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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
BE Computer
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Official Gujarat Technological University (GTU) examination paper 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.
Transcribed for student exam preparation from Gujarat Technological University official examination archives. Questions, syllabus guidelines, and curriculum marking schemes remain the intellectual property of Gujarat Technological University.
2140706 Numerical and Statistical Methods for Computer Engineering
Official GTU PDF · Summer 2024
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