university, bhopal assignment question paper - Madhya Pradesh ...

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From Pre Page Q1. Show that the collection of all feasible solutions to LP problems constitutes a conver set whose extreme pairts correspond to the basic feasible solutions. Q2. State the priiciple of optionality in dynamic programming and give a methematical formalation of a dynamic programming problem. Q3. What is scpoe of O.R. in daily life. Q4. Define convex programming. Q5. Write short notes on the following (a) Network simplex method (b) Game Theory
M P BHOJ (OPEN) UNIVERSITY, BHOPAL ASSIGNMENT QUESTION PAPER 2009-10 CLASS : M.Sc. Final SUBJECT: Mathematics Paper - IV - Integral transform with applications funsZ'k %& 1- lHkh iz'u Lo;a dh gLrfyfi esa gy djuk vfuok;Z gSA 2- nksuksa l=h; iz'ui= gy djuk vfuok;Z gsa 3- l=h; dk;Z mÙkjiqfLrdk ds vafre i`"B ij lacaf/kr fo"k; dh laiUu laidZ d{kkvksa dh frfFk;ksa ,oa ijke'kZnkrk ds uke ,oa in dk vo'; mYys[k djsaA 5- l=h; dk;Z mÙkjiqfLrdk,a tek djus dh vafre frfFk 20 vizsy 2010 gSA 4- vafre frfFk mijkar l=h; dk;Z mÙkjiqfLrdkvksa dks ekU; ugha djrs gq, ewY;kafdr ugha dh tkosxhA 6- l=h; dk;Z mÙkjiqfLrdk,a tek djus dh jlhn vo'; izkIr dj ysaA 7- nks l=h; dk;Z izkIrkadksa esa ls fdlh ,d esa vf/kdre vad dh iwoZ izpfyr O;oLFkk ds LFkku ij nksuksa l=h; dk;ksZa ds izkIrkadksa ds vkSlr vad l=kar ijh{kk ifj.kke esa tksM+s tk,axsA lHkh iz'uksa ds vad leku gSaA First Assignment Max Marks - 30 Q1. Find the Laplace transform of t 2 , 0 < t < 2 F(t) = t – 1, 2 < t < 3 7, t > 3 Q2. Solve ( t D 2 + (1-2t) D – 2) y = 0 , where y(0) = 1 , y’(0) = 2 . Q3. An alternating EMF esinωt is applied to an inductance L & a capacitance C in series. Show that the current in the circuit is { eω / (n 2 - ω 2 ) L} (cos ωt – cosnt), where n 2 = 1/ LC . Q4. Find the fourier series for the periodic function f(x) defined by - π where - π < x < 0 f(x) = x 0 < x < π Q5. A string is stretched between the fixed points (0,0) & (1,0) & released at rest from the position u(x, 0) = A sin 2πx. Find the displacement u(x, t). Second Assignment Max Marks - 30 Q1. Using Laplace transform solve d 2 y/dx 2 + y = 0, under the condition that y = 1 , dy/dt = 0, when t = 0. Q2. Find L -1 {log(s 2 +1/s(s+1)) Q3. Find the surface satisfying t = 6x 3 y, containing two lines y = 0 = z, y =1 = z using partial differential equation. Q4. Find the Fourier half range cosine series of the function 2t, 0< t
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