Free Printable UBA10-Numerical Methods

1.

Using Newton-Raphson method, find a root correct to three decimal places of the equation x³ - 3x - 5 = 0

a)

2.275

b)

2.279

c)

2.222

d)

None of these

2.

We wish to solve x² - 2 = 0 by Newton Raphson technique. If initial guess is x₀ = 1.0, subsequent estimate of x (i.e. x₁) will be

a)

1.414

b)

1.5

c)

2

d)

None of these

3.

The order of convergence in Newto-Raphson method is

a)

2

b)

3

c)

0

d)

1

4.

The sufficient condition for Gauss-seidal mathod is

a)

Linear

b)

Diagonally dominant

c)

Diagonal matrix

d)

None of these

5.

Find the iterative formula for finding the value of √N where N is a positive real number, using Newton-Raphson method.

a)

x_n+1=[x_n+(N/x_n)]

b)

x_n+1=(1/2)[x_n+(N/x_n)]

c)

x_n+1=[x_n+(N/x_n)]/3

d)

x_n+1=[x_n-1+(N/x_n)]

6.

The order of convergence in fixed point iteration method is

a)

2

b)

3

c)

0

d)

1

7.

Which of the following vector is not an initial vector when we find the largest eigen value by Power mentod

a)

Transpose of (1 0 0)

b)

Transpose of (0 1 1)

c)

Transpose of (0 1 0)

d)

Transpose of (0 0 0)

8.

Sum of the eigen values of a matrix A is equal to

a)

Determinat of A

b)

Trace of A

c)

sum of minors of the main diagonal elements

d)

None of these

9.

Find the root lies between for the function 3x-cosx=1 is

a)

0 & 1

b)

1&2

c)

2&3

d)

None of these

10.

Express the equation f(x)=x³+x²-100=0 as x=g(x) bt iteration method

a)

10/√(x+1)

b)

(100-x²)^1/3

c)

(100-x³)^1/2

d)

100/(x²+x)

11.

Find f(2) for the data f(0) = 1, f(1) = 3 and f(3) = 55 using Newton's divided difference formula.

a)

25

b)

21

c)

23

d)

32

12.

Given the two points $\left(a,f\left(a\right)\right),\left(b,f\left(b\right)\right)$ , the linear Lagrange polynomial $f1\left(x\right)$ that passes through these two points is given by

a)

$f1\left(x\right)=\frac{x-b}{a-b}f\left(a\right)+\frac{x-a}{a-b}f\left(b\right)$

b)

$f1\left(x\right)=\frac{x}{b-a}f\left(a\right)+\frac{x}{b-a}f\left(b\right)$

c)

$f1\left(x\right)=f\left(a\right)+\frac{f\left(b\right)-f\left(a\right)}{b-a}\left(b-a\right)$

d)

$f1\left(x\right)=\frac{x-b}{a-b}f\left(a\right)+\frac{x-a}{b-a}f\left(b\right)$

13.

Based on the data given, which is the suitable type of polynomial to do the approximation?

a)

Linear

b)

Quadratic

c)

Cubic

d)

Quartic

14.

f(x)-f(x-h)=

a)

$\Delta f\left(x\right)$

b)

$\nabla f\left(x\right)$

c)

E(x)

d)

none

15.

Backward difference operator pronounced as

a)

delta

b)

lamda

c)

nabla

d)

alpha

16.

$\Delta^2y_0=$

a)

$\Delta y_1-\Delta y_0$

b)

$\Delta y_0-\Delta y_1$

c)

$\Delta^2y_1-\Delta^2y_0$

d)

$\Delta y_1+\Delta y_0$

17.

Estimate f(1.5) using Lagrange interpolation.

a)

−0.8673

b)

-0.7214

c)

−0.9773

d)

-0.9113

18.

a)

3.125

b)

3.327

c)

3.542

d)

3.837

19.

In numerical integration the width of the sub intervals is given by

a)

$h=\frac{x_n-x_0}{n}$

b)

$h=\frac{x_n+x_0}{n}$

c)

$h=\frac{x_0-x_n}{n}$

d)

none of thesse

20.

In Trapezoidal rule, for the interval (2,5) if h=0.5 then the value of n is_________

a)

5

b)

2

c)

6

d)

4

21.

Simpson’s 1/3 rule is applicable for five ordinates.

a)

True

b)

False

22.

Simpson’s 3/8 rule is applicable for nine ordinates.

a)

True

b)

False

23.

Find f(2) for the data f(0) = 1, f(1) = 3 and f(3) = 55 using Newton's divided difference formula.

a)

25

b)

21

c)

23

d)

32

24.

The general form of a first order ODE is $\frac{dy}{dt}=f\left(t,y\right)$

a)

True

b)

False

25.

Given above is the general formula for forth order Runge-Kutta method. What is w?

a)

w denotes the evaluation (step) of RK method

b)

w denotes the consistency of RK method

c)

w are contants, any real numbers R

26.

Given $\frac{\text{d}y}{\text{d}x}=1-y,\ y\left(0\right)=0$ using a step size of h=0.1 , the value of y(0.2) using Euler’s method is most nearly

a)

0.1

b)

0.119

c)

0.19

d)

0.01

27.

18. Trapezoidal formula is also known as __________.

a)

A. Simpson’z rule

b)

B. Co-ordinate method

c)

C. Prismoidal method

d)

D. Average end area method.

28.

Simpson’s 1/3 rule is applicable for five ordinates.

a)

True

b)

False

29.

By Trapezoidal rule,

\int_{x_0}^{x_n}ydx=---

a)

$\frac{h}{2}\left(y_0+2\left(y_1+y_2+...+y_{n-1}\right)+y_{n_{ }}\right)$

b)

$\frac{h}{2}\left(y_0-2\left(y_1+y_2+...+y_{n-1}\right)+y_{n_{ }}\right)$

c)

$\frac{h}{2}\left(y_0+2\left(y_1+y_2+...+y_{n-1}\right)-y_{n_{ }}\right)$

d)

$\frac{h}{3}\left(y_0+2\left(y_1+y_2+...+y_{n-1}\right)+y_{n_{ }}\right)$

30.

In Trapezoidal rule, for the interval (0,1) if h=0.25 then the value of n is_________

a)

1

b)

2

c)

3

d)

4

UBA10-Numerical Methods

Total questions: 30

Worksheet time: 1hrs 25mins

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