Round off the number 865250 to four significant figures and compute absolute error, relative error.
Find a root of the equation 𝑥3 − 4𝑥 − 9 = 0, using the bisection method. Carry out computations upto the 6th iteration.
Define ill-conditioned system. Solve the following system by Gauss sediel method: 27𝑥 + 6𝑦 − 𝑧 = 85, 6𝑥 + 15𝑦 + 2𝑧 = 72 , 𝑥 + 𝑦 + 54𝑧 = 110
Evaluate ∫ 𝑑𝑥 1+𝑥2 6 0 by trapezoidal rule taking h = 1.
Using Runge-Kutta method of fourth order, Solve for y at x = 1.2, 1.4 . Given that dy dx = 2xy+ex x2+xex and y(1) = 0.
Using Euler’s method, find an approximate value of y at 𝑥 = 1 taking h = 0.1. Given that 𝑑𝑦 𝑑𝑥 = 𝑥 + 𝑦 and 𝑦(0) = 1.
Find the number of roots of the equation 𝑥3 − 3𝑥2 − 4𝑥 + 13 = 0 in the interval [-1,0].
Find a real root of the equation xlog10x = 1.2 by regula falsi method correct to three decimal places.
Find the polynomial f(x) using Lagrange’s formula and hence find f(3) for following table: x 0 1 2 5 f(x) 2 3 12 147
Find a root of the equation 𝑥3 − 2𝑥 − 5 = 0 by secant method correct to three decimal places.
Find the polynomial using interpolation formula for the following values. Hence evaluate f(4). x 0 1 2 3 f(x) 1 2 1
Find a root of the equation 𝑥4 − 𝑥 = 10 by Newton Raphson method correct to two decimal places.
Evaluate ∫ 𝑥2 1+𝑥3 𝑑𝑥 1 0 by Simpson’s 1/3rd rule taking h = 0.25.
x 6 7 7 8 8 8 9 9 10 y 5 5 4 5 4 3 4 3
Find a root of the equation 𝑥3 − 2𝑥2 + 𝑥 − 2 = 0 by Bairstow method. Carry first iteration with 𝑝0 = 𝑞0 = 0.
Evaluate ∫ 1 1+𝑥 𝑑𝑥 3 0 with n=6 by using Simpson’s 3/8th rule.
x 0 1 2 3 4 y 1 1.8 1.3 2.5 6.3
Class 0-8 8-16 16-24 24-32 32-40 40-48 Frequency 8 7 16 24 15
Calculate the two regression coefficients from the following data and find correlation coefficient. x 7 4 8 6 5 y 6 5 9 8
A sample of 3 items is selected at random from a box containing 10 items of which 4 are defective. Find the expected number of defective items.
x 2 4 5 6 8 11 y 18 12 10 8 7
x 6 2 10 4 8 y 9 11 5 8
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Official Gujarat Technological University (GTU) examination paper and step-by-step solutions for Numerical and Statistical Methods for Computer Engineering (Summer 2024, B.E. · Computer Engineering, Sem 4). Features complete 70-mark regular & remedial examination pattern, official marking distribution across all 5 questions, and direct 1-click official PDF download.
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