Round off the number 865250 to four significant figures and compute absolute error, relative error.
[3 marks]Find a root of the equation x3 −4x−9 = 0, using the bisection method. Carry out computations upto the 6th iteration.
[4 marks]Define ill-conditioned system. Solve the following system by Gauss sediel method: 27x +6y−z = 85, 6x +15y+2z = 72 , x+y+54z = 110
[7 marks]6 dx Evaluate ∫ by trapezoidal rule taking h = 1. 0 1+x2
[3 marks]Prove that (1) E = eℎD (2) ℎD = log (1+∆)
[4 marks]Using Runge-Kutta method of fourth order, Solve for y at x = 1.2,1.4 . Given dy 2xy+ex that = and y(1) = 0. dx x2+xex
[7 marks]Using Euler’s method, find an approximate value of y at x = 1 taking h = 0.1. dy Given that = x +y and y(0) = 1. dx
[7 marks]Find the number of roots of the equation x3 −3x2 −4x +13 = 0 in the interval [-1,0].
[3 marks]Find a real root of the equation xlog x = 1.2 by regula falsi method correct to10 three decimal places.
[4 marks]Find the polynomial f(x) using Lagrange’s formula and hence find f(3) for following table: x 0 1 2 f(x) 2 3 12 147
[5 marks]Derive iterative formula for √N.
[3 marks]Find a root of the equation x3 −2x−5 = 0 by secant method correct to three decimal places.
[4 marks]Find the polynomial using interpolation formula for the following values. Hence evaluate f(4). x 0 1 2 f(x) 1 2 1
[10 marks]Find a root of the equation x4 −x = 10 by Newton Raphson method correct to two decimal places.
[3 marks]Evaluate ∫ 1 x2 dx by Simpson’s 1/3rd rule taking h = 0.25.04 0 1+x3
[ marks]Fit a straight line to the following data: x 6 7 7 8 8 8 9 9 y 5 5 4 5 4 3 4 3 OR1
[3 marks]Find a root of the equation x3 −2x2 +x−2 = 0 by Bairstow method. Carry first iteration with p = q = 0.00
[3 marks]Evaluate ∫ 3 1 dx with n=6 by using Simpson’s 3/8th rule. 0 1+x
[4 marks]Fit a second degree parabola to the following data: x 0 1 2 3 y 1 1.8 1.3 2.5 6.3
[4 marks]Calculate the arithmetic mean for the following data: Class 0-8 8-16 16-24 24-32 32-40 40-48 Frequency 8 7 16 24 15
[7 marks]Find the first four moments for the set of numbers 2,4,6,8.
[4 marks]Calculate the two regression coefficients from the following data and find correlation coefficient. x 7 4 8 6 y 6 5 9 8
[2 marks]Asample 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.
[3 marks]Calculate the correlation coefficient between x and y using the following data: x 2 4 5 6 8 11 y 18 12 10 8 7
[5 marks]Obtain the two regression lines from the following data: x 6 2 10 4 y 9 11 5 8
[7 marks]