Free Printable Numerical CSE B

1.

How many Significant digits are in the number of 0.002060

a)

3

b)

4

c)

5

d)

2

2.

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

a)

$-1.4321\times10^{-5}$

b)

$1.4321\times10^{-5}$

c)

$1.4321\times10^{-3}$

d)

$3.2022\times10^{-3}$

3.

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

a)

no solution

b)

unique solution

c)

Infinite solution

d)

May or may not have solution

4.

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 $y^{\left(1\right)}=$ ?

a)

0.75

b)

1

c)

1.75

d)

0

5.

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:

a)

$x_1=1.5$

b)

$x_1=0.5$

c)

$x_1=2$

d)

$x_1=2.5$

6.

The order of convergence for Bisection method is

a)

1

b)

2

c)

1.5

d)

1.618

7.

a)

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

b)

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

c)

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

d)

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

8.

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

a)

1

b)

2.0602

c)

2.3010

d)

2.1386

9.

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

a)

Euler's method

b)

Runge-Kutta method

c)

Modified Euler's method

d)

matrix inversion method

10.

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

is:

a)

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

b)

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

c)

$x_{n+1}=x_n-\frac{a}{x_n}$

d)

$x_{n+1}=2\ x_n$

Numerical CSE B

Total questions: 10

Worksheet time: 26mins

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