...Sample Paper – 2011 Class – X Subject –Social Science Time: 3hours M.M.: 80 Instructions : 1. The question paper has 36 questions in all. All questions are compulsory. 2. Marks are indicated against each question. 3. This question paper consist of two parts i.e. Part I and Part II. Part I of the question paper contains Multiple Choice Questions (MCQs) from serial Number 1 to 16 of 1 mark each. These sixteen questions of Part I are to be answered on a separate sheet provided. This part has to be completed in first 30 minutes only and the answer sheet must be handed over to the invigilator before starting Part II. 4. In Part II, there are twenty questions from serial no. 17 to 36 which are to be attempted in 2 hours and 30 minutes. This part should be attempted the stipulated only after time given for Part I. 5. Questions from serial number 17 to 31 are 3 marks questions. Answer of these questions should not exceed 80 words each 6. Questions from serial number 32 to 35 are 4 marks questions. Answer of these questions should not exceed 100 words each 7. Question number 36 is a map question of 4 marks from Geography only. After completion, attach the map inside your answer book. ……………………………………………………………………………………………… Part I 1. To which century the spread of disease- carrying germs has been traced to? (a) 5th century (b) 7th century (c) 9th century (d) 11th century ...
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...Runge-Kutta method The formula for the fourth order Runge-Kutta method (RK4) is given below. Consider the problem y = f (t, y) y(t0 ) = α Define h to be the time step size and ti = t0 + ih. Then the following formula w0 = α k1 = hf (ti , wi ) k2 = hf k3 = hf k1 h ti + , wi + 2 2 h k2 ti + , wi + 2 2 k4 = hf (ti + h, wi + k3 ) 1 wi+1 = wi + (k1 + 2k2 + 2k3 + k4 ) 6 computes an approximate solution, that is wi ≈ y(ti ). Let us look at an example: y = y − t2 + 1 y(0) = 0.5 1 The exact solution for this problem is y = t2 + 2t + 1 − 2 et , and we are interested in the value of y for 0 ≤ t ≤ 2. 1. We first solve this problem using RK4 with h = 0.5. From t = 0 to t = 2 with step size h = 0.5, it takes 4 steps: t0 = 0, t1 = 0.5, t2 = 1, t3 = 1.5, t4 = 2. Step 0 t0 = 0, w0 = 0.5. Step 1 t1 = 0.5 k1 k2 K3 K4 w1 Step 2 t2 = 1 k1 k2 K3 K4 w2 = hf (t1 , w1 ) = 0.5f (0.5, 1.425130208333333) = 1.087565104166667 = hf (t1 + h/2, w1 + k1 /2) = 0.5f (0.75, 1.968912760416667) = 1.203206380208333 = hf (t1 + h/2, w1 + k2 /2) = 0.5f (0.75, 2.0267333984375) = 1.23211669921875 = hf (t1 + h, w1 + K3 ) = 0.5f (1, 2.657246907552083) = 1.328623453776042 = w1 + (k1 + 2k2 + 2k3 + k4 )/6 = 2.639602661132812 1 = hf (t0 , w0 ) = 0.5f (0, 0.5) = 0.75 = hf (t0 + h/2, w0 + k1 /2) = 0.5f (0.25, 0.875) = 0.90625 = hf (t0 + h/2, w0 + k2 /2) = 0.5f (0.25, 0.953125) = 0.9453125 = hf (t0 + h, w0 + K3 ) = 0.5f (0.5, 1.4453125) = 1.09765625 = w0 + (k1 + 2k2 + 2k3 + k4 )/6 = 1.425130208333333 Step 3 t3 = 1.5 k1...
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...computer software. The use of numerical analysis is described, and the 2. order Runge-Kutta method is explained. The strides influence on the result is explained. The computer software FPRO is used to make a very advanced simulation of the water rocket experiment. The structure of the software is thoroughly explained in the paper. Using the computer software Tracker a graph over the height as a function of time was produced. The result of the water rocket experiment is compared with the simulation from FPRO. Using the computer software FPRO I resolved a differential equation for the rockets momentum. The error sources influence are discussed at the end. Some advices if someone should do the same experiment, is mentioned at the end. Opgaveformulering * En vandrakets bevægelse undersøges eksperimentelt og resultatet sammenlignes med en matematisk model. * Vandrakettens bevægelse filmes og en graf over højden som funktion af tiden fremstilles. * En differentialligning for rakettens impuls løses numerisk ved hjælp af programmet FPRO. Programmets struktur skal forklares grundigt i rapporten. * Runge-Kuttas-metode af anden orden skal forklares Løsningens afhængighed af skridtlængden skal undersøges. Indholdsfortegnelse Abstract 1 Opgaveformulering 1 Indledning 3 Teoretisk del 4 Numerisk løsning 4 Eulers metode 4 2. ordens Runge-Kutta 5 Euler vs. 2. ordens Runge-Kutta 5 Simulationsprogrammet FPRO 6 Raketprincippet 8 Newtons tredje lov 8 Newtons...
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...Relationships a distraction??? Guys a question before I start off with my topic. How many of u guys are committed here or are in a relationship here..Married people also included… Wooo… quite a lot.. so how many of u guys think this relationship is a distraction?? So my topic for today is that are Relationships a distraction ?? be it work or studies.. That big question that omg u r in a relationship. Imagine the posts we see in fb. What my parents think-----Beta toh haath se nikal gaya… What my friends think---yaar ab toh teri nikal padi yaar.. What my teachers think/boss think---this guy is going in the wrong direction ..iska kuch nae ho sakta What actually happens--- reminds me a song from pyaar ka punchnama …Ban gaya kutta dekho ban gaya kutta.. Actually there are researches..emperical ones done on this topic.. These are the facts:- “No A 4 U: The Relationship between Multitasking and Academic Performance” Juncoa, Reynol; Cotten, Shelia R. Computers & Education, 2012, Vol. 59, Issue 2, September 2012, 505-514. doi: http://dx.doi.org/10.1016/j.compedu.2011.12.023. Findings: The researchers examine how the use of Facebook — and engagement in other forms of digital activity — while trying to complete schoolwork was associated with college students’ grade point averages. Students gave the researchers permission to see their grades. The participant group was 64% female, and 88% were of traditional college age, 18 to 22 years old. The study’s findings include: During...
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...HISTORY OF EULER METHOD Leonhard Euler Leonhard Euler was one of the giants of 18th Century mathematics. Like the Bernoulli’s, he was born in Basel, Switzerland, and he studied for a while under Johann Bernoulli at Basel University. But, partly due to the overwhelming dominance of the Bernoulli family in Swiss mathematics, and the difficulty of finding a good position and recognition in his hometown, he spent most of his academic life in Russia and Germany, especially in the burgeoning St. Petersburg of Peter the Great and Catherine the Great. (1707 - 1783) Today, Euler is considered one of the greatest mathematicians of all time. His interests covered almost all aspects of mathematics, from geometry to calculus to trigonometry to algebra to number theory, as well as optics, astronomy, cartography, mechanics, weights and measures and even the theory of music. There are many different methods that can be used to approximate solutions to a differential equation and in fact whole classes can be taught just dealing with the various methods. We are going to look at one of the oldest and easiest to use here. This method was originally devised by Euler and is called, oddly enough, Euler’s Method. General first order IVP; Where f(t,y) is a known function and the values in the initial condition are also known numbers. From the second theorem in...
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...A k-ω Turbulence Model for Quasi-Three-Dimensional Turbomachinery Flows Rodrick V. Chima* NASA Lewis Research Center Cleveland, Ohio 44135 Abstract A two-equation k-ω turbulence model has been developed and applied to a quasi-three-dimensional viscous analysis code for blade-to-blade flows in turbomachinery. The code includes the effects of rotation, radius change, and variable stream sheet thickness. The flow equations are given and the explicit Runge-Kutta solution scheme is described. The k-ω model equations are also given and the upwind implicit approximate-factorization solution scheme is described. Three cases were calculated: transitional flow over a flat plate, a transonic compressor rotor, and a transonic turbine vane with heat transfer. Results were compared to theory, experimental data, and to results using the Baldwin-Lomax turbulence model. The two models compared reasonably well with the data and surprisingly well with each other. Although the k-ω model behaves well numerically and simulates effects of transition, freestream turbulence, and wall roughness, it was not decisively better than the Baldwin-Lomax model for the cases considered here. The Baldwin-Lomax model is popular because it is easy to implement (at least in 2-D) and works fairly well for predicting overall turbomachinery performance. However, the model has both numerical and physical problems. Numerical problems include awkward implementation in 3-D, difficulty in finding the length scale [2]...
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...Output For “C” code of BISECTION METHOD This Program will find the Root of the Equation f(x) = x^3 - 4x -9 ************ By Bisection Method ************ Enter the range in which root lies................. Enter the value for the lower limit - 2 Enter the value for the upper limit - 3 Enter the limit of error allowed - 0.00001 The value of function at 2.000000 is = -9.000000 The value of function at 3.000000 is = 6.000000 Iterations Start now............................ The value of function at 2.500000 is = -3.375000 The value of function at 2.750000 is = 0.796875 The value of function at 2.625000 is = -1.412109 The value of function at 2.687500 is = -0.339111 The value of function at 2.718750 is = 0.220917 The value of function at 2.703125 is = -0.061077 The value of function at 2.710938 is = 0.079423 The value of function at 2.707031 is = 0.009049 The value of function at 2.705078 is = -0.026045 The value of function at 2.706055 is = -0.008506 The value of function at 2.706543 is = 0.000270 The value of function at 2.706299 is = -0.004118 The value of function at 2.706421 is = -0.001924 The value of function at 2.706482 is = -0.000827 The value of function at 2.706512 is = -0.000279 The Approximate root of the above function is = 2.706528 and the value of function is = -0.000004 The number of Iterations are = 16 Output For “C” code of NEWTON – RAPHSON METHOD This Program will find the Root of the Equation f(x) =...
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...Syed Abuzar Naqvi ENGL 511 04 Jan. 2015 The Role of Equivalence in Translation Theory and Practice. Abstract This paper highlights the development of translation studies, and equivalence as a form translation theory. It reveals the fact that translation theory and translation practice both are inseparable from each other. It tries to discover an approach which shall guide translators to produce relatively good translations. Though exploration and explication of this theory is multidimensional hence debatable but it is beneficial nonetheless to present the same plurality of views. Although equivalence may be considered the vital issue in translation but its interpretation, significance, and applicability remains debatable within the field of translation theory. It further explains how translation keeps oscillating between the equivalence and lack of equivalence. However,this paper continues to study, criticize, and even judge the translation according to the criteria of equivalence. Finally, the role of equivalence and translation theory is exemplified in the translation fromUrdu into English of short story and poems by various authors. The main aim of this paper is to introduce reader tothe concept of translation studies, and theory of equivalence.The English term translation was first introduced in around 1340. It was derived either from Old French translation or more directly from the Latin ‘translatio’ that means transporting,which itself coming from the participle...
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...MAE 334 Introduction to Computers and Instrumentation Lab 2 (Week 1,2,3 &4): Motor modeling and position control Author: Deepak Kumar Lab Partner: DE SILVA T C J Date: 4/24/2012 4:02 PM Lab TA: Reza Lab Section: L6 –Monday 6:30-9:00 PM Integrity Statement: I understand the importance of ethical behavior in engineering practice and the seriousness of plagiarism. I am pleased to confirm that this work is our own independent effort. All of the data processing and graph preparation is our own. We prepared the written text in this report independently and we did not copy the work of anyone else into our report. Signature #1: JEEVAN SUPARMANIAM Lab Manual & Title Sheet | | 5% | MATLAB Development | | 10% | Notebook Review | | 10% | Post Lab Oral Presentation | | 25% | Results | | 25% | Discussion of Results | | 15% | Quality | | 10% | Total Score | | 100% | Objectives Week 1 * To model DC motor velocity as first and second order systems and simulate with Simulink * To simulate PD closed loop controller using Simulink Week 2 * To develop an understanding of the basic Quanser Inc., QuaRC Software servo motor software and hardware setup and connections * To quantify the values of K and τ from the experimental data using the MATLAB curve fitting toolbox and from the time series graph * To develop an understanding of how the system responds to different input signals Week 3 (&4) * To study the transient...
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...Proton R&D Plan Storage Ring EDM Collaboration, 18 Nov. 2009 7. Spin Coherence Time (C.J.G. Onderwater) Overview The sensitivity with which an EDM can be sought for is to a good approximation given by sd ∝ 1 PE N T tot A Here P is the (transverse) polarization of the beam at the time of injection, E the effective electric field, N the number of particles stored per fill, Ttot the total running time of the experiment, τ a characteristic time scale and A the analyzing power of the polarimeter. The characteristic timescale depends on the lifetime of the beam in the storage ring, tbeam, which is predominantly determined by the extraction towards the polarimeter, and the polarization lifetime tpol. Given a polarization lifetime the former can be tuned to yield optimal sensitivity, typically tbeam≈2tpol. In this case τ is proportional to tpol. The sensitivity is thus inversely proportional to (the square-root of) the polarization lifetime. Maximization of tpol thus optimizes the sensitivity of the experiment. The proposed experimental sensitivity is based on a projected polarization lifetime of 1000 seconds, i.e. 108−109 particle revolutions. Such lifetimes are routinely achieved for the polarization component perpendicular to the beam orbit plane, i.e. parallel to the invariant spin field. This relies on the use of snakes, spin rotators, etc. Little experience is available with transversely polarized beams. Notable examples are the muon g-2 experiment at BNL...
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...(y(3:end)-y(1:end-2))./(x(3:end)-x(1:end-2)); % central difference dy = cos(x); % 實際微分值 plot(x, dy, x(2:end), d,'o', x(1:end-1), d,'x', x(2:end-1), dc,'^') xlabel('x'); ylabel('Derivative') 1 0.8 0.6 0.4 Derivative 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 0 0.5 1 1.5 x 2 2.5 3 3.5 工程問題中常微分方程式的解 常微分方程式 常微分方程式之形式： dy = f (t, y) dt 一般解之形式： yi +1 = yi + φ h φ 是斜率 增量函數 (increment function)，被用來自舊值yi 斜率或增量函數 斜率 外插到新值yi+1，h為步長大小 (step size)。 步長大小 此方法稱為單步方法 (one-step method)，因為增量函數的 單步方法 值是根據單一點 i 的資訊。 歐拉法 在ti處的一次微分形式提供了直接的斜率估計： dy = f (t i , yi ) dt ti φ = f ( ti , yi ) yi +1 = yi + f ( ti , yi ) h 此公式即稱為歐拉法 歐拉法 (Euler's method) 。新的值y 利用斜率（等於在t處的一 階微分）在步長大小h上做 線性外插來得到預測值。 倫基－庫達法 倫基－庫達 倫基－庫達(RK)法(Runge-Kutta methods)可以達到泰勒級數 法...
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...Mathematical Biosciences xxx (2011) xxx–xxx Contents lists available at SciVerse ScienceDirect Mathematical Biosciences journal homepage: www.elsevier.com/locate/mbs Observer-based techniques for the identification and analysis of avascular tumor growth Filippo Cacace a, Valerio Cusimano a, Luisa Di Paola a,⇑, Alfredo Germani a,b a b Università Campus Bio-Medico di Roma, via Álvaro del Portillo, 21, 00128 Roma, Italy Dipartimento di Ingegneria Elettrica e dell’Informazione, Università degli Studi dell’Aquila, Poggio di Roio, 67040 L’Aquila, Italy article info Article history: Received 20 July 2010 Received in revised form 1 October 2011 Accepted 3 October 2011 Available online xxxx Keywords: Tumor growth Gompertz model Non-linear observer Non-linear systems discretization abstract Cancer represents one of the most challenging issues for the biomedical research, due its large impact on the public health state. For this reason, many mathematical methods have been proposed to forecast the time evolution of cancer size and invasion. In this paper, we study how to apply the Gompertz’s model to describe the growth of an avascular tumor in a realistic setting. To this aim, we introduce mathematical techniques to discretize the model, an important requirement when discrete-time measurements are available. Additionally, we describe observed-based techniques, borrowed from the field of automation theory, as a tool to estimate the model unknown...
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...Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright (C) 1988-1992 by Cambridge University Press. Programs Copyright (C) 1988-1992 by Numerical Recipes Software. Permission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copying of machinereadable files (including this one) to any server computer, is strictly prohibited. To order Numerical Recipes books or CDROMs, visit website http://www.nr.com or call 1-800-872-7423 (North America only), or send email to directcustserv@cambridge.org (outside North America). Numerical Recipes in C The Art of Scientific Computing Cambridge New York Port Chester Melbourne Sydney EXXON Research and Engineering Company Harvard-Smithsonian Center for Astrophysics Department of Physics, Cornell University CAMBRIDGE UNIVERSITY PRESS William T. Vetterling Saul A. Teukolsky Brian P. Flannery Second Edition William H. Press Polaroid Corporation Published by the Press Syndicate of the University of Cambridge The Pitt Building, Trumpington Street, Cambridge CB2 1RP 40 West 20th Street, New York, NY 10011-4211, USA 477 Williamstown Road, Port Melbourne, VIC, 3207, Australia Copyright c Cambridge University Press 1988, 1992 except for §13.10 and Appendix B, which are placed into the public domain, and except for all other computer programs and procedures, which are Copyright c Numerical Recipes Software 1987, 1988, 1992...
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...Formulario de integrales c 2001-2005 Salvador Blasco Llopis Este formulario puede ser copiado y distribuido libremente bajo la licencia Creative Commons Atribuci´n 2.1 Espa˜a. o n S´ptima revisi´n: Febrero e o Sexta revisi´n: Julio o Quinta revisi´n: Mayo o Cuarta revisi´n: Mayo o Tercera revisi´n: Marzo o 2005 2003 2002 2001 2001 1. 1.1. 1.1.1. Integrales indefinidas Funciones racionales e irracionales Contienen ax + b (1) (2) (3) (4) (5) 1.1.2. (ax + b)n dx = 1 (ax + b)n+1 + C, a(n + 1) n=1 dx 1 = ln |ax + b| + C ax + b a dx 1 x +C = ln x(ax + b) a ax + b 1 1 dx =− · +C 2 (1 + x) 1+ x 1 2 1 1 xdx =− · − · +C (1 + bx)3 2b (1 + bx)2 2b 1 + bx Contienen √ ax + b (6) (7) √ 2(3bx − 2a)(a + bx)3/2 +C x a + bxdx = 15b2 √ x 2(bx − 2a) a + bx √ dx = +C 3b2 a + bx 1 (8) dx = x a + bx √ √ 1 √ ln a (9) 1.1.3. √ a + bx dx = 2 a + bx + a x √ √ √a+bx−√a + C, a+bx+ a √2 arctan a+bx + C, −a −a a>0 a0 xdx 1 =√ +C 2 )3/2 2 ± a2 ±a x x0 dx 1 1 a+x x + C = arctanh = ln a2 − x2 2a a−x a a (a2 dx x = √ +C 2 )3/2 2 a2 − x2 −x a √ x2 ± a 2 1 x a2 ± x2 + a2 ln x + a2 ± x2 + C = 2 √ 1 a2 2 2 (+) 2 x√a + x + 2 arcsenhx + C 2 1 x a2 − x2 + a arccoshx + C (−) 2 2 1 2 (x ± a2 )3/2 + C 3 Contienen (15) x2 ± a2 dx = = (16) (17) (18) (19) (20) (21) x x3 √ x2 ± a2 dx = 1 2 x2 + a2 dx = ( x2 − a2 )(a2 + x2 )3/2 + C 5 5 x2 − a2 − a · arc cos a +C |x| x2 − a 2 dx = x √ √ dx x = a · arcsenh + C a x2 + a 2 x2...
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...Introduction to the C Programming Language Science & Technology Support High Performance Computing Ohio Supercomputer Center 1224 Kinnear Road Columbus, OH 43212-1163 Table of Contents • • • • • • • • • Introduction C Program Structure Variables, Expressions, & Operators Input and Output Program Looping Decision Making Statements Array Variables Strings Math Library Functions • • • • • • • • • User-defined Functions Formatted Input and Output Pointers Structures Unions File Input and Output Dynamic Memory Allocation Command Line Arguments Operator Precedence Table 2 C Programming Introduction • Why Learn C? 3 C Programming Why Learn C? • • • • • • • • • Compact, fast, and powerful “Mid-level” Language Standard for program development (wide acceptance) It is everywhere! (portable) Supports modular programming style Useful for all applications C is the native language of UNIX Easy to interface with system devices/assembly routines C is terse 4 C Programming C Program Structure • • • • • Canonical First Program Header Files Names in C Comments Symbolic Constants 5 C Programming Canonical First Program • The following program is written in the C programming language: #include main() { /* My first program */ printf("Hello World! \n"); } • • C is case sensitive. All commands in C must be lowercase. C has a free-form line structure. End of each...
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