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- Applied Mathematics-3 - M-3
- 2019
- PYQ
**Biju Patnaik University of Technology Rourkela Odisha - BPUT**- Computer Science Engineering
- B.Tech
**23 Views**- Uploaded 5 months ago

Registration No : Total Number of Pages : 02 B.Tech PMA4E001 4th Semester Regular / Back Examination 2018-19 APPLIED MATHEMATICS-III BRANCH : AEIE, AERO, AUTO, BIOMED, BIOTECH, CIVIL, CSE, ECE, EEE, EIE, ELECTRICAL, ENV, ETC, FAT, IEE, IT, MANUTECH, MECH, METTA, MINERAL, MINING, MME, PE, PLASTIC, PT, TEXTILE Time : 3 Hours Max Marks : 100 Q.CODE : F1005 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. Part- I Only Short Answer Type Questions (Answer All-10) Q1 a) b) Why∫ :| | ( ) (2 x 10) =0 Determine zeros and poles of the function ( ) = ( ) . c) Determine residue of the function ( ) = ( d) Round-off the number 4.5126 to four significant figures and write the relative percentage error. Write the period of ( ) = . How many nodes are required to obtain a polynomial of degree 10 in Lagrange’s Interpolation? Find [ , , ] for given tabulated values. e) f) g) X f(x) h) i) 1 20 6 45 ) at = . 10 90 12 98 13 110 j) A fair coin is tossed 6 times. Determine the probability of getting exactly 2 heads. A continuous random variable has probability distribution (1 − ), 0< <1 ( )= what is the value of . , ℎ In which distribution mean and variance are same? a) Part- II Only Focused-Short Answer Type Questions- (Answer Any Eight out of Twelve) Explain whether the function ( , ) = is harmonic or not. If yes, determine the b) corresponding analytic function ( ). Calculate : Q2 :| | c) Calculate Laurent series of ( ) = ( − 9)( + ) valid for 2 < | | < 3 . (6 x 8)

d) Calculate the value of the integral by using Residue integration method. :| | e) f) g) ( − 1) on the interval [0,2] using trapezoidal rule Approximate the integral of ( ) = usingℎ = 0.2 . If is normally distributed with mean 0 and variance 1, find ( ≥ −1.64), (−1.96 ≤ ≤ 1.96), ( ≤ 1), ( ≥ 1). Formulate (1.5) for given tabulated points. x 0 1 3 4 f(x) -12 0 6 12 h) Calculate the value of (0.4) by using Euler’s method for = −2 , (0) = 1, ℎ = 0.2 and compare the result with its actual value. i) Design a parabola = x 10 Y 14 j) Calculate residues at the poles for the given function ( ) = ( k) l) + + in least square sense to the following data 12 15 23 20 17 23 25 21 ) ( ) . Determine probability distribution function for a continuous random variable with probability density (1 − ), 0< <1 ( )= . Hence find ( < 0.3) (0.4 < < 0.6). 0 ℎ Evaluate (1.2)by using Newton’s forward difference interpolation for given tabulated values. x f(x) 0 1 1 1.5 2 2.2 3 3.1 4 4.3 Part-III Only Long Answer Type Questions (Answer Any Two out of Four) Q3 a) (10) Prove that 5 + 3 sin b) Q4 Discuss Taylor’s series of ( ) = ( )( ) = 2 (6) in the region | + 1| < 1. Classify a polynomial for given tabulated values. Hence find (0.5)and X -1 0 2 f(x) -8 3 1 ′ (0.5). (16) 3 2 Q5 Evaluate (1.3) by using Runge-Kutta method of order 4 for initial value problem = + , (1) = 0 by taking ℎ = 0.1 . (16) Q6 Using a sample of 10 values with mean 14.5 from a normal population with variance 0.25, test the hypothesis = 15.0 against the alternative = 14.5 on the 5% level. (16)

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