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

*****************

2

This post was last modified on 04 March 2021