Subject Code: 2140606
--- Content provided by FirstRanker.com ---
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER- IV EXAMINATION — SUMMER 2020
Subject Name: NUMERICAL AND STATISTICAL METHODS FOR CIVIL ENGINEERING
Time: 10:30 AM TO 01:00 PM
Total Marks: 70
--- Content provided by FirstRanker.com ---
Instructions:
- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
Q.1 (a) There are 3 Red and 2 Black balls in a box. If 2 balls are selected at random, find the expected number of Black balls. [03]
--- Content provided by FirstRanker.com ---
(b) Construct an Interpolating polynomial of degree 2 which takes the following values [04]
| x | -1 | 0 | 1 | 3 |
| y | 2 | 1 | 0 | -1 |
(c) By using Method of least squares, fit a second degree parabola y=a+bx+cx2 to the following data. [07]
| x | 0 | 1 | 2 | 3 | 4 |
| y | 1 | 1.8 | 1.3 | 2.5 | 2.3 |
Q.2 (a) Considering following tabular values, Determine the area bounded by the given curve and X-axis between x =7.47 to x =7.52 by Trapezoidal rule. [03]
| x | 7.47 | 7.48 | 7.49 | 7.50 | 7.51 | 7.52 |
| Y | 1.93 | 1.95 | 1.98 | 2.01 | 2.03 | 2.06 |
(b) Using Simpson’s 3/8 rule, evaluate ?16 Y dx with n=6. [04]
(c) Use Gauss-Seidel method to obtain the solution of the system [07]
--- Content provided by FirstRanker.com ---
6x+ y+z=105, 4x+8y+3z =155, 5x+4y—-10z=65OR
Q.2 (a) 4 Coins are tossed simultaneously. What is the probability of getting (a) Two heads (b) At least two heads (c) At most two heads [03]
(b) Use Bisection method to find the real root of equation 2sinx—x =0 [04]
(c) Find a real root of x3+x—1= 0, correct to four decimal places using Newton-Raphson method. [07]
--- Content provided by FirstRanker.com ---
Q.3 (a) Using Newton’s divided difference method, find f(9) from the given data: [03]
| X | 5 | 7 | 11 | 13 | 17 |
| f(x) | 150 | 392 | 1452 | 2366 | 5202 |
(b) Using Simpson’s 1/3 rule, evaluate ?03 cos(x) dx taking 6 sub intervals. [04]
(c) Solve the following linear system using Gauss Elimination method: [07]
2x+y+z=10, 3x+2y+3z=18, x+4y+9z=16
Q.4 (a) Use second order Runge-Kutta method to find y(1.2) with h =0.1 [03]
--- Content provided by FirstRanker.com ---
(b) Use the Secant method to find approximate root of equation xex —1=0 [04]
(c) Using Taylor’s series method, obtain the solution of dy/dx = x2 + y2, y(0)=1. Find the value of y(1.1) [07]
OR
Q.4 (a) Use Euler's Method to find y(0.2) from the differential equation dy/dx = y - (2x/y), y(0)=1 [03]
(b) Evaluate ?-11 (1/(1+x2)) dx using the Gaussian Integration formula with n = 2. [04]
--- Content provided by FirstRanker.com ---
(c) Given that dy/dx = x-y2, y(0)=0, y(0.2)=0.02, y(0.4)=0.0795, y(0.6) =0.1762 Evaluate y(0.8) by Milne’s Predictor — Corrector method. [07]
Q.5 (a) The following table gives marks obtained by 50 students in a subject of Civil. Find the Median. [03]
| Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
| No. of Students | 16 | 12 | 18 | 3 | 1 |
(b) Find the correlation coefficient from the following data: [04]
| X | 1 | 2 | 3 | 4 | 5 |
| Y | 6 | 8 | 11 | 9 | 12 |
(c) Calculate karl Pearson’s co-efficient of skewness from the following data: [07]
| x | 0-100 | 100-200 | 200-300 | 300-400 | 400-500 | 500-600 | 600-700 | 700-800 |
| S | 6 | 10 | 18 | 20 | 15 | 12 | 10 | 9 |
OR
--- Content provided by FirstRanker.com ---
Q.5 (a) Find the mean and standard deviation of a group of data points: 3,4,6,7,9,15 [03]
(b) Ten Students got the following percentage of marks in Mathematics and Statistics. Calculate the correlation coefficient. [04]
| Roll no. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Maths | 78 | 36 | 98 | 25 | 75 | 82 | 90 | 62 | 65 | 39 |
| Statistics | 84 | 51 | 91 | 60 | 68 | 62 | 86 | 58 | 53 | 47 |
(c) A study of the amount of rainfall and the quality of air pollution removed produced the following data: [07]
| Daily rainfall x | 4.3 | 4.5 | 5.9 | 5.6 | 6.1 | 5.2 | 3.8 | 2.1 | 7.5 |
| Particulate removed y | 126 | 121 | 116 | 118 | 114 | 118 | 132 | 141 | 108 |
(a) Find the equation of the regression line to predict the particulate removed from the amount of daily rainfall.
(b) Find the amount of particulate removed when daily rainfall is x = 4.8 units.
--- Content provided by FirstRanker.com ---
Date:29/10/2020
--- Content provided by FirstRanker.com ---
This download link is referred from the post: GTU BE 2020 Summer Question Papers || Gujarat Technological University