता]] | ||
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|Exponential and Logarithmic Functions | |Exponential and Logarithmic Functions | ||
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|[[चरघातांकी तथा लघूगणकीय फलन]] | |[[चरघातांकी तथा लघूगणकीय फलन]] | ||
| Line 243: | Line 283: | ||
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|Logarithmic Differentiation | |Logarithmic Differentiation | ||
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|[[लघूगणकीय अवकलन]] | |[[लघूगणकीय अवकलन]] | ||
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|Derivatives of Functions in Parametric Forms | |Derivatives of Functions in Parametric Forms | ||
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|[[फलनों के प्राचलिक रूपों के अवकलज]] | |[[फलनों के प्राचलिक रूपों के अवकलज]] | ||
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|Second Order Derivative | |Second Order Derivative | ||
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|[[द्वितीय कोटि का अवकलज]] | |[[द्वितीय कोटि का अवकलज]] | ||
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|Mean Value Theorem | |Mean Value Theorem | ||
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|[[माध्यमान प्रमेय]] | |[[माध्यमान प्रमेय]] | ||
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|Point of discontinuity | |Point of discontinuity | ||
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|[[असांतत्य का बिंदु]] | |[[असांतत्य का बिंदु]] | ||
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|Continuous function | |Continuous function | ||
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|[[संतत फलन]] | |[[संतत फलन]] | ||
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|Natural exponential function | |Natural exponential function | ||
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|[[प्राकृतिक चरघातांकी फलन]] | |[[प्राकृतिक चरघातांकी फलन]] | ||
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|Rolle's theorem | |Rolle's theorem | ||
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|[[रोले का प्रमेय]] | |[[रोले का प्रमेय]] | ||
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|Application of Derivatives | |Application of Derivatives | ||
|Rate of Change of Quantities | |Rate of Change of Quantities | ||
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|अवकलज के अनुप्रयोग | |अवकलज के अनुप्रयोग | ||
|[[राशियों के परिवर्तन की दर]] | |[[राशियों के परिवर्तन की दर]] | ||
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|Increasing and Decreasing Functions | |Increasing and Decreasing Functions | ||
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|[[वर्धमान और ह्रासमान फलन]] | |[[वर्धमान और ह्रासमान फलन]] | ||
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|Tangents and Normals | |Tangents and Normals | ||
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|[[स्पर्श रेखाएँ और अभिलंब]] | |[[स्पर्श रेखाएँ और अभिलंब]] | ||
| Line 309: | Line 360: | ||
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|Approximations | |Approximations | ||
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|[[सन्निकटन]] | |[[सन्निकटन]] | ||
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|Maxima and Minima | |Maxima and Minima | ||
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|[[उच्चतम और निम्नतम]] | |[[उच्चतम और निम्नतम]] | ||
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|PROOFS IN MATHEMATICS | |PROOFS IN MATHEMATICS | ||
|What is a Proof? | |What is a Proof? | ||
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|गणित में प्रमाण/उपपत्ति | |गणित में प्रमाण/उपपत्ति | ||
|[[प्रमाण/उपपत्ति क्या है ?]] | |[[प्रमाण/उपपत्ति क्या है ?]] | ||
|- | |- | ||
|'''''PART-II''''' | |'''''PART-II''''' | ||
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|Integrals | |Integrals | ||
|Integration as an Inverse Process of Differentiation | |Integration as an Inverse Process of Differentiation | ||
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|समाकलन | |समाकलन | ||
|[[समाकलन को अवकलन के व्युत्क्रम प्रक्रम के रूप में]] | |[[समाकलन को अवकलन के व्युत्क्रम प्रक्रम के रूप में]] | ||
| Line 339: | Line 395: | ||
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|Methods of Integration | |Methods of Integration | ||
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|[[समाकलन की विधियाँ]] | |[[समाकलन की विधियाँ]] | ||
| Line 345: | Line 402: | ||
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|Integrals of Some Particular Functions | |Integrals of Some Particular Functions | ||
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|[[कुछ विशिष्ट फलनों के समाकलन]] | |[[कुछ विशिष्ट फलनों के समाकलन]] | ||
| Line 351: | Line 409: | ||
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|Integration by Partial Fractions | |Integration by Partial Fractions | ||
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|[[आंशिक भिन्नों द्वारा समाकलन]] | |[[आंशिक भिन्नों द्वारा समाकलन]] | ||
| Line 357: | Line 416: | ||
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|Integration by Parts | |Integration by Parts | ||
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|[[खंडशः समाकलन]] | |[[खंडशः समाकलन]] | ||
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|Definite Integral | |Definite Integral | ||
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|[[निश्चित समाकलन]] | |[[निश्चित समाकलन]] | ||
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|Fundamental Theorem of Calculus | |Fundamental Theorem of Calculus | ||
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|[[कलन की आधारभूत प्रमेय]] | |[[कलन की आधारभूत प्रमेय]] | ||
| Line 375: | Line 437: | ||
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|Evaluation of Definite Integrals by Substitution | |Evaluation of Definite Integrals by Substitution | ||
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|[[प्रतिस्थापन द्वारा निश्चित समाकलनों का मान ज्ञात करना]] | |[[प्रतिस्थापन द्वारा निश्चित समाकलनों का मान ज्ञात करना]] | ||
| Line 381: | Line 444: | ||
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|Some Properties Definite Integrals | |Some Properties Definite Integrals | ||
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|[[निश्चित समकलनों के कुछ गुणधर्म]] | |[[निश्चित समकलनों के कुछ गुणधर्म]] | ||
| Line 387: | Line 451: | ||
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|Indefinite Integral | |Indefinite Integral | ||
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|[[अनिश्चित समाकलन]] | |[[अनिश्चित समाकलन]] | ||
| Line 393: | Line 458: | ||
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|Integral Calculus | |Integral Calculus | ||
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|[[समाकलन-गणित]] | |[[समाकलन-गणित]] | ||
| Line 399: | Line 465: | ||
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|Integration | |Integration | ||
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|[[समाकलन]] | |[[समाकलन]] | ||
| Line 405: | Line 472: | ||
|Application of Integrals | |Application of Integrals | ||
|Area under Simple Curves | |Area under Simple Curves | ||
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|समकलनों के अनुप्रयोग | |समकलनों के अनुप्रयोग | ||
|[[साधारण वक्रों के अंतर्गत क्षेत्रफल]] | |[[साधारण वक्रों के अंतर्गत क्षेत्रफल]] | ||
| Line 411: | Line 479: | ||
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|Area between Two Curves | |Area between Two Curves | ||
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|[[दो वक्रों के मध्यवर्ती क्षेत्र का क्षेत्रफल]] | |[[दो वक्रों के मध्यवर्ती क्षेत्र का क्षेत्रफल]] | ||
| Line 417: | Line 486: | ||
|Differential Equations | |Differential Equations | ||
|Basic Concepts | |Basic Concepts | ||
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|अवकल समीकरण | |अवकल समीकरण | ||
|[[आधारभूत संकल्पनाएँ]] | |[[आधारभूत संकल्पनाएँ]] | ||
| Line 423: | Line 493: | ||
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|General and Particular Solution of a Differential Equations | |General and Particular Solution of a Differential Equations | ||
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|[[अवकलन समीकरण का व्यापक एवं विशिष्ट हल]] | |[[अवकलन समीकरण का व्यापक एवं विशिष्ट हल]] | ||
| Line 429: | Line 500: | ||
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|Formation of a Differential Equation whose General Equation is given | |Formation of a Differential Equation whose General Equation is given | ||
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|[[दिए हुए व्यापक हल वाले अवकल समीकरण का निर्माण]] | |[[दिए हुए व्यापक हल वाले अवकल समीकरण का निर्माण]] | ||
| Line 435: | Line 507: | ||
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|Methods of Solving First Order, First Degree Differential Equations | |Methods of Solving First Order, First Degree Differential Equations | ||
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|[[प्रथम कोटि एवं प्रथम घात के अवकल समीकरणों को हल करने की विधियाँ]] | |[[प्रथम कोटि एवं प्रथम घात के अवकल समीकरणों को हल करने की विधियाँ]] | ||
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|Differential Equation | |Differential Equation | ||
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|[[अवकल समीकरण]] | |[[अवकल समीकरण]] | ||
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|Vector Algebra | |Vector Algebra | ||
|Some Basic Concepts | |Some Basic Concepts | ||
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|सदिश बीजगणित | |सदिश बीजगणित | ||
|[[कुछ आधारभूत संकल्पनाएँ]] | |[[कुछ आधारभूत संकल्पनाएँ]] | ||
| Line 453: | Line 528: | ||
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|Types of Vectors | |Types of Vectors | ||
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|[[सदिशों के प्रकार]] | |[[सदिशों के प्रकार]] | ||
| Line 459: | Line 535: | ||
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|Addition of Vectors | |Addition of Vectors | ||
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|[[सदिशों का योगफल]] | |[[सदिशों का योगफल]] | ||
| Line 465: | Line 542: | ||
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|Multiplication of Vector by a Scalar | |Multiplication of Vector by a Scalar | ||
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|[[एक अदिश से सदिश का गुणन]] | |[[एक अदिश से सदिश का गुणन]] | ||
| Line 471: | Line 549: | ||
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|Product of Two Vectors | |Product of Two Vectors | ||
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|[[दो सदिशों का गुणनफल]] | |[[दो सदिशों का गुणनफल]] | ||
| Line 477: | Line 556: | ||
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|Scalars | |Scalars | ||
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|[[अदिश]] | |[[अदिश]] | ||
| Line 483: | Line 563: | ||
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|Vectors | |Vectors | ||
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|[[सदिश]] | |[[सदिश]] | ||
| Line 489: | Line 570: | ||
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|Position vector | |Position vector | ||
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|[[स्थिति सदिश]] | |[[स्थिति सदिश]] | ||
| Line 495: | Line 577: | ||
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|Direction cosines | |Direction cosines | ||
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|[[दिक्-कोसाइन]] | |[[दिक्-कोसाइन]] | ||
| Line 501: | Line 584: | ||
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|zero vector | |zero vector | ||
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|[[शून्य सदिश (गणितीय परिपेक्ष)]] | |[[शून्य सदिश (गणितीय परिपेक्ष)]] | ||
| Line 507: | Line 591: | ||
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|Unit vector | |Unit vector | ||
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|[[मात्रक सदिश]] | |[[मात्रक सदिश]] | ||
| Line 513: | Line 598: | ||
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|Co-initial vectors | |Co-initial vectors | ||
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|[[सह-आदिम सदिश]] | |[[सह-आदिम सदिश]] | ||
| Line 519: | Line 605: | ||
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|Collinear vectors | |Collinear vectors | ||
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|[[संरेख सदिश]] | |[[संरेख सदिश]] | ||
| Line 525: | Line 612: | ||
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|Equal vectors | |Equal vectors | ||
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|[[समान सदिश]] | |[[समान सदिश]] | ||
| Line 531: | Line 619: | ||
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|Negative of a vector | |Negative of a vector | ||
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|[[ऋणात्मक सदिश]] | |[[ऋणात्मक सदिश]] | ||
| Line 537: | Line 626: | ||
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|Triangle law of vector addition | |Triangle law of vector addition | ||
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|[[सदिश योग का त्रिभुज नियम]] | |[[सदिश योग का त्रिभुज नियम]] | ||
| Line 543: | Line 633: | ||
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|Parallelogram law of vector addition | |Parallelogram law of vector addition | ||
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|[[सदिश योग का समांतर चतुर्भुज नियम]] | |[[सदिश योग का समांतर चतुर्भुज नियम]] | ||
| Line 549: | Line 640: | ||
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|Projection vector | |Projection vector | ||
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|[[प्रक्षेप सदिश]] | |[[प्रक्षेप सदिश]] | ||
| Line 555: | Line 647: | ||
|Three Dimensional Geometry | |Three Dimensional Geometry | ||
|Direction Cosines and Direction Ratios of a Line | |Direction Cosines and Direction Ratios of a Line | ||
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|त्रि-विमीय ज्यामिति | |त्रि-विमीय ज्यामिति | ||
|[[रेखा के दिक्-कोज्या व दिक्- अनुपात]] | |[[रेखा के दिक्-कोज्या व दिक्- अनुपात]] | ||
| Line 561: | Line 654: | ||
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|Equation of a Line in Space | |Equation of a Line in Space | ||
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|[[अंतरिक्ष में रेखा का समीकरण]] | |[[अंतरिक्ष में रेखा का समीकरण]] | ||
| Line 567: | Line 661: | ||
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|Angle between Two Lines | |Angle between Two Lines | ||