GTU BE 2019 Summer Question Papers || Gujarat Technological University
GUJARAT TECHNOLOGICAL UNIVERSITY
SEMESTER-IV(NEW) — EXAMINATION - SUMMER 2019
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Subject Code:2140706 Date:15/05/2019
Subject Name: Numerical and Statistical Methods for Computer Engineering
Time:02:30 PM TO 05:00 PM
Total Marks: 70
Instructions:
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- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
| Q.1 (a) | Find the percentage error in the area of an ellipse when errors of 2% and 3 % are made in measuring its major and minor axes respectively. | 03 |
| (b) | Using the bisection method, find a root of f(x)=2x-3sinx—5=0 correct up to three decimal places. | 04 |
| (c) | Interpolate the function y= f(x)at point x=1.5using the following tabulated data. | 07 |
| X | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| y | 1 | 8 | 27 | 64 | 125 | 216 | 343 | 512 |
| Q.2 (a) | Using trapezoidal rule find the value of the integral ? dx / (1+x) with h =1. | 04 |
| (b) | Discuss false position method. | 03 |
| (c) | Fit a second-degree parabola to the following data using method of least squares. | 07 |
| X | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| y | 1 | 1.8 | 1.3 | 2.5 | 6.3 |
OR
| (c) | Find the cubic spline in the interval [0, 2] for the following data: | 07 |
| X | 0 | 2 | 4 | 6 |
|---|---|---|---|---|
| y | 1 | 9 | 41 | 41 |
| Q.3 (a) | Apply Budan's theorem to find the number of roots of the equation x4 —3x2 —4x+13 in the interval [—3,—2] and [—2,—1] | 03 |
| (b) | Find an iterative formula for vN , where N is a positive number and hence, find vE correct up to four decimal places. | 04 |
| (c) | Using Gauss Seidel method solve the following equations: --- Content provided by FirstRanker.com --- 5x+y-z=102x+4y+z=14 x+y+8z=20 | 07 |
OR
| (a) | Prove that (i)(1+?)(1-?)=1 (ii)?=(?-?) | 03 |
| (b) | Find y(32) from the following table: | 04 |
| X | 25 | 30 | 35 | 40 |
|---|---|---|---|---|
| y | 0.2707 | 0.3027 | 0.3386 | 0.3794 |
| Q.4 (a) | Using Simpson's 1/3 rule, find ? e-x dx, by taking n=6 (limits 0 to 1) | 03 |
| (b) | Find the median of the following data: | 04 |
| Age greater than (in years) | 0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 |
|---|---|---|---|---|---|---|---|---|
| No. of persons | 230 | 218 | 200 | 165 | 123 | 73 | 28 | 8 |
| (c) | Solve dy/dx =y- 2x , y(0) =1 in the range 0 | 07 | |
OR
| Q.4 (a) | Write the formula for Runge-Kutta second order method. | 03 |
| (b) | Use Lagrange's interpolation formula to find the value of y (10) for given data: | 04 |
| X | 5 | 6 | 9 | 11 |
|---|---|---|---|---|
| y | 12 | 13 | 14 | 16 |
| (c) | Using Runge- Kutta method of fourth order, solve for y (0.1), y (0.2) and y (0.3) given that y' =xy+3y, y(0)=1. | 07 |
| Q.5 (a) | Develop a C program for bisection method. | 03 |
| (b) | Two unbiased dice are thrown at random. Find the probability distribution of the sum of the numbers on them. Also find the mean and variance. | 04 |
| (c) | Calculate the coefficient of correlation for the following pairs of x and y: | 07 |
| X | 17 | 19 | 21 | 26 | 20 | 28 | 26 | 27 |
|---|---|---|---|---|---|---|---|---|
| y | 23 | 27 | 25 | 26 | 27 | 25 | 30 | 33 |
OR
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| Q.5 (a) | Discuss type of Regression. | 03 |
| (b) | Find the regression coefficient of y on x for the following data: | 04 |
| X | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| y | 160 | 180 | 140 | 180 | 200 |
| (c) | Given dy/dx = (x2 + y2), y(0) = 1, y(0.2)=2.0033, y(0.4) =2.1755, y(0.6) =2.2493 , find y (0.8) using Milne's Predictor Corrector method. | 07 |
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