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

Registration No : Total Number of Pages : 02 B.Tech PCE4E001 4th Semester Regular / Back Examination 2018-19 APPLIED MATHEMATICS - III BRANCH : CHEM Time : 3 Hours Max Marks : 100 Q.CODE : F1004 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. Q1 a) b) Part- I Only Short Answer Type Questions (Answer All-10) Write the period of the function ( ) = ( ) Determine singularities of the function ( ) = ( c) d) e) f) g) h) i) j) Q2 a) b) (2 x 10) ) Determine residues of the function ( ) = at = 1 Find the mean of the distribution = 4 − 2 where ( ) = ( > 0) Round-off the number 4.5126 to four significant figures and determine the relative percentage error. If the probability of producing a defective screw is p = 0.01, then what is the probability that a lot of 100 screws will contain more than 2 defectives ? Let X be a continuous random variable with distribution function (1 + ), 2≤ ≤5 ( )= . Determine 0, ℎ State ( ) = is analytic or not. In rolling two fair dice, what is the probability of obtaining a sum greater than 3 but not exceeding 6 ? State Trapezoidal rule of numerical integration for 20 node points. 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 corresponding harmonic conjugate ( , ). Calculate∫ :| | ( )( ) c) Design Laurent Series of ( ) = d) Calculate residue about the pole ( ) = e) Calculate (0.5) for given tabulated points. x 0 1 f(x) -12 0 valid for 2 < | | < 5 . ( )( ) 3 6 4 12 f) Evaluate (1.2)by using Newton’s forward difference interpolation formula for given tabulated values. x 0 1 2 3 4 f(x) 1 1.5 2.2 3.1 4.3 g) 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. (6 x 8)

h) i) j) k) l) Approximate the integral of ( ) = on the interval [0,2] using trapezoidal rule using ℎ = 0.2 . The probability density function of babies, x years, being brought to a postnatal clinic is (2 − ), 0 < < 2 given by, ( ) = 0, ℎ If 60 babies are brought in on a particular day, how many are expected to be under 8 months old? Determine mean and variance for a continuous random variable x with probability density 3 0< <1 ( ) = 2 (1 − ), 0, ℎ The breaking strength X (Kg) of a certain type of plastic block is normally distributed with a mean of 1500 kg and a standard deviation of 50kg. What is the maximum load such that we can expect no more than 5% of the blocks to break? If a random variable has a Poisson distribution such that (1) = (2), Hence determine (4). Part-III Only Long Answer Type Questions (Answer Any Two out of Four) Q3 a) b) Q4 (8) Evaluate Evaluate Taylor’s series of ( ) = ( )( ) 5 + 3 cos in the region | + 2| < 1. Evaluate a polynomial for given tabulated values. Hence find (0.3)and X -1 0 2 f(x) -8 3 1 (8) ′ (0.3). (16) 3 2 Q5 Describe probability distribution function for a continuous random variable probability density (1 − ), 0< <1 ( )= . Hence find ( < 0.3) (0.4 < < 0.6). 0 ℎ Q6 Fit a parabola x Y = + 10 14 + in least square sense to the following data 12 15 23 17 23 25 with (16) (16) 20 21

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