{"id":67834,"date":"2024-08-11T10:53:38","date_gmt":"2024-08-11T05:23:38","guid":{"rendered":"https:\/\/www.seminarsonly.com\/news\/?p=67834"},"modified":"2024-08-11T12:20:35","modified_gmt":"2024-08-11T06:50:35","slug":"21mat21-model-question-paper-with-answers","status":"publish","type":"post","link":"https:\/\/seminarsonly.com\/news\/21mat21-model-question-paper-with-answers\/","title":{"rendered":"21mat21 Model Question Paper with Answers"},"content":{"rendered":"

21mat21 Model Question Paper with Answers<\/span><\/h1>\n

If you are looking for “21mat21 Model Question Paper” then these are the top 10 pages, where you can get your previous years Question Paper “with Answers” at ease.<\/strong><\/em><\/p>\n

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Model Question Paper-I with effect from 2021<\/a><\/h3>\n
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https:\/\/vtu.ac.in \u203a pdf \u203a 21MAT21set1<\/span><\/cite><\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Model Question Paper<\/em>-I with effect from 2021. USN. Second Semester B.E Degree Examination. Advanced Calculus and Numerical Methods (21MAT21<\/em>). TIME: 03 Hours.<\/div>\n<\/div>\n
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VTU Advanced Calculus and Numerical Methods Question …<\/a><\/h3>\n
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https:\/\/www.vturesource.com\u00a0\u203a … \u203a 2 SEM<\/span><\/cite><\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Download<\/em>\u00a0VTU Advanced Calculus and Numerical Methods of 2nd semester Physics Cycle with subject code\u00a021MAT21<\/em>\u00a02021 scheme\u00a0Question Papers<\/em>.<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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model question paper ug & pg<\/a><\/h3>\n
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https:\/\/vtu.ac.in \u203a model-question-paper-b-e-b-tech-b-arch<\/span><\/cite><\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Model Question paper<\/em>\u00a0B.E\/B.Tech\/B.Arch Program 1st & 2nd semester (2021 scheme ). 1. 21MAT11 Calculus and Linear Algebra.<\/div>\n<\/div>\n<\/div>\n
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VTU Model Question Paper of B.E. \/ B.Tech 1st and 2nd …<\/a><\/h3>\n
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https:\/\/www.forum.universityupdates.in \u203a threads \u203a vtu-…<\/span><\/cite><\/div>\n<\/div>\n<\/div>\n<\/div>\n
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25 Jan 2022\u00a0\u2014\u00a0<\/span>VTU\u00a0Model Question Paper<\/em>\u00a0of B.E. \/ B.Tech 1st …\u00a021MAT21<\/em>\u00a0Advanced Calculus and Numerical Methods …\u00a0pdf<\/em>. 210.7 KB \u00b7 Views: 3,752. 21ELN24set2.pdf<\/em>.<\/div>\n<\/div>\n<\/div>\n
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21mat21 Model Question Paper<\/span><\/h2>\n

Visvesvaraya Technological University<\/strong><\/p>\n

Second Semester B.E.\/B.Tech. Examination, (Year) \/ (Month)<\/strong><\/p>\n

Advanced Calculus and Numerical Methods<\/strong><\/p>\n

Subject Code: 21MAT21<\/strong><\/p>\n

Time: 3 Hours<\/strong><\/p>\n

Max. Marks: 100<\/span><\/strong><\/p>\n

Note:<\/span><\/strong> Answer any <\/span>FIVE<\/span><\/strong> full questions, choosing at least <\/span>ONE<\/span><\/strong> question from each module.<\/span><\/p>\n

Module – 1<\/span><\/strong><\/h3>\n
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  1. \n

    a. Find the<\/span> directional derivative of \u03d5 = x^2yz + 4xz^2 at the point (1,-2,-1) in the direction of the vector 2i – j – 2k. (06 Marks) b. If F = (x + y + 1)i + j – (x + y)k, show that F.curl F = 0. (07 Marks) c. Verify Green’s theorem for \u222b_C [(xy + y^2)dx + x^2dy], where C is the closed curve bounded by y = x and y = x^2. (07 Marks)<\/strong><\/p>\n

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    a. Find the constants a, b, and c such that the vector F = (axy – z^3)i + (bx^2 + z)j + (bxz^2 + cy)k is irrotational. Also, find the scalar potential function \u03d5 such that F = \u2207\u03d5. (06 Marks) b. Using Gauss divergence theorem, evaluate \u222c_S F.n dS where F = 4xi – 2y^2j + z^2k and S is the surface bounded by the region x^2 + y^2 = 4, z = 0 and z = 3. (07 Marks) c. Verify Stoke’s theorem for F = (2x – y)i – yz^2j – y^2zk, where S is the upper half surface of the sphere x^2 + y^2 + z^2 = 1 and C is its boundary. (07 Marks)<\/strong><\/p>\n<\/li>\n<\/ol>\n

    Module – 2<\/strong><\/h3>\n
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      a. Solve \u2202^2z\/\u2202x^2 – \u2202^2z\/\u2202x\u2202y – 2\u2202^2z\/\u2202y^2 = sin(x + 2y). (06 Marks) b. Solve the equation \u2202u\/\u2202t = a^2 \u2202^2u\/\u2202x^2 subject to the conditions: i) u is not infinite as t \u2192 \u221e ii) u = 0 when x = 0 and x = l for all t iii) u = lx – x^2 when t = 0 and 0 < x < l. (07 Marks) c. Derive one dimensional wave equation in the standard form. (07 Marks)<\/strong><\/p>\n<\/li>\n

    2. \n

      a. Form the partial differential equation by eliminating the arbitrary functions f and g from z = f(x + ct) + g(x – ct). (06 Marks) b. Solve (\u2202^2z\/\u2202x\u2202y) = sin x sin y for which \u2202z\/\u2202y = -cos y when x = 0 and z = 0 when y is an odd multiple of \u03c0\/2. (07 Marks) c. Obtain the solution of two-dimensional Laplace’s equation by the method of separation of variables. (07 Marks)<\/strong><\/p>\n<\/li>\n<\/ol>\n

      Module – 3<\/strong><\/h3>\n
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      1. \n

        a. Find the real root of the equation x log_10 x = 1.2 by Regula-Falsi method correct to four decimal places. (06 Marks) b. Apply Gauss-Seidel iteration method to solve the equations: 20x + y – 2z = 17 3x + 20y – z = -18 2x – 3y + 20z = 25. (07 Marks) c. Find the largest eigenvalue and the corresponding eigenvector of the matrix A = [[2,-1,0],[-1,2,-1],[0,-1,2]] by power method, taking the initial eigenvector as [1, 1, 1]^T. (07 Marks)<\/p>\n<\/li>\n

      2. \n

        a. Using Newton-Raphson method, find the real root of the equation 3x = cos x + 1 near x = 0.5 correct to four decimal places. (06 Marks) b. Using Relaxation method, solve the following system of linear equations: 9x – 2y + z = 50 x + 5y – 3z = 18 -2x + 2y + 7z = 19. (07 Marks) c. Using Rayleigh’s power method, find the smallest eigenvalue and the corresponding eigenvector of the matrix A = [[4,1,0],[1,20,1],[0,1,4]] by taking the initial approximation as [1, 0, 0]^T. (07 Marks)<\/strong><\/p>\n<\/li>\n<\/ol>\n

        Module – 4<\/strong><\/h3>\n
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        1. a. From the following table of values of x and y, obtain dy\/dx and d^2y\/dx^2 for x = 1.2.<\/li>\n<\/ol>\n\n\n\n\n
          x<\/th>\n1.0<\/th>\n1.2<\/th>\n1.4<\/th>\n1.6<\/th>\n1.8<\/th>\n2.0<\/th>\n2.2<\/th>\n<\/tr>\n
          y<\/td>\n2.7183<\/td>\n3.3201<\/td>\n4.0552<\/td>\n4.9530<\/td>\n6.0496<\/td>\n7.3891<\/td>\n9.0250<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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          (06 Marks)<\/strong><\/p>\n

          b. Evaluate \u222b_0^6 dx\/(1 + x^2) by using: i) Trapezoidal rule ii) Simpson’s 1\/3 rule iii) Simpson’s 3\/8 rule. (07 Marks) c. Using Euler’s modified method, solve the initial value problem dy\/dx = log_e(x + y), y(0) = 2 to find y(0.2) and y(0.4) by taking h = 0.2. (07 Marks)<\/p>\n

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          1. a. The following table gives the values of density of saturated water for various temperatures of saturated steam.<\/span><\/li>\n<\/ol>\n
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            Temperature<\/span> (\u00b0C)<\/th>\n100<\/th>\n150<\/th>\n200<\/th>\n250<\/th>\n300<\/th>\n<\/tr>\n
            Density (kg\/m^3)<\/td>\n958<\/td>\n917<\/td>\n865<\/td>\n799<\/td>\n712<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n

            Find by Newton’s divided difference formula, the density of water when the saturated steam temperature is 175\u00b0C. (06 Marks) b. Evaluate \u222b_0^1 e^x dx by taking six equal strips using Weddle’s rule. (07 Marks) c. Apply Runge-Kutta method of fourth order to find an approximate value of y when x = 0.2 given that dy\/dx = x + y and y = 1 when x = 0. (07 Marks)<\/strong><\/p>\n

            Module – 5<\/strong><\/h3>\n
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              a. Find by Taylor’s series method the value of y at x = 0.1 to five places of decimals from dy\/dx = x^2y – 1, y(0) = 1. (06 Marks) b. Solve numerically using Milne’s predictor-corrector method the differential equation dy\/dx = 1\/(x + y) with initial conditions y(0) = 2, y(0.2) = 2.0933, y(0.4) = 2.1755, y(0.6) = 2.2493 to compute y(0.8). (07 Marks) c. Solve the equation \u2202u\/\u2202t = \u2202^2u\/\u2202x^2 subject to the conditions u(x, 0) = sin \u03c0x, 0 \u2264 x \u2264 1; u(0, t) = u(1, t) = 0 using Bender-Schmidt method, taking h = 1\/3 and k = 1\/36. (07 Marks)<\/strong><\/p>\n<\/li>\n

            2. \n

              a. Using modified Euler’s method, find an approximate value of y when x = 0.3 given that dy\/dx = x + y and y = 1 when x = 0. (06 Marks)<\/p>\n<\/li>\n<\/ol>\n

              b. Use Milne’s method to find y(0.8) given that dy\/dx = (1 + y^2)\/x with y(0.4) = 1, y(0.5) = 1.1114, y(0.6) = 1.25, y(0.7) = 1.4286. (07 Marks)<\/p>\n

              c. Solve \u2202^2u\/\u2202t^2 = \u2202^2u\/\u2202x^2, 0 < x < 1, t > 0 given u(x, 0) = 0, \u2202u\/\u2202t (x, 0) = 0 for 0 < x < 1, u(0, t) =<\/p>\n

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              21 Mat 21 | PDF<\/a><\/h3>\n
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              https:\/\/www.scribd.com \u203a document \u203a 21mat21<\/span><\/cite><\/div>\n<\/div>\n<\/div>\n<\/div>\n
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              The\u00a0question paper<\/em>\u00a0will have ten questions. Each question is set for 20 marks. 2. There will be 2 questions from each module. Each of the two questions under a\u00a0…<\/div>\n<\/div>\n<\/div>\n
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              Question Paper with Solution Maths<\/a><\/h3>\n
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              https:\/\/klsvdit.edu.in \u203a ae_global_templates=question-pa…<\/span><\/cite><\/div>\n<\/div>\n<\/div>\n<\/div>\n
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              Advanced Calculus and Numerical Methods (18MAT21):\u00a0Paper<\/em>-1\u00a0Paper<\/em>-2\u00a0Paper<\/em>-3\u00a0Paper<\/em>-4. Transform Calculus, Fourier Series and Numerical Techniques (21MAT31):\u00a0…<\/div>\n<\/div>\n
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              21MAT21 Advanced Calculus and Numerical Methods<\/a><\/h3>\n
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              https:\/\/vtupulse.com \u203a First Year CBCS Notes<\/span><\/cite><\/div>\n<\/div>\n<\/div>\n<\/div>\n
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              VTU Semester End Exam and\u00a0Model Question Papers<\/em>. Summary. Here you can\u00a0download<\/em>\u00a0the\u00a021MAT21<\/em>\u00a0Advanced Calculus and Numerical Methods VTU Notes and question\u00a0…<\/div>\n<\/div>\n
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              21MAT21 – Solution of Model Question Paper – II<\/a><\/h3>\n
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              https:\/\/www.scribd.com \u203a document \u203a 21MAT21-solutio…<\/span><\/cite><\/div>\n<\/div>\n<\/div>\n<\/div>\n
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              21MAT21<\/em>– solution of\u00a0model question paper<\/em>\u00a0-II (1) – Free\u00a0download<\/em>\u00a0as\u00a0PDF<\/em>\u00a0File (.pdf<\/em>) or read online for free.\u00a0Question paper<\/em>.<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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              21mat21 Model Question Paper with Answers If you are looking for “21mat21 Model Question Paper” then these are the top 10 pages, where you can get your previous years Question…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5921],"tags":[],"class_list":["post-67834","post","type-post","status-publish","format-standard","hentry","category-india"],"yoast_head":"\n21mat21 Model Question Paper with Answers - Seminarsonly.com<\/title>\n<meta name=\"description\" content=\"If you are looking for "21mat21 Model Question Paper" then these are the top 10 pages, where you can get your previous years Question Paper "with Answers" at ease.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/seminarsonly.com\/news\/21mat21-model-question-paper-with-answers\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"21mat21 Model Question Paper with Answers\" \/>\n<meta property=\"og:description\" content=\"If you are looking for "21mat21 Model Question Paper" then these are the top 10 pages, where you can get your previous years Question Paper "with Answers" at ease.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/seminarsonly.com\/news\/21mat21-model-question-paper-with-answers\/\" \/>\n<meta property=\"og:site_name\" content=\"Seminarsonly.com\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/facebook.com\/seminarsonly\" \/>\n<meta property=\"article:published_time\" content=\"2024-08-11T05:23:38+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-08-11T06:50:35+00:00\" \/>\n<meta name=\"author\" content=\"Freddy John\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@seminarsonly\" \/>\n<meta name=\"twitter:site\" content=\"@seminarsonly\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Freddy John\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"6 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/seminarsonly.com\/news\/21mat21-model-question-paper-with-answers\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/seminarsonly.com\/news\/21mat21-model-question-paper-with-answers\/\"},\"author\":{\"name\":\"Freddy John\",\"@id\":\"https:\/\/seminarsonly.com\/news\/#\/schema\/person\/75cf706896b7210fb0a84651adc258bd\"},\"headline\":\"21mat21 Model Question Paper with Answers\",\"datePublished\":\"2024-08-11T05:23:38+00:00\",\"dateModified\":\"2024-08-11T06:50:35+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/seminarsonly.com\/news\/21mat21-model-question-paper-with-answers\/\"},\"wordCount\":1125,\"articleSection\":[\"India\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/seminarsonly.com\/news\/21mat21-model-question-paper-with-answers\/\",\"url\":\"https:\/\/seminarsonly.com\/news\/21mat21-model-question-paper-with-answers\/\",\"name\":\"21mat21 Model Question Paper with Answers - 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