Download GTU (Gujarat Technological University Ahmedabad) B.Tech/BE (Bachelor of Technology/ Bachelor of Engineering) 2020 Winter 4th Sem 2141703 Numerical Techniques And Statistical Methods Previous Question Paper
Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE- SEMESTER?IV (NEW) EXAMINATION ? WINTER 2020
Subject Code:2141703 Date:09/02/2021
Subject Name:Numerical Techniques & Statistical Methods
Time:02:30 PM TO 04:30 PM Total Marks:47
Instructions:
1. Attempt any THREE questions from Q.1 to Q.6 .
2. Q.7 is compulsory.
3. Make suitable assumptions wherever necessary.
4. Figures to the right indicate full marks.
MARKS
Q.1 (a) An approximate value of p is 3.1428571 and its true value is 3.1415925. Compute
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the absolute and relative errors.
(b) An incomplete frequency distribution is given as follows:
Variable
10-20 20-30 30-40 40-50 50-60
60-70
70-80
Frequency
12
30
f1
65
f2
25
18
Given that the median value is 46, determine the value of f
04
1 and f2 .
(c) Solve the following system by Gauss-Seidal iteration method:
27x 6y z 85
6x 15 y 2z 72
x y 54 z 110
07
Q.2 (a) Find the value of f(5) by using Lagrange's interpolation method for the given data
x
1
2
3
4
7
f(x) 2
4
8
16
128
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(b) Solve the equation 3
x 3x 5 0 by using Newton Raphson method, correct up
to four decimal places.
04
(c) Use Simpson's 1/3 and Simpson's 3/8 rule to evaluate the following integral
1
1 dx
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1 2
0
x
Q.3 (a)
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Use Taylor's series method to find the approximate value of y
)
2
.
1
(
if
dy
x y ; y )
1
( 0 .
dx
1
(b) Population of a town was given below:
Year(x)
18
19
19
19
1931
91
01
11
21
Population (y)
46
66
81
93
101
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(in thousands)
Compute the population for the year 1925.
(c) Using Runge-Kutta method to find the approximate value of y(0.2) if
dy
2
x y , given that y(0) 1 taking h = 0.1.
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dx
Q.4 (a) Use Euler's method with h = 0.1 to find the solution of the equation
dy
2
2
x y , given that y(0) 0 in the range 0 x 5 .
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dx
(b) Find first derivatives at x = 1.1 from the following table
X
1
1.2
1.4
1.6
1.8
2.0
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f(x)
0
0.1280 0.5440 1.2960 2.4320 4.0000
(c) Using Milne's Predictor Corrector method to obtain y(0.4) by solving
dy ex
2
y given that y( )
0 ,
2 y(
)
1
.
0
,
01
.
2
y(
)
2
.
0
,
04
.
2
y(
)
3
.
0
09
.
2
.
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dx
Q.5 (a) A can hit a target 4 times in 5 shots, B, 3 times in 4 shots and C, 2 times in 3 shots.
They fire a volley (it means one shot each). Find the probability that the target will
be hit.
03
(b) Out of 800 families with 4 children each how many families would be expected to
have (i) at least one boy (ii) 2 boys and 2 girls
Assume equal probabilities for boys and girls.
04
(c) Five coin are tossed 3200 times and the following results are obtained:
Number of heads
0
1
2
3
4
5
Frequency
80
570
1100
900
500
50
If 2
for 5 d. f at 5% level of significance be 11.07, test the hypothesis that the
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coins are unbiased.
Q.6 (a) A factory produces razor blades. The probability of its being defective is 1/500. In
10,000 packets of 10 blades each, calculate the approximate numbers of packets
have 2 defective blades.
03
(b) If Skulls are classified as A, B, C according as the length and breadth index as
under 75, between 75 and 80, or over 80; find the approximately mean and the
standard deviation of the classes in which A are 58% , B are 38% and C are 4%
given
t
1
f t
t
e 2 /2dt f (0.20) = 0.08 and f (1.75) = 0.46.
2
04
0
2
(c) In a bolt factory, machines A, B, and C manufacture 25%, 35% and 40% of the
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total of their output 5%, 4% and 2% are defective bolts. A bolt is drawn at random
from the product and is found to be defective. What are the chances that it was
manufactured by machines A, B, or C?
Q.7
In an experiment on immunization of cattle from tuberculoses the following result
were obtained:
Affected
Unaffected
Inoculated
12
26
Not Inoculated
16
6
Examine the effect of vaccine in controlling the susceptibility to tuberculoses.
(Given that for 5% level of significance 2
for 1 d. f is 3.841, for 2 d. f. is 5.99
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and for 3 d. f is 7.815).
OR
Q.7
The heights of 9 males of a given locality are found to be 45, 47, 50, 52, 48, 47,
49, 53, 51 inches. Is it reasonable to believe that the average height is differ
significantly from assumed mean 47.5 inches? (Given that for 5% level of
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significance t for 7 d. f is 2.365, for 8 d. f. is 2.306 and for 9 d. f. is 2.262)
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This post was last modified on 04 March 2021