Numerical CSE B

How many Significant digits are in the number of 0.002060

• 3

• 4

• 5

• 2

If you round off  $\sqrt{5}$  to four decimal places , then the corresponding relative error is

•  $-1.4321\times10^{-5}$  

•  $1.4321\times10^{-5}$  

•  $1.4321\times10^{-3}$  

•  $3.2022\times10^{-3}$  

If in $Ax=B$  , the number of variables are greater than the number of equations then the system have : 

• no solution

• unique solution

• Infinite solution

• May or may not have solution

Consider the following system of linear equations $3y-2z=3,\ \ \ \ \ 2x-y+4z=27,\ \ \ \ 4x-y-3z=3$  Use Gauss-Seidel method  with the initial value  $x^{\left(0\right)}=0,\ y^{\left(0\right)}=0,\ z^{\left(0\right)}=0$ , the value of  $y^{\left(1\right)}=$  ?

• 0.75

• 1

• 1.75

• 0

Starting from $x_0=1\$  , one step of Newton-Raphson method in solving the equation  $x^3+3x-7=0$  gives the next value  $\left(x_1\right)$  as: 

•  $x_1=1.5$  

•  $x_1=0.5$  

•  $x_1=2$  

•  $x_1=2.5$  

The order of convergence for Bisection method is

• 1

• 2

• 1.5

• 1.618

• $l_{21}=2,\ u_{11}=1,\ u_{12}=3,\ u_{22}=2$

• $l_{21}=2,\ u_{11}=1,\ u_{12}=2,\ u_{22}=2$

• $l_{21}=2,\ u_{11}=1,\ u_{12}=2,\ u_{22}=-3$

• $l_{21}=2,\ u_{11}=1,\ u_{12}=2,\ u_{22}=5$

If   $\frac{\text{d}y}{\text{d}x}=\log_{10}\left(x+y\right)$  and  $y\left(0\right)=2$ , Then the value of   $y\left(0.2\right)$  in one step using Euler's method is

• 1

• 2.0602

• 2.3010

• 2.1386

Which one of the following method is a Predictor corrector method.

• Euler's method

• Runge-Kutta method

• Modified Euler's method

• matrix inversion method

Newton's formula for finding the square root of  $a\ \left(a>0\right)$ 

is: 

•  $x_{n+1}=\frac{1}{2}\left(x_n-\frac{a}{x_n}\right)$  

•  $x_{n+1}=\frac{1}{2}\left(x_n+\frac{a}{x_n}\right)$  

•  $x_{n+1}=x_n-\frac{a}{x_n}$  

•  $x_{n+1}=2\ x_n$