Engineering Mathematics 4 - Jun 2013
Mechanical Engineering (Semester 4)
TOTAL MARKS: 100
TOTAL TIME: 3 HOURS (1) Question 1 is compulsory.
(2) Attempt any four from the remaining questions.
(3) Assume data wherever required.
(4) Figures to the right indicate full marks. 1 (a) Use modified Euler's method to solve dy/dx=x+y, y(0)=1 at x=0.1 for three iterations taking h=0.1.(6 marks) 1 (b) Solve dy/dx=x+y, x=0, y=1 at x=0.2 using Runge-Kutta method. Take h=0.2(7 marks) 1 (c) Using Milne's predictor-corrector method find y(0.3) correct to three decimals given.
ii) Two different digits from 1 to 9 are selected. What is the probability that the sum of the two selected digits is odd if '2' one of the digits selected.(7 marks) 6 (c) Three machine A, B, C produce 50%, 30%, 20% of the items. The percentage of defective items are 3, 4, 5 respectively. If the item selected is defective what is the probability that it is from machine A? Also find the total probability thatn an item is defective.(7 marks) 7 (a) The p.d.f of x is
Find k. Also p(x?5), p(3<x?6).< a="">
</x?6).<></span>(6 marks) 7 (b) A die is thrown 8 times. Find the probability that '3' falls,
i) Exactly 2 times
ii) At least once
iii) At te most 7 times.(7 marks) 7 (c) In a certain town the duration of shower has mean 5 minutes. What is the probability that shower will last for i) 10 minutes or more; ii) less than 10 minutes; iii) between 10 and 12 minutes.(7 marks) 8 (a) What is null hypothesis, alternative hypothesis significance level?(6 marks) 8 (b) The nine items of a sample have the following values: 45, 47, 50, 52, 48, 47, 49, 53, 51. Does the mean of these differ significantly from the assumed mean 47.5. Apply student's t-distribution at 5% level of significance. (t0.05 for 8df=2.31).(7 marks) 8 (c) In experiments on a pea breading. The following frequencies of seeds were obtained:
is the experiment is in the agreement of theory which predicts proportion of frequencies 9:3:3:1 (x2 0.05, 3df=7.815).(7 marks)