Taxonomy for Mathematics Articles-12th Class: Difference between revisions
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|Relations | |Relations | ||
| | |Ramamurthy | ||
Mani | |||
| | | | ||
|[[संबंध]] | |[[संबंध]] | ||
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|Functions | |Functions | ||
| | |Ramamurthy | ||
Mani | |||
| | | | ||
|[[फलन]] | |[[फलन]] | ||
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|Inverse Trignometric Functions | |Inverse Trignometric Functions | ||
|Basic Concepts | |Basic Concepts | ||
| | |Mani | ||
|प्रतिलोम त्रिकोणमितीय फलन | |प्रतिलोम त्रिकोणमितीय फलन | ||
|[[आधारभूत संकल्पनाएँ]] | |[[आधारभूत संकल्पनाएँ]] | ||
| Line 81: | Line 83: | ||
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|Properties of Inverse Trigonometric Functions | |Properties of Inverse Trigonometric Functions | ||
| | |Mani | ||
| | | | ||
|[[प्रतिलोम त्रिकोणमितीय फलनों के गुणधर्म]] | |[[प्रतिलोम त्रिकोणमितीय फलनों के गुणधर्म]] | ||
| Line 88: | Line 90: | ||
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|Inverse of a function | |Inverse of a function | ||
| | |Mani | ||
| | | | ||
|[[फलन का प्रतिलोम]] | |[[फलन का प्रतिलोम]] | ||
| Line 127: | Line 129: | ||
| | | | ||
|Symmetric and Skew Symmetric Matrices | |Symmetric and Skew Symmetric Matrices | ||
| | |Mani | ||
| | | | ||
|[[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 | ||
| | |Mani | ||
| | | | ||
|[[आव्यूह पर प्रारंभिक संक्रिया(आव्यूह रूपांतरण)]] | |[[आव्यूह पर प्रारंभिक संक्रिया(आव्यूह रूपांतरण)]] | ||
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|Order of a matrix | |Order of a matrix | ||
| | |Mani | ||
| | | | ||
|[[आव्यूह की कोटि]] | |[[आव्यूह की कोटि]] | ||
|- | |- | ||
| | | | ||
| | | | ||
|Negative of a matrix | |Negative of a matrix | ||
| | |Mani | ||
| | | | ||
|[[आव्यूह का ऋण आव्यूह]] | |[[आव्यूह का ऋण आव्यूह]] | ||
| Line 212: | Line 165: | ||
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|Difference of matrices | |Difference of matrices | ||
| | |Mani | ||
| | | | ||
|[[आव्यूहों का अंतर]] | |[[आव्यूहों का अंतर]] | ||
|- | |- | ||
|4 | |4 | ||
| Line 241: | Line 187: | ||
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| | | | ||
|Area of a Triangle | |Area of a Triangle - Determinants | ||
| | |Ramamurthy | ||
Mani | |||
| | | | ||
|[[त्रिभुज का क्षेत्रफल - सारणिक]] | |[[त्रिभुज का क्षेत्रफल - सारणिक]] | ||
| Line 257: | Line 204: | ||
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|Adjoint and Inverse of a Matrix | |Adjoint and Inverse of a Matrix | ||
| | |Ramamurthy | ||
Mani | |||
| | | | ||
|[[आव्यूह के सहखंडज और व्युत्क्रम]] | |[[आव्यूह के सहखंडज और व्युत्क्रम]] | ||
| Line 264: | Line 212: | ||
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|Application of Determinants and Matrices | |Application of Determinants and Matrices | ||
| | |Mani | ||
| | | | ||
|[[सारणिकों और आव्यूहों के अनुप्रयोग]] | |[[सारणिकों और आव्यूहों के अनुप्रयोग]] | ||
|- | |- | ||
|5 | |5 | ||
|Continuity and Differentiablity | |Continuity and Differentiablity | ||
|Continuity | |Continuity | ||
| | |Mani | ||
|सांतत्य तथा अवकलनीयता | |सांतत्य तथा अवकलनीयता | ||
|[[सांतत्य]] | |[[सांतत्य]] | ||
| Line 292: | Line 226: | ||
| | | | ||
|Differentiability | |Differentiability | ||
| | |Mani | ||
| | | | ||
|[[अवकलनीयता]] | |[[अवकलनीयता]] | ||
| Line 299: | Line 233: | ||
| | | | ||
|Exponential and Logarithmic Functions | |Exponential and Logarithmic Functions | ||
| | |Mani | ||
| | | | ||
|[[चरघातांकी तथा लघूगणकीय फलन]] | |[[चरघातांकी तथा लघूगणकीय फलन]] | ||
| Line 306: | Line 240: | ||
| | | | ||
|Logarithmic Differentiation | |Logarithmic Differentiation | ||
| | |Mani | ||
| | | | ||
|[[लघूगणकीय अवकलन]] | |[[लघूगणकीय अवकलन]] | ||
| Line 313: | Line 247: | ||
| | | | ||
|Derivatives of Functions in Parametric Forms | |Derivatives of Functions in Parametric Forms | ||
| | |Mani | ||
| | | | ||
|[[फलनों के प्राचलिक रूपों के अवकलज]] | |[[फलनों के प्राचलिक रूपों के अवकलज]] | ||
| Line 320: | Line 254: | ||
| | | | ||
|Second Order Derivative | |Second Order Derivative | ||
| | |Mani | ||
| | | | ||
|[[द्वितीय कोटि का अवकलज]] | |[[द्वितीय कोटि का अवकलज]] | ||
| Line 327: | Line 261: | ||
| | | | ||
|Mean Value Theorem | |Mean Value Theorem | ||
| | |Mani | ||
| | | | ||
|[[माध्यमान प्रमेय]] | |[[माध्यमान प्रमेय]] | ||
|- | |- | ||
| | | | ||
| | | | ||
|Rolle's theorem | |Rolle's theorem | ||
| | |Mani | ||
| | | | ||
|[[रोले का प्रमेय]] | |[[रोले का प्रमेय]] | ||
| Line 362: | Line 275: | ||
|Application of Derivatives | |Application of Derivatives | ||
|Rate of Change of Quantities | |Rate of Change of Quantities | ||
| | |Mani | ||
|अवकलज के अनुप्रयोग | |अवकलज के अनुप्रयोग | ||
|[[राशियों के परिवर्तन की दर]] | |[[राशियों के परिवर्तन की दर]] | ||
| Line 369: | Line 282: | ||
| | | | ||
|Increasing and Decreasing Functions | |Increasing and Decreasing Functions | ||
| | |Mani | ||
| | | | ||
|[[वर्धमान और ह्रासमान फलन]] | |[[वर्धमान और ह्रासमान फलन]] | ||
| Line 376: | Line 289: | ||
| | | | ||
|Tangents and Normals | |Tangents and Normals | ||
| | |Mani | ||
| | | | ||
|[[स्पर्श रेखाएँ और अभिलंब]] | |[[स्पर्श रेखाएँ और अभिलंब]] | ||
| Line 383: | Line 296: | ||
| | | | ||
|Approximations | |Approximations | ||
| | |Mani | ||
| | | | ||
|[[सन्निकटन]] | |[[सन्निकटन]] | ||
| Line 390: | Line 303: | ||
| | | | ||
|Maxima and Minima | |Maxima and Minima | ||
| | |Mani | ||
| | | | ||
|[[उच्चतम और निम्नतम]] | |[[उच्चतम और निम्नतम]] | ||
|- | |- | ||
|'''''PART-II''''' | |'''''PART-II''''' | ||
| Line 411: | Line 317: | ||
|Integrals | |Integrals | ||
|Integration as an Inverse Process of Differentiation | |Integration as an Inverse Process of Differentiation | ||
| | |Mani | ||
|समाकलन | |समाकलन | ||
|[[समाकलन को अवकलन के व्युत्क्रम प्रक्रम के रूप में]] | |[[समाकलन को अवकलन के व्युत्क्रम प्रक्रम के रूप में]] | ||
| Line 418: | Line 324: | ||
| | | | ||
|Methods of Integration | |Methods of Integration | ||
| | |Mani | ||
| | | | ||
|[[समाकलन की विधियाँ]] | |[[समाकलन की विधियाँ]] | ||
| Line 425: | Line 331: | ||
| | | | ||
|Integrals of Some Particular Functions | |Integrals of Some Particular Functions | ||
| | |Mani | ||
| | | | ||
|[[कुछ विशिष्ट फलनों के समाकलन]] | |[[कुछ विशिष्ट फलनों के समाकलन]] | ||
| Line 432: | Line 338: | ||
| | | | ||
|Integration by Partial Fractions | |Integration by Partial Fractions | ||
| | |Mani | ||
| | | | ||
|[[आंशिक भिन्नों द्वारा समाकलन]] | |[[आंशिक भिन्नों द्वारा समाकलन]] | ||
| Line 439: | Line 345: | ||
| | | | ||
|Integration by Parts | |Integration by Parts | ||
| | |Mani | ||
| | | | ||
|[[खंडशः समाकलन]] | |[[खंडशः समाकलन]] | ||
| Line 446: | Line 352: | ||
| | | | ||
|Definite Integral | |Definite Integral | ||
| | |Mani | ||
| | | | ||
|[[निश्चित समाकलन]] | |[[निश्चित समाकलन]] | ||
| Line 453: | Line 359: | ||
| | | | ||
|Fundamental Theorem of Calculus | |Fundamental Theorem of Calculus | ||
| | |Mani | ||
| | | | ||
|[[कलन की आधारभूत प्रमेय]] | |[[कलन की आधारभूत प्रमेय]] | ||
|- | |- | ||
| | | | ||
| | | | ||
|Some Properties Definite Integrals | |Some Properties Definite Integrals | ||
| | |Mani | ||
| | | | ||
|[[निश्चित समकलनों के कुछ गुणधर्म]] | |[[निश्चित समकलनों के कुछ गुणधर्म]] | ||
| Line 474: | Line 373: | ||
| | | | ||
|Indefinite Integral | |Indefinite Integral | ||
| | |Mani | ||
| | | | ||
|[[अनिश्चित समाकलन]] | |[[अनिश्चित समाकलन]] | ||
|- | |- | ||
|9 | |9 | ||
|Application of Integrals | |Application of Integrals | ||
|Area under Simple Curves | |Area under Simple Curves | ||
| | |Mani | ||
|समकलनों के अनुप्रयोग | |समकलनों के अनुप्रयोग | ||
|[[साधारण वक्रों के अंतर्गत क्षेत्रफल]] | |[[साधारण वक्रों के अंतर्गत क्षेत्रफल]] | ||
| Line 502: | Line 387: | ||
| | | | ||
|Area between Two Curves | |Area between Two Curves | ||
| | |Mani | ||
| | | | ||
|[[दो वक्रों के मध्यवर्ती क्षेत्र का क्षेत्रफल]] | |[[दो वक्रों के मध्यवर्ती क्षेत्र का क्षेत्रफल]] | ||
| Line 509: | Line 394: | ||
|Differential Equations | |Differential Equations | ||
|Basic Concepts | |Basic Concepts | ||
| | |Mani | ||
|अवकल समीकरण | |अवकल समीकरण | ||
|[[आधारभूत संकल्पनाएँ]] | |[[आधारभूत संकल्पनाएँ]] | ||
| Line 516: | Line 401: | ||
| | | | ||
|General and Particular Solution of a Differential Equations | |General and Particular Solution of a Differential Equations | ||
| | |Mani | ||
| | | | ||
|[[अवकलन समीकरण का व्यापक एवं विशिष्ट हल]] | |[[अवकलन समीकरण का व्यापक एवं विशिष्ट हल]] | ||
| Line 523: | Line 408: | ||
| | | | ||
|Formation of a Differential Equation whose General Equation is given | |Formation of a Differential Equation whose General Equation is given | ||
| | |Mani | ||
| | | | ||
|[[दिए हुए व्यापक हल वाले अवकल समीकरण का निर्माण]] | |[[दिए हुए व्यापक हल वाले अवकल समीकरण का निर्माण]] | ||
| Line 530: | Line 415: | ||
| | | | ||
|Methods of Solving First Order, First Degree Differential Equations | |Methods of Solving First Order, First Degree Differential Equations | ||
| | |Mani | ||
| | | | ||
|[[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]] | ||
| Line 537: | Line 422: | ||
| | | | ||
|Differential Equation | |Differential Equation | ||
| | |Mani | ||
| | | | ||
|[[अवकल समीकरण]] | |[[अवकल समीकरण]] | ||
| Line 543: | Line 428: | ||
|11 | |11 | ||
|Vector Algebra | |Vector Algebra | ||
| | | | ||
| | | | ||
|सदिश बीजगणित | |सदिश बीजगणित | ||
| | | | ||
|- | |- | ||
| | | | ||
| | | | ||
|Types of Vectors | |Types of Vectors | ||
| | |Mani | ||
| | | | ||
|[[सदिशों के प्रकार]] | |[[सदिशों के प्रकार]] | ||
| Line 558: | Line 443: | ||
| | | | ||
|Addition of Vectors | |Addition of Vectors | ||
| | |Mani | ||
| | | | ||
|[[सदिशों का योगफल]] | |[[सदिशों का योगफल]] | ||
| Line 565: | Line 450: | ||
| | | | ||
|Multiplication of Vector by a Scalar | |Multiplication of Vector by a Scalar | ||
| | |Mani | ||
| | | | ||
|[[एक अदिश से सदिश का गुणन]] | |[[एक अदिश से सदिश का गुणन]] | ||
| Line 572: | Line 457: | ||
| | | | ||
|Product of Two Vectors | |Product of Two Vectors | ||
| | |Mani | ||
| | | | ||
|[[दो सदिशों का गुणनफल]] | |[[दो सदिशों का गुणनफल]] | ||
| Line 579: | Line 464: | ||
| | | | ||
|Scalars | |Scalars | ||
| | |Mani | ||
| | | | ||
|[[अदिश]] | |[[अदिश]] | ||
| Line 586: | Line 471: | ||
| | | | ||
|Vectors | |Vectors | ||
| | |Mani | ||
| | | | ||
|[[सदिश]] | |[[सदिश]] | ||
| Line 593: | Line 478: | ||
| | | | ||
|Position vector | |Position vector | ||
| | |Mani | ||
| | | | ||
|[[स्थिति सदिश]] | |[[स्थिति सदिश]] | ||
| Line 600: | Line 485: | ||
| | | | ||
|Direction cosines | |Direction cosines | ||
| | |Mani | ||
| | | | ||
|[[दिक्-कोसाइन]] | |[[दिक्-कोसाइन]] | ||
|- | |- | ||
| | | | ||
| | | | ||
|Triangle law of vector addition | |Triangle law of vector addition | ||
| | |Mani | ||
| | | | ||
|[[सदिश योग का त्रिभुज नियम]] | |[[सदिश योग का त्रिभुज नियम]] | ||
| Line 656: | Line 499: | ||
| | | | ||
|Parallelogram law of vector addition | |Parallelogram law of vector addition | ||
| | |Mani | ||
| | | | ||
|[[सदिश योग का समांतर चतुर्भुज नियम]] | |[[सदिश योग का समांतर चतुर्भुज नियम]] | ||
|- | |- | ||
|12 | |12 | ||
|Three Dimensional Geometry | |Three Dimensional Geometry | ||
|Direction Cosines and Direction Ratios of a Line | |Direction Cosines and Direction Ratios of a Line | ||
| | |Mani | ||
|त्रि-विमीय ज्यामिति | |त्रि-विमीय ज्यामिति | ||
|[[रेखा के दिक्-कोज्या व दिक्- अनुपात]] | |[[रेखा के दिक्-कोज्या व दिक्- अनुपात]] | ||
| Line 677: | Line 513: | ||
| | | | ||
|Equation of a Line in Space | |Equation of a Line in Space | ||
| | |Mani | ||
| | | | ||
|[[अंतरिक्ष में रेखा का समीकरण]] | |[[अंतरिक्ष में रेखा का समीकरण]] | ||
| Line 684: | Line 520: | ||
| | | | ||
|Angle between Two Lines | |Angle between Two Lines | ||
| | |Mani | ||
| | | | ||
|[[दो रेखाओं के मध्य का कोण]] | |[[दो रेखाओं के मध्य का कोण]] | ||
| Line 691: | Line 527: | ||
| | | | ||
|Shortest Distance between Two Lines | |Shortest Distance between Two Lines | ||
| | |Mani | ||
| | | | ||
|[[दो रेखाओं के मध्य न्यूनतम दूरी]] | |[[दो रेखाओं के मध्य न्यूनतम दूरी]] | ||
| </ | |||