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- Applied Mathematics-1 - M-1
- 2018
- PYQ
**Biju Patnaik University of Technology Rourkela Odisha - BPUT**- Mechanical Engineering
- B.Tech
**613 Views**- 8 Offline Downloads
- Uploaded 10 months ago

Registration No : Total Number of Pages : 02 B.Tech PME3D001 3rd Semester Regular Examination 2018-19 APPLIED MATHEMATICS BRANCH : MECH Time : 3 Hours Max Marks : 100 Q.CODE : E982 Answer Question No.1 (Part-1) which is compulsory, any EIGHT from Part-II and any TWO from Part-III. The figures in the right hand margin indicate marks. b) Part- I Short Answer Type Questions (Answer All-10) What is the method of separating variables as a method of getting solution of partial differential equation? Give an example. Find the Taylor series of ( ) = at z=1. c) The Residue of ( ) = ( d) e) Solve the partial differential equation + =0 By what physical law did we obtain the equation of the vibrating string?What is the name of the equation? A fair coin is tossed 400 times.If X is the number of heads obtained, find the expected value and variance of X. A book has four misprints per page (on average), what is the probability that a page open at random will have no misprints on it? Define type-I and type-II error in hypothesis testing. Express Laplace Equation in Polar co-ordinates. Find the mean and variance of Binomial Distribution. Q1 a) f) g) h) i) j) Q2 a) b) c) d) e) f) g) h) i) )( ) at z=3. Part- II Focused-Short Answer Type QuestionsTwelve) 6 Verify z is analytic or not. Evaluate the integral:∫ ∞ ∞( (Answer Any Eight out of ) Using Residue theorem,evaluate the following integral ∮ 2| = 4. Solve: x (r 2 xs x 2 t ) p 2 x 3 by Monge’s method , :| − Derive the solution of Heat equation for the bar with insulated ends using variable separable method. In a sample of 8 observations, the sum of squared deviation of items from the mean was 94.5. In other sample of 10 observations, the value was found by 101.7.Test whether the difference is significant at 5% level of significance? Define Cauchy-Riemann equation and determine the value ofa andb such that the given function u ax 3 by 3 is Harmonic and find Harmonic conjugate. Find the McLaurin’s series expansion and also find the Radius of convergencecos 2 Check the nature of singularity of the following function: (i) ( )= (2 x 10) (ii) ( ) = . (6 x 8)

j) k) Transform the equation +6 transform and solve it. A function defined as follows : +9 = 0 to normal form using suitable x 1 0 2 f ( x ) ( x 2) 7 0 1 x 2 x2 (i) Show that it is a density function. (ii) Find the expectation and variance. (iii) Find the distribution function. l) In a certain Factory turning out razor blades there is a small chance of 0.002 for any blade to be defective. The blades are supplied in packets of 10.Calculates approximate number of packets containing: (i) no defective (ii) one defective (iii) two defective blades in a consignment of 10,000 packets. Part-III Long Answer Type Questions (Answer Any Two out of Four) Q3 Q4 Find all Taylor and Laurent Series of f ( z ) a) b) Q5 a) b) Q6 2z 3 with center zero. z 3z 2 2 (16) 2% of the fuses manufactured by a farm are found to be defective, find the probability that a box containing 200 fuses contains (i) no defective (ii) three or more defectives The probability of a man hitting a target is ¼. How many times must he fire so that the probability of his hitting the target at least once is greater than 2/3 ? (8) Evaluate the integral: ∫ . State and prove D-Alembert’s solutions of wave equation. (8) By using Least square method for the following data, find out a) Regression line of y on x b) Regression line of x on y (16) c) 2 Fit a parabola y ax bx c x : 1 2 3 y : 2 5 3 4 8 5 7 (8) (8)

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