Rajasthan Technical University 2009 B.Tech Mechanical Engineering Numerical Methods and Applied Statistics - Question Paper
Rajasthan tech. University
B.tech six sem (Main/back)
Year 2009
Numerical Methods and Applied Statistics
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Tola! No. of Questions : 5| |Total No. of Pages :4
[2079)
B.Tech. Vlth Semester (Main/Back) Examination - 2009 Mechanical Engineering Numerical Methods and Applied Statistics 6E3054
Time: 3 Hours Maximum Marks: 80
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- * MifcPassing Marks : 24
Instructions to Candidates: "
Attempt overall Five Questions selecting one question from each unit. All questions carry equal marks. (Schematic diagrams must be shown wherever necessary. Any data youfeel missing may suitably be assumed and stated clearly. Units of quantities used/calculated must be stated Clearly.)
Unit-I
1. a) Find the real root of the following by bisection method, correct to two
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decimal places /(i)=3\/64 (10)
b) What is necessary condition for convergence of Newton-Raphson method? Discuss its convergence behaviour (6)
OR
a) Apply/Newton 'ftaptisoh method to solve die equation 2(x-3)=log0
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correct to three decimal places. (10)
b) Explain the false-position bisection method to solve a one variable equation.
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(6)
Unit - II
2. a) Solve the given set of linear simultaneous equations by Gauss elimination
method
(8)
|
3x, -at, +2x, =12 | |
|
x, +2x: +3x. =11 | |
|
2x, -2x, -jc, =2 | |
|
From die following iabwjBr v and x = degree | |
|
x |
/(*) |
|
0.5 |
-2.625 |
|
0.7 |
-2.567 |
|
1.0 |
-2.00 |
|
1.2 |
-1.232 |
|
1.5 |
0.625 |
6E3054 / 3000 (1) [Contd....
Using Newton forward difference method, find
j>(0)=6, j'(l)=_y(2)=5, >'{3)=T5,>(4)50. , (8)
The following table gives the values of x and / (*)
J f(x)
0.4 0.916
0.5 0.693
0.7 0.307
0.8 0.223 .
EstUWttWhe using Lagrange inter polation. Also find the
order of polynomial you would use in the problem. (8)
Unit - III
Evaluate the following integral by employing Simpsons % rule :
' f'sinxCosxdx (8)
dy_y-x
G,ven ~Jx~TTx with y = 1 for * = 0
Find y approximately for x = 0.1 by Eulers method (five steps). (8) OR
dy
Use Runga-Kutta method to solve
forxs 1.4. Initially x= 1, v = 2 (take h - 0.2) (8)
The table of values for /(x)=?x is given as ~ -----
* m
1.6 4.953
1.8 6.050 2.0 7.389 2.2 9.025 2.4 11.023
2.6 12.464
2.8 16.445
Use trapezoidal rule to obtain the integral of/(x) in the interval from x = 1.8 to 'Ato*4nd*the ajnoulit of error incurred. (8)
In a sample of 1000 cases the mean of a certain test is 14.40 ancTer isTB. Assuming normality of distribution.
i) How many individuals score between 12 and 16?
ii) How many score above 18? Below 8?
iii) What are the chances that any individual selected at random will score ? above 15? (8)
6E3054 (2) [Contd....
Calculate the coefficient of corrclqiien from the following data. x y - >r TtZL, vG> a
-5 *
15
16 14 13 11 12
0 *4fir $ *> *
t Ao*inu-wv\. - t*4s <> - em,'
oft
The following data give the. life span (in years) of a sample of people. Find the mean, median, mode, staMar'l deviation, and coefficient of variation of the age of the sample. What wthe percentage number of people within + 2<r limits? <
Age Frequency
10-20 4 ;l!
20-30 6 a
30-40 5.;.
40-50 1(\.
- z&: '
22
24
70-80 80-90 90-100
100-110 1 With the help of the following data
6
2
(8)
7 1
3 ' 5
i) Fit the two regression lines
ii) Calculate Karl pearscm coefficient
iii) Find explained and unexplained variation
(8)
iv) Calculate the standard error of the estimate by the two lines.
6E3054 (3) [Contd._
Unit - V
5. a) in an antimaterial campaign in a certain area quinine was administered to 812 persons out of total populltion of 3248. The number of fever cases in shown below. Discuss the usefulness of quinine in checking Malaria
|
Treatment |
Quinine |
No Ouinine |
Total |
|
Fever |
20 |
220 |
240 |
|
No Fever |
792 |
2216 |
3008 |
|
Total |
812 |
2436 |
3248 |
b) Two different types of Drug* A trwpd
inrr<a<fipgn>pighf* pi<tim>. wSce given drug A while 7 person were given drug B. The increase in weight is given below. Do the two drugs differ significantly, at 5% level of significance, with regard to their effect in increasing weight?
Drug A Drug B
8 10 12 8 13 12
9 15
3 6
8
11' (8)
___
a) *i |r-nilrTj irri? r,~ ' .......[ .......*f
conduct records are exemplary and to 5 boys whose records are very poor. Data are given below
|
Group 1 |
Group 2 |
|
110 |
115 |
|
112 |
112 |
|
95 |
109 |
|
105 |
112 |
|
111 |
117 |
|
97 | |
|
112 | |
|
102 |
Is the dfffcreiwxhaanaeikgfoup means significant at the 0.05 level and at the 0.01 level? * . - (8)
b) An auto company decided to introduce a new six cylinder ear whose mean petrol consumption in claimed to be lower than that of the existing auto engine. It was found that the mean petrol consumption fo? the 50 cars was
10 Km per litre with a standard deviation of 3.5 Km per litre. Test for the company at 5% level of significance whether the claim of the new car petrol consumption is 9.5 Km perlitre on the average is acceptable. (8)
6F3054 (4)
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Attachment: |
| Earning: Approval pending. |
