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- Mathematics-4 - M-4
- 2019
- PYQ
**Biju Patnaik University of Technology Rourkela Odisha - BPUT**- Civil Engineering
- B.Tech
**61 Views**- Uploaded 5 months ago

Registration No : Total Number of Pages : 02 B.Tech BSCM1210 4th Semester Back Examination 2018-19 MATHEMATICS- IV BRANCH: AERO, AUTO, BIOMED, CHEM, CIVIL, ENV, FASHION, FAT, MANUFAC, MANUTECH, MARINE, MECH, METTA, MME, PE, PLASTIC, TEXTILE Time : 3 Hours Max Marks : 70 Q.CODE : F1009 Answer Question No.1 which is compulsory and any five from the rest. The figures in the right-hand margin indicate marks. Q1 a) b) c) d) e) f) g) h) i) j) Answer the following questions : Round-off the number 6.5126 to four significant figures and write the relative percentage error. What is Truncation error? Write using Lagrange interpolation how many nodes or arguments are required to obtain a polynomial of degree 10. (2 x 10) Let = −2 , (0) = 1 with step size ℎ = 0.2 then by Euler’s method find the value of (0.4) ? A continuous random variable has probability distribution (1 − ), 0< <1 ( )= what is the value of . , ℎ Define Linear Interpolation. Define Type-1 and Type-2 error in sampling distribution. State two differences between Binomial and Poisson distribution. Write down the range of correlation coefficient. We want to draw random samples of two gaskets from a lot of 10 gaskets out of which 3 gaskets are defective. Then find the probability function of the random variable X = Number of defective in the sample, if we perform the operation without replacement. Q2 a) b) Using Bisection method formulate the real root of the equation − − 1 = 0 Using Newton-Raphson method formulate the real roots of the equation (up to three iterations) −5 +3=0 (5) (5) Q3 a) Calculate mean and variance for a continuous random variable density 3 0< <1 ( ) = 2 (1 − ), 0, ℎ with probability (5) b) Calculate probability distribution function for a continuous random variable with probability density (1 − ), 0< <1 ( )= . 0 ℎ (5)

Q4 a) Evaluate (1.2)by using Newton’s forward difference interpolation formula for given tabulated values. x f(x) b) 0 1 1 1.5 a) 3 3.1 4 4.3 Formulate (1.5) for given tabulated points. x f(x) Q5 2 2.2 0 -12 (5) (5) 1 0 3 6 4 12 Calculate the correlation coefficient for the following heights (in inches) of (5) fathers (X) and their sons (Y) b) Q6 65 66 67 68 69 70 71 72 67 68 65 68 72 72 69 71 Calculate the mean and standard deviation of the sampling distribution of mean of 300 random samples of size = 36 are drawn from a population of = 1500 which is normally distributed with mean = 22.4 and standard deviation = 0.048, if sampling is done (a) with replacement (b) without replacement Evaluate a parabola data x Y 10 14 = + 12 17 + in least square sense to the following 15 23 23 25 Evaluate (1.3) by using Runge-Kutta method of order 4 for initial value problem = + , (1) = 0 by taking ℎ = 0.1 . Q8 a) Write short answer on any TWO : Show that, in Binomial distribution variance is greater than mean. b) Write down the methodology involved in finding the roots of equation c) Write down the characteristics of Normal distribution. (10) 20 21 Q7 numerically. (5) (10) (5 x 2)

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