Download GTU B.Tech 2020 Summer 4th Sem 2140706 Numerical And Statistical Methods For Computer Engineering Question Paper

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GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER- IV EXAMINATION — SUMMER 2020

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Subject Code: 2140706 Date: 29/10/2020

Subject Name: NUMERICAL AND STATISTICAL METHODS FOR COMPUTER ENGINEERING

Time: 10:30 AM TO 01:00 PM Total Marks: 70

Instructions:

1. Attempt all questions.

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2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.

MARKS

Q.1 (a) Find the relative error if the number X =0.004997 is 03

1. truncated to three decimal places.

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2. rounded off to three decimal places.

(b) Find the negative root of x’ —7x+3 = 0 by the bisection method 04 correct up to three decimal places.

(c) Using Gauss Jacobi method solve the following system of the equations: 07
8x—y+2z=13
x—-10y+3z=17

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Q.2 (a) Using trapezoidal rule to evaluate ∫ dx, dividing the interval into four equal parts. 03
₀² 1/(2+ x²)

(b) By using Lagrange’s interpolation formula, find y(10). 04
X 5 6 9 11

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(c) Using the Runge-Kutta method of fourth order, solve 10 dy/dx =x²+3y, y(0)=1 at x=0.1, x =0.2 taking h =0.1 07
OR
(c) Using Euler’s method find the approximate value of y at x=1.5 taking h =0.1. Given that dy/dx =(y-x)/√x and y(1)=2. 07

Q.3 (a) Using Newton Raphson method find the positive root of x² —x—10 =0 correct up to three decimal places. 03

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(b) Fit a least square quadratic curve to the following data: 04
X 1 2 3 4
y 1.7 1.8 2.3 3.2
Estimate y(2.4).

(c) Find the regression coefficients b_xy and b_yx hence, find the correlation coefficient between x and y for the following data 07

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Q.4 (a) Using Simpson’s 1/3 rule, find ∫ e^x dx, by taking n = 6. 03
₀^0.6

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(b) Using Newton’s divided difference formula, compute f(10.5) from the following data: 04
X 10 11 13 17
f(x) 2.3026 2.3979 2.5649 2.8332

(c) Solve x⁴ —8x³ +39x² —62x + 50 by using Lin Bairstow method up to third iteration starting with p₀ = q₀ =0. 07

Q.4 (a) Find a real root of the equation xlog₁₀ x=1.2 by the regula falsi method. 03

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(b) The first four moments of distribution about x =2 are 1, 2.5, 5.5 and 16. Calculate the four moments about X and about zero. 04

(c) Given that dy/dx = (1/2)x² + (1/2)y², y(0) =1, y(0.1)=1.06, y(0.2)=1.12, y(0.3) =1.21 evaluate y(0.4) by Milne’s predictor-corrector method. 07
OR

Q.4 (a) Find the arithmetic mean form the following data: 03
Marks less than 10 20 30 40 50 60

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(b) (i) Obtain relation between Δ and E. 04
(ii) Obtain relation between D and E.

(c) Obtain cubic spline for every subinterval from the following data 07
X 0 1 2 3

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Q.5 (a) Two unbiased coins are tossed. Find expected value of number of heads. 03

(b) By Simpson’s 3/8 rule, evaluate ∫ dx taking h = 1/6 04
₀¹ 1/x

(c) From the following table, estimate the number of students who obtained marks between 40 and 45. 07

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Q.5 (a) Using Budan’s theorem find the number of roots of the equation S(x)=x⁵—4x³ +3x² ~10x+8 =0 in the interval [-1,0]. 03

(b) Find the positive solution of x—2sinx =0, correct up to three decimal places starting from x₀=2 and x₁ =1.9. Using secant method. 04

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(c) Using Gauss Siedel method solve the following system of the equations: 07
3x—-0.1y-0.2z=17.85
0.1x+7y-0.3z=-19.3
0.3x-0.2y+10z=71.4

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