Computer Oriented Numerical Analysis Solved Assignment of Bsc IT

1 . Define error, relative error and absolute error. Give example of each.

2 . Find the rate of convergence of Newton Raphson Method.

3 . By using Regula Falsi method find the root of 15 correct up to 2 decimal places.

4 . Solve the following set of equations by using Gauss Elimination Method. 2x+3y+4z = 12 3x+y+z = 4 x+4y+z = 5

5 .

CASE STUDY

1.

2.

3.

ASSIGNMENT C

Question No: 1

Round off the number 0.859378 to four significant digits.

1. 0.8594
2. 0.8593
3. 8593
4. 8.593

Question No: 2

Truncate the number 0.859378 to four significant digits.

1. 0.8594
2. 0.8593
3. 8593
4. None

Question No: 3

The formula for Regula Falsi method is

Question No: 4

1. 1.234
2. 1.666
3. 1.9823
4. None of the above

Question No: 5

1. x0=1, x1=2
2. x0=0, x1=1
3. x0=0, x1=-1
4. x0=-1, x1=-2

Question No: 6

1. 2.3568
2. 2.995
3. 2.09
4. 2.135

Question No: 7

1. .479
2. .3854
3. .4053
4. .793

Question No: 8

Which method has the fastest convergence?

1. Bisection method
2. Newton Raphson Method
3. Regula Falsi Method
4. Iterative Method

Question No: 9

In Bisection method the initial approximation x0 and x1 are chosen such that

1. f(x0).f(x1)<0
2. f(x0).f(x1)>0
3. f(x0).f(x1)=0
4. f(x0)-f(x1) is negative.

Question No: 10

   d) None

Question No: 11

1. Transcendental equation
2. Algebraic Equation
3. Polynomial Equation
4. None of the above

Question No: 12

          d) None of these

Question No: 13

Which one is true?

Question No: 14

If ei+1/eip = 1 then rate of convergence is said to be

1. Linear
2. Quadratic
3. p
4. None

Question No: 15

Rate of convergence of Newton Raphson method is

1. 1
2. 2
3. 3
4. Can’t be determined

Question No: 16

Inverse of inverse of a matrix A is

1. A-1
2. 1/A
3. A
4. None of these

Question No: 17

For Matrix A and B of same order, AB=BA

1. True
2. FALSE
3. Can’t be determined
4. None of these

Question No: 18

Which one is an integration method?

1. Trapezoidal Method
2. Newton Raphson Method
3. Jacobi Method
4. None

Question No: 19

Which one is not an interpolation method?

1. Lagrange’s Method
2. Newton Forward Method
3. Newton Divided Difference Formula
4. Bisection Method

Question No: 20

Round off the number 0.259378 to four significant digits.

1. 0.2594
2. 0.2593
3. 2594
4. None

Question No: 21

Truncate the number 0.159378 to four significant digits.

1. 0.1594
2. 0.1593
3. 1593
4. 1.594

Question No: 22

Which one is true?

1. y1=y0-h
2. y1=y0/h
3. y1=y0+h
4. None

Question No: 23

The formula for Bisection method is

1. x2=(x0+x1)/2
2. x2=(x0-x1)/2
3. x2= x2=(x0*x1)/2
4. None

Question No: 24

Cramer’s rule fails for

1. Δ = 2
2. Δ = 1
3. Δ =0
4. None

Question No: 25

To solve a set of linear algebraic equations, the method is:

1. Gauss Jordan
2. Jacobi
3. Gauss Elimination
4. None

Question No: 26

1. (1,6)
2. (2,3)
3. (2,2)
4. None

Question No: 27

Equation of line is:

1. y=c
2. y=ax2+c
3. y=ax+c
4. None

Question No: 28

Δ² yₒ is

1. y2-2y1+y0
2. y2+2y1+y0
3. y2+y1+y0
4. None

Question No: 29

Runga Kutta method is used for

1. Differentiation
2. Integration
3. Differential Equation
4. None of these

Question No: 30

Trapezoida formula is

1. h/2[yₒ+yn+2(y1+y2+….+yn)]
2. [yₒ+yn+2(y1+y2+….+yn)]
3. 3h/8[yₒ+yn+2(y1+y2+….+yn)]
4. None of these

Question No: 31

For Simpson’s 3/8 rule, the value of n is

1. 1
2. 2
3. 3
4. 4

Question No: 32

Accuracy of Simpson’s method is better than Trapezoidal method.

1. True
2. False
3. Can’t say
4. ,

Question No: 33

Divided Difference formula can also be used for equi-distant points:

1. True
2. False
3. Can’t say
4. ,

Question No: 34

(1+Δ)(1+?)=

1. 1
2. 0
3. Δ
4. None

Question No: 35

1. 3
2. 4.3
3. 2.9
4. None of these

Question No: 36

 In Question 34, what is the value of F’(x) at x=0

1. 1
2. 2
3. 3
4. None of these

Question No: 37

For getting the solution of non-linear equation, which method uses the tangent

1. Bisection
2. Iterative
3. Newton Raphson
4. Regula Falsi

Question No: 38

Jordan method is a refinement over Gausee’s method

1. True
2. False
3. Can’t say
4. ,

Question No: 39

Numerical Solutions always give accurate solution

1. True
2. False
3. ,
4. ,

Question No: 40

What will be the relative error if 2/3 is approximated to 0.667?

1. 0.0005
2. 0.0006None
3. 0.005
4. None