# Engineering Mathematics â IV - Gandhi Institute For Education

## Transcription

Engineering Mathematics â IV - Gandhi Institute For Education

Prepared by Dr.Binayak Sahu Sample Questions Engineering Mathematics – IV - by Dr.Binayak Sahu Gandhi Institute for Education and Technology, Baniatangi, Bhubaneswar ALWAYS REMEMBER THE FOLLOWING TIPS : Never read Mathematics, but write Mathematics : Do not believe in reading Mathematics. Always adopt pen and paper for doing Mathematics otherwise you will be simply deceiving yourself. Regularity in Mathematics : The most important thing in the study of mathematics is regularity in its studies. Do not postpone your daily work in mathematics. My dear students, never forget to ask a doubt, if you have any, write in my e-mail ID: [email protected] GIET, Baniatangi, Bhubaneswar Engineering Mathematics – IV Page - 1 - Prepared by Dr.Binayak Sahu Engineering Mathematics - IV 1. State the rules of rounding off a decimal number. 2. What is ill conditioning of a system of linear equations? Explain 3. State the conditions under which an experiment will involve Poisson distribution. 4. What is a standard random variable? What are the mean and standard deviation of a standard random variable? 5. Find 10 (1 x)(1 2 x 2 )(1 3x3 )(1 4 x 4 ) using h = 1. 6. Estimate y (0.25) and y(0.5) from y x y 2 , y(0) 1.1 using Euler’s method choosing h = 0.25. 7. Sketch F ( x) if f (0) f (1) 1/ 4 and f (3) 1/ 2. 8. If X is a random variable with mean 50 and standard deviation 5, find the mean and variance of 25 – 2X. 9. Determine a 95% confidence interval or the mean of a normal population with variance 2 16, using a sample of size 196 with mean 75. 10. If the probability of hitting a target is 0.42 and five shots are fired independently, what is the probability that the target will be hit at least twice? Long type questions: 1. Find a solution of the equation x 4 x 0.12 0 by using fixed point iteration method, correct up to three decimal places. You can take the initial solution x0 1. GIET, Baniatangi, Bhubaneswar Engineering Mathematics – IV Page - 2 - Prepared by Dr.Binayak Sahu 2. Describe Lagrange Interpolation technique and find the value of f (0) for the given data. x: -2 -1 2 4 5 f (x): - 9 -1 11 23 69 3. Estimate f (3) if f (1.1) 10, f (2.3) 5.7, f (3.9) 25.8 and f (6.7) 78.9 using Newton’s interpolation formula based on divided differences. 4. Using Gauss-Seidel iteration method solve the following system of linear equations correct up to three decimal places. 6 x1 15x2 2 x3 72 x1 x2 54 x3 110 27 x1 6 x2 x3 85 5. Find the numerical solution y(0.2) for the differential equation y x 2 y 2 with the initial condition y(0) = 1 using h = 0.1 by RungeKutta 4th order method. 6. Find the approximated root of the equation e x sin ( x) x 2 0 by Newton’s method correct up to 3-decimal places using the initial approximation x0 3. 2 7. Evaluate the integral e dx x which is correct up to 6 decimal 1 places by Simpson’s one third rule. 8. A box contains r red balls and b black balls. If two balls are drawn from the box without replacement one after another and the color of the first ball is unknown, then that is the probability for getting a black ball in the second draw. GIET, Baniatangi, Bhubaneswar Engineering Mathematics – IV Page - 3 - Prepared by Dr.Binayak Sahu 9. If a die is rolled 5 times, then what is the probability of getting 6 sixes. 10. If a probability book having 500 pages contains 300 misprints, then find the probability that a page of same book contains exactly 2 misprints. 11. A batch of 200 iron rods consists of 50 oversized rods, 50 undersized rods and 100 rods of desired length. If two rods are drawn at random without replacement, what is the probability of obtaining (i) two rods of desired length (ii) exactly one of the desired length (iii) none of the desired length. 12. Let X be the random variable denoting the ratio of sales to profits of some firm. Assume that X has the distribution function F ( x) 0 = ( x2 4) / 5 =1 13. if x < 2 if 2 x 3 if x 3 A pressure control apparatus contains three electronic tubes. The apparatus will not work unless all tubes are operative. If the probability of failure of each tube during some interval of time is 0.017, what is the corresponding probability of failure of the apparatus? 14. Let X (in mm) be the thickness of washers a machine turns out. Assume that X has the density f ( x) Kx if 0.9 x 1.1 and f ( x) 0 otherwise. Find K, what is the probability that a washer will have any thickness between 0.94 mm and 1.03 mm? GIET, Baniatangi, Bhubaneswar Engineering Mathematics – IV Page - 4 - Prepared by Dr.Binayak Sahu 15. Find the density function of X. Also find the probability that X lies between 20% to 40% profit range. 16. The copper content (%) in brass of 10 samples are given below 65, 65, 64, 63, 65, 66, 63, 64, 62, 63 Assuming that the population from which the above samples are drawn is normal, determine a 99% confidence interval for the mean of the population. Given that ( z ) : 0.9 z : 1.282 17. 0.95 1.645 0.975 1.960 0.99 2.326 0.995 2.576 Find the coefficient of correlation between x and y from the following data table: x 5.5 6.5 7.5 8.5 9.5 10.5 11.4 y 10.9 7.8 8.3 6.2 7.1 18. 5.3 4.5 Find the regression line of y (expansion of gelatin [%]) on x (humidity) of air [%]) using the following data: (x, y) = (10, 0.8), (20, 1.6) (30, 2.3), (40, 2.8). GIET, Baniatangi, Bhubaneswar Engineering Mathematics – IV Page - 5 -