Numerical IT

How many Significant digits are in the number of 0.007050

• 3

• 4

• 5

• 6

If the number 37.46235 rounded of to four significant
digits then the percentage error is

•  $6.27\times10^3$  

•  $6.27\times10^{-5}$  

•  $6.27\times10^5$  

•  $6.27\times10^{-3}$  

Which of the following operations are allowed in Gauss-Elimination method ?

• Swapping two columns

• Multiply a row by zero

• Swapping two rows

• Addition of two columns

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: 

• 1.5

• 0.5

• 2

• 2.5

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

• 2

The order of convergence for Bisection method is

• 1

• 0.5

• 2

• 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

• 1.0602

• 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 $a\ \left(>0\right)$ is: 

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

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

•  $x_{n+1}=x_n-\frac{a}{x_n}$  

•  $x_{n+1}=2\ x_n$