Tiêu đề 2023 Apr-May- Mathematics-III.pdf ✅

Printed Pages - 6+2=8 Roll No.: B000311(014) B.Tech. (Third Semester) Examinatio April-May 2023 (Civil Engg, Branch) Time Allowed : Three hours MATHEMATICS-III Maximum Marks : 100 () cos'21 Minimum Pass Marks : 35 (ü) sin' 2/ 1. (a) Find the Laplce transforms of: Note : Attempt all questions. Part (a) is compulsory of each question and attempt any two from (b), (c) and (d) of each questions. Unit-I ITUTE O LIBRARY BO00311 (014) RAIPUR. (C.G.) E AMOLOG 4 PTO
(b) Apply oonvolution theorem to evaluate (c) Use transtorms mothod to olve: d'x dt =e with x 2, (d) Find the inverse Laplace transform of : Ss+3 (s-1)(s'+2s+S) (b) Solve: Unit-II the arbitrary functions from f(+y', z-y)=0 dr 2. (a) Fom the partial differential equations by climinating dt BO00311(014 (r-)p+('-z)g= | at =() 8 4 8 8 (c) Solve: X a:, o'z6°2= cos(2.xi*y) ax? Ox ôy Solve : P (X) : a'z a'z =2 ôu (d) Using the method of separation of variables, solve 8 |3| 1 3k Or 3. (a) The probability density function of a variate X is : COS Xcos 2 y -+u, where, u(x, 0) =6e P(Xs2)>3. Unt-lI 5k 3 7k 4 B000311(e14) 9k 5 What will be the minimum value of k so that 8 6 1k 13k 4 PTO
(b) In a normal distribution. 31% of the items ar under 45 and 8% are over 64. Find the mean and S.D. of the distribution. (c) The following data are the number of seeds germinating out of 10 on damp filter paper for 80 sets of seeds. Fit a binomial distribution to these data : x: 0 6 1 2 3 |4| 20 28 12 8 F () 122 4 5 12 1 60 from the following table : (d) Fit a Poisson distribution to the set of observation: 8 5 6 7 Unit-IV 0 6 13 2 15 4. (a) Using Lagrange's interpolation formula, find y (10) 9 14 3 2 BO00311(014) 11 8 9 10 16 0 0 Stirling's fomula and Bessel's fomula. 4 0 1 (b) Given the following table, find y (35), by using 8 8 4 8 |5| 20 30 40 50 512 439 346 243 (c) The population of a town is as follows : Year x: 1941 19$1 1961 1971 198I 1991 Population 24 in lakhs y : 20 29 36 46 51 formula : (d) From the following table find f(r) and hence f(6) using Newton's Divided Difference interpolation f«): 1 Unit-V 2 5 5. (a) ) Write the formulas for fourth onder Runge-Kutta method. d 7 (b) Solve the equation =1-y.given y (0) =0, using (ü) Write the formula for Adams-Bashforth method. 2 Modified Euler's method and tabulate the solutions at x01, 0:2 and 0-3. BO003 11(014) 8 2 PTO 6 0
(c) Using Runge-Kutta method of fourth order, find 4,420] |61 y (0:8) correct to 4 decimat places if : de dy 1 d 2 *y-x,y (0-6)= 1-7379 (d) Using Adams-Bashforth method, find y (0-4) given 8 ,y (0-1) = 101, y (0-2) - 1-022, y (0-3) = 1-023 Or Using Milne's method, find y (4:4) given 5ry' +y'-2 =0 and y (4) = 1,y (4-1) = 1-0049, y (4-2) = 1-0097 and y (43) = 1-0143. 8 BO00311(014)