Download GTU (Gujarat Technological University Ahmedabad) B.Tech/BE (Bachelor of Technology/ Bachelor of Engineering) 2020 Summer 4th Sem 2141703 Numerical Techniques And Statistical Methods Previous Question Paper
Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER? IV EXAMINATION ? SUMMER 2020
Subject Code: 2141703 Date:26/10/2020
Subject Name: NUMERICAL TECHNIQUES & STATISTICAL METHODS
Time: 10:30 AM TO 01:30 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 (a) Using usual notations show that (1/2 + -1/2 ) (1 + )1/2 = 2 + .
03
(b) Explain different types of errors in Numerical computation.
04
(c) Evaluate 0.5
using Romberg's method, correct to 3 decimal places.
07
0
Q.2 (a) Explain Bisection method to solve the algebraic equation.
03
(b) A random variable x has the following probability distribution:
04
0
1
2
3
1/6
3/8
3/8
1/8
Find the standard deviation of x for the given distribution.
(c) If (100) = 10.63, (150) = 13.03, (200) = 15.04, (250) = 16.81,
07
(300) = 18.42, (350) = 19.90 and (400) = 21.27 , find the value of
(218).
OR
(c) Evaluate f(9) using Lagrange's interpolation formula for the below given
07
values:
x
5
7
11
13
17
f(x) 150 392 1452 2366 5202
Q.3 (a) State Trapezoidal rule, Simpson's 1/3rd rule and Simpson 3/8th rule.
03
(b) Solve, by Gauss Jacobi iteration method, the equations
04
20 + - 2 = 17; 3 + 20 - = -18; 2 - 3 + 20 = 25.
(c) Using Runge-Kutta method of fourth order, solve 2-2
=
with (0) = 07
2+2
1 at = 0.2.
OR
Q.3 (a) Evaluate 1
using Gauss quadrature formula of three points.
03
0
-2
(b) Solve, by Gauss Seidel iteration method, the equations
04
2 + + 6 = 9; 8 + 3 + 2 = 13; + 5 + = 7.
(c) Solve the boundary-value problem 2 - = 0 with (0) = 0 and (2) = 07
2
3.62686 by finite difference method.
Q.4 (a) Calculate the median for the following data:
03
Class
0-30
30-60
60-90
90-120
120-150 150-180
Interval
Frequency 8
13
22
27
18
7
(b) A die is thrown six times. If getting an odd number is a success, find the 04
probability of (i) at least five success and (ii) at most five success.
(c) Represent the following information in form of a network. Find average duration time 07
or expected time of each activity and obtain the critical path.
1
Activity
1- 2-
2-
3-
4-
4-
5-
5-
7-
8-
9-
6-
2
3
4
4
5
6
7
8
9
9
10 10
Optimistic
4
1
8
3
2
3
3
4
4
2
4
4
time
Most Likely
9
5 10
6
4
7
7
8
9
6
11
7
time
Pessimistic
14 18 17
8
5
10 10
9
14 10 18
9
time
OR
Q.4 (a) Calculate the mode for the following data:
03
Class
0-10
10-20
20-30
30-40
40-50
Interval
(b) A book contains 100 misprints distributed randomly throughout its 100 pages. 04
What is the probability that a page observed at random contains at least 2
misprints.
(c) Draw PERT ? diagram after finding out expected time & find critical path.
07
Activity
Sequence
Optimistic
Most Likely
Pessimistic Time
Time
Time
A
1-2
7
12
13
B
1-3
7
10
12
C
2-5
8
13
15
D
3-5
10
12
22
E
5-6
10
14
18
Q.5 (a) A card is drawn at random from a pack of 52cards. What is the probability that 03
the card is a spade or a king?
(b) A tire company is suspicious to claim that the average lifetime of certain tires 04
is at least 28000 km. To check the claim, the company takes the sample of 40
tires and gets a mean life time of 27463 km with standard deviation of 1348
km. Test the hypothesis at 1% level of significance.
(c) Fit a Poisson distribution for the following data and test the goodness of fit.
07
x
0
1
2
3
4
f
112
73
30
4
1
OR
03
Q.5 (a) Define a term random variable and explain different types of random variable.
(b) The mean of 35 sample of the thermal conductivity of a certain kind of cement 04
brick is 0.343 with standard deviation of 0.010. Test the hypothesis that the
population mean is 0.340 at 5% level of significance.
(c) Fit a binomial distribution for the following data showing the survey of 800 07
familie
s with 4 children and test the goodness of fit.
No. of boys
0
1
2
3
4
No. of girls
4
3
2
1
0
No. of families
32
178
290
238
64
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This post was last modified on 04 March 2021