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Mth603 Solved MCQS for Final Term Exam

 

Exact solution of 2/3 is not exists.

TRUE

FALSE

 

The Jacobi’s method is A method of solving a matrix equation on a matrix that has ____ zeros along its main diagonal.

 

 No

At least one

 

 

A 3 x 3 identity matrix have three and __________eigen values.

 Same

Different

 

 

 Eigenvalues of a symmetric matrix are all _______

 Real

Complex

Zero

Positive

 

The Jacobi iteration converges, if A is strictly diagonally dominant

TRUE

FALSE

 

Below are all the finite difference methods EXCEPT _________.

 

 Jacobi’s method

Newton’s backward difference method

Stirlling formula

Forward difference method

 

If n x n matrices A and B are similar, then they have the same eigenvalues (with the same multiplicities).

TRUE

FALSE

 

 

If A is a nxn triangular matrix (upper triangular, lower triangular) or diagonal matrix, the eigenvalues of A are the diagonal entries of A.

 

TRUE

FALSE

 

The characteristics polynomial of a 3x 3 Identity matrix is __________, if x is the Eigen values of the given 3 x 3 identity matrix. Where symbol ^ shows power.

 

(X-1)^3

(x+1)^3

 X^3-1

 X^3+1

 

 

Two matrices with the same characteristic polynomial need not be similar.

 

TRUE

FALSE

 

 

 

Bisection method is a

 

Bracketing method

Open method

 

Regula Falsi means

 

Method of Correct position

Method of unknown position

Method of false position

Method of known position

 

 

Eigenvalues of a symmetric matrix are all _________.

Select correct option:

 

            Real

            Zero

            Positive

            Negative

 

An eigenvector V is said to be normalized if the coordinate of largest magnitude is equal to zero.

Select correct option:

 

            TRUE

            FALSE

 

 

 

 

 

 

 

Exact solution of 2/3 is not exists.

Select correct option:

 

            TRUE

            FALSE

 

 

The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric ________ definite matrices A.

Select correct option:

 

            Positive

            Negative

 

 

 

 

Differences methods find the ________ solution of the system. 

Select correct option:

 

            Numerical

            Analytical

 

 

 

 

 

The Power method can be used only to find the eigenvalue of A that is largest in absolute value—we call this Eigenvalue the dominant eigenvalue of A.

Select correct option:

 

            TRUE

            FALSE

 

 

 

 

 

 

The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its ________.

Select correct option:

 

            Main diagonal

            Last column

            Last row

            First row    

 

 

 

 

 

 

 

If A is a nxn triangular matrix (upper triangular, lower triangular) or diagonal matrix , the eigenvalues of A are the diagonal entries of A. 

Select correct option:

 

            TRUE

            FALSE

 

 

 

 

A 3 x 3 identity matrix have three and different Eigen values.

Select correct option:

 

            TRUE

            FALSE

 

Newton Raphson method falls in the category of

 

Bracketing method

Open Method

Iterative Method

Indirect Method

 

 

Newton Raphson method is also known as

Tangent Method

Root method

Open Method

Iterative Method

 

Secant Method uses values for approximation

 

1

3

2

4

 

Secant Method is than bisection method for finding root

Slow

Faster

 

In Newton Raphson method

 

Root is bracketed

Root is not bracketed

 

Regula falsi method and bisection method are both

 

Convergent

Divergent

 

In bisection method the two points between which the root lies are

 

Similar to each other

Different

Not defined

Opposite

 

In which methods we do not need initial approximation to start

Indirect Method

Open Method

Direct Method

Iterative Method

 

Root may be

 

Complex

Real

Complex or real

None

 

In Regula falsi method we choose points that have signs

 

2 points opposite signs

3 points opposite signs

2 points similar signs

None of the given

 

In a bounded function values lie between

1 and -1

1 and 2

0 and 1

0 and -2

 

Newton Raphson method is a method which when it leads to division of number close to zero

Diverges

Converges

 

Which of the following method is modified form of Newton Raphson Method?

Regula falsi method

Bisection method

Secant method

Jacobi’s Method

 

Which 1 of the following is generalization of Secant method?

Muller’s Method

Jacobi’s Method

Bisection Method

N-R Method

 

 

Secant Method needs starting points

 

2

3

4

1

Near a simple root Muller’s Method converges than the secant method

 

Faster

Slower

 

If   S is an identity    matrix, then

 

        

        

        

           All are true

 

If we retain r+1 terms in Newton’s forward difference formula, we obtain a polynomial of degree ---- agreeing with  at

 

        r+2

        r+1

        R

        R-1

P in Newton’s forward difference formula is defined as

 

            

 

        

        

      

Octal numbers has the base

 

           10

             2

             8

            16

Newton’s divided difference interpolation formula is used when the values of the independent variable are

 

       Equally spaced

 

        Not equally spaced

 

        Constant

        None of the above

 

Given the following data

 

0

1

2

4

1

1

2

5

 

Value of is

 

      1.5

 

       3

       2

 

       1

 

If is approximated by a polynomial  of degree n then the error is given by

 

        

           

 

Let  denotes the closed interval spanned by . Then vanishes ------times in the interval .

 

        N-1

        N+2

        N

        N+1

 Differential operator in terms of forward difference operator is given by

 

        

        

        

        

 Finding the first derivative of at =0.4 from the following table:

 

 

0.1

0.2

0.3

0.4

 

1.10517

1.22140

1.34986

1.49182

 

Differential operator in terms of ----------------will be used.

 

 

 

 

       Forward difference operator

        Backward difference operator

        Central difference operator

       All of the given choices

                                              

 

For the given table of values

0.1

0.2

0.3

0.4

0.5

0.6

0.425

0.475

0.400

0.452

0.525

0.575

 

, using two-point equation will be calculated as.............

 

 

 

        -0.5

        0.5

        0.75

        -0.75

  

 In Simpson’s 1/3 rule, is of the form

 

        

       ►

       ►

       ►

   

 

 While integrating, , width of the interval, is found by the formula-----.

 

        

      

        

        None of the given choices

 

   

 

 To apply Simpson’s 1/3 rule, valid number of intervals are.....

 

        7

        8

        5

        3

   

 For the given table of values

0.1

0.2

0.3

0.4

0.5

0.6

0.425

0.475

0.400

0.452

0.525

0.575

 

, using three-point equation will be calculated as ……

 

      17.5

      12.5

       7.5

     -12.5

   

 To apply Simpson’s 1/3 rule, the number of intervals in the following must be

 

        2

        3

        5

        7

   

 To apply Simpson’s 3/8 rule, the number of intervals in the following must be

 

       10

       11

       12

       13

   

 

 If the root of the given equation lies between a and b, then the first approximation to the root of the equation by bisection method is ……

 

 

 

 

       

        

        

        None of the given choices

   

 

............lies in the category of iterative method.

 

        Bisection Method

        Regula Falsi Method

       Secant Method

        All of the given choices                                                                                                

 For the equation, the root of the equation lies in the interval......

 

 

        (1, 3)

        (1, 2)

        (0, 1)

        (1, 2)

   

 

 Rate of change of any quantity with respect to another can be modeled by

 

        An ordinary differential equation

        A partial differential equation

 

        A polynomial equation

 

       None of the given choices

 

  

 If

Then the integral of this equation is a curve in

 

        None of the given choices

 

        Xt-plane

        Yt-plane

       Xy-plane

   

 

  In solving the differential equation

                 

,   By Euler’s method  is calculated as

 

        1.44

       1.11

        1.22

        1.33

   

 In second order Runge-Kutta method

 is given by

 

        

        

        

        None of the given choices

 

   

 In fourth order Runge-Kutta method,   is given by

 

                                                                                                         

      

        

        

 In fourth order Runge-Kutta method,  is given by

 

        

        

        

       None of the given choices

 

 

Adam-Moulton P-C method is derived by employing

 

       Newton’s backward difference interpolation formula

       Newton’s forward difference interpolation formula

        Newton’s divided difference interpolation formula

        None of the given choices

 

The need of numerical integration arises for evaluating the definite integral of a function that has no explicit ____________ or whose antiderivative is not easy to obtain

 

Derivatives

Antiderivative

 

If then system will have a

Definite solution

Unique solution

Correct solution

No solution

 

If  then

There is a unique solution

There exists a complete solution

There exists no solution

None of the above options

 

Direct method consists of method

2

3

5

4

We consider Jacobi’s method Gauss Seidel Method and relaxation method as

Direct method

Iterative method

Open method

All of the above

 

In Gauss Elimination method Solution of equation is obtained in

3 stages

2 stages

4 stages

5 stages

 

Gauss Elimination method fails if any one of the pivot values becomes

Greater

Small

Zero

None of the given

 

Changing the order of the equation is known as

 

Pivoting

Interpretation

 

Full pivoting is than partial pivoting

Easy

More complicated

 

The following is the variation of Gauss Elimination method

 

Jacobi’s method

Gauss Jordan Elimination method

 

Courts reduction method is also known as Cholesky Reduction method

True

False

 

Jacobi’s method is also known as method of Simultaneous displacement

True

False

Gauss Seidel method is also known as method of Successive displacement

False

True

 In Jacobi’s method approximation calculated is used for

Nothing

Calculating the next approximation

Replaced by previous one

All above

 

In Gauss Seidel method approximation calculated is replaced by previous one

True

False

 

Relaxation method is derived by

South well

Not defined

 

Power method is applicable for only

Real metrics

Symmetric

 Unsymmetrical

Both symmetric and real

 

 

The process of eliminating value of y for intermediate value of x is know as interpolation

True

False

 

 

 

In Richardson’s extrapolation method, we usually use two different step sizes ………and …… to yield a higher order method.

 

h, h/2             

h, h/3

h, h/4

None

 

In Simpson’s 3/8 rule, we divide the interval of integration into n sub-intervals. Where n is divisible by.....

 

3                     

4

5

None

1-Generally, Adams methods are superior if output at many points is needed.

 

  • True
  • False

 

2- Euler's method is only useful for a few steps and small step sizes; however Euler's method together with Richardson extrapolation may be used to increase the ____________.

 

  • order and accuracy
  • divergence

 

 

3- The first lngrange polynomial with equally spaced nodes produced the formula for __________.

 

  • Simpson's rule
  • Trapezoidal rule
  • Newton's method
  • Richardson's method

 

4- The need of numerical integration arises for evaluating the indefinite integral of a function that has no explicit antiderivative or whose antiderivative is not easy to obtain.

 

  • TRUE
  • FALSE

 

5- The Trapezoidal Rule is an improvement over using rectangles because we have much less "missing" from our calculations. We used ________ to model the curve in trapezoidal Rule

 

  • straight lines
  • curves
  • parabolas
  • constant

 

6-     The Euler method is numerically unstable because of ________ convergence of error.

  • Slow
  • Fast
  • Moderate
  • No

 

 

7-     Adams – Bashforth is a multistep method.

 

  • True
  • False

 

8-     The need of numerical integration arises for evaluating the definite integral of a function that has no explicit ____________ or whose antiderivative is not easy to obtain.

 

 

  • Antiderivative
  • Derivatives

 

 

9-     In Runge – Kutta Method, we do not need to calculate higher order derivatives and find greater accuracy.

 

  • True
  • False

 

 

10-An indefinite integral may _________ in the sense that the limit defining it may not exist.

 

 

  • Diverge
  • Converge

 

11-The Trapezoidal Rule is an improvement over using rectangles because we have much less "missing" from our calculations. We used ________ to model the curve in trapezoidal Rule.

 

  • straight lines
  • curves
  • parabolas
  • constant

 

 

12-An improper integral is the limit of a definite integral as an endpoint of the interval of integration approaches either a specified real number or 8 or -8 or, in some cases, as both endpoints approach limits.

  • True
  • False

 

13-Euler's Method numerically computes the approximate derivative of a function.

 

  • True
  • False

 

14-If we wanted to find the value of a definite integral with an infinite limit, we can instead replace the infinite limit with a variable, and then take the limit as this variable goes to _________.

 

  • Constant
  • Finite
  • Infinity
  • zero

Question : While solving a system of linear equations, which of the following approach is economical for the computer memory?

Select correct option:

          Direct

          Iterative

          Analytical

          Graphical

 

 Question :The basic idea of relaxation method is to reduce the largest residual to ………….

Select correct option:

          One

          Two

          Zero

          None of the given choices

 

Question:   The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its ________.

Select correct option:

main diagonal

last column

last row

first row

Question: If A is a nxn triangular matrix (upper triangular, lower triangular) or diagonal matrix , the eigenvalues of A are the diagonal entries of A.

Select correct option:

TRUE

FALSE

Question :  A 3 x 3 identity matrix have three and different eigen values.

Select correct option:

TRUE

FALSE

 

Question :  Which of the following is a reason due to which the LU decomposition of the system of linear equations; x+y = 1, x+y =2 is not possible?

Select correct option:

          Associated coefficient matrix is singular

          All values of l’s and u’s can’t be evaluated

          Determinant of coefficient matrix is zero

          All are equivalent

 

 

         

Question :  Gauss - Jordan Method is similar to ……….

Select correct option:

          Gauss–Seidel method

          Iteration’s method

          Relaxation Method

          Gaussian elimination method

         

Question  : While using Relaxation method, which of the following is the largest Residual for 1st iteration on the system; 2x+3y = 1, 3x +2y = - 4 ?

Select correct option:

          -4

          3

          2

          1

 

Question : Gauss–Seidel method is also known as method of …………….

Select correct option:

          Successive displacement

          Iterations

          False position

          None of the given choices

 

Question  : Jacobi’s Method is a/an………………

Select correct option:

          Iterative method

          Direct method

Question : The characteristics polynomial of a 3x 3 identity matrix is __________, if x is the eigen values of the given 3 x 3 identity matrix. where symbol ^ shows power.

Select correct option:

(x-1)^3

(x+1)^3                           

x^3-1

x^3+1

 

Question : The Power method can be used only to find the eigenvalue of A that is largest in absolute value—we call this eigenvalue the dominant eigenvalue of A.

Select correct option:

TRUE

FALSE

 

 Question: In …………… method, a system is reduced to an equivalent diagonal form using elementary transformations.

Select correct option:

          Jacobi’s

          Gauss-Seidel

          Relaxation

          Gaussian elimination

 

Question : The linear equation: 2x+0y-2=0 has -------- solution/solutions. 

Select correct option: 

 

 unique

  no solution

  infinite many

  finite many

 

Question : Under elimination methods, we consider, Gaussian elimination and ……………methods. 

Select correct option: 

 

 Gauss-Seidel

 Jacobi 

 Gauss-Jordan elimination

 None of the given choices

 

Question : Which of the following method is not an iterative method? 

Select correct option: 

 

 Jacobi’s method 

 Gauss-Seidel method

 Relaxation methods  

Gauss-Jordan elimination method

 

 Question : An eigenvector V is said to be normalized if the coordinate of largest magnitude is equal to zero.

Select correct option:

TRUE

FALSE

 

Question : Exact solution of 2/3 is not exists.

Select correct option:

TRUE

Page No.72

FALSE

 

Question : When the condition of diagonal dominance becomes true in Jacobi’s Method. Then its means that the method is ……………. 

Select correct option: 

 

 Stable 

 Unstable 

 Convergent 

 Divergent 

 

 

 

Question :  Gauss–Seidel method is similar to ………. 

Select correct option: 

 

 Iteration’s method

 Regula-Falsi method

 Jacobi’s method

 None of the given choices

 

Question :  Sparse matrices arise in computing the numerical solution of ……………. 

Select correct option: 

 

 Ordinary differential equations

 Partial differential equations

 Linear differential equations

 Non-linear differential equations

 

 

    

Question : While solving by Gauss-Seidel method, which of the following is the first Iterative solution for the system; x-2y =1, x+4y=4 ?

Select correct option:

 

(1, 0.75)

(0,0)

(1,0)

(0,1)

 

Question:  While solving a system of linear equations by Gauss Jordon Method, after all the elementary row operations if there lefts also zeros on the main diagonal then which of the is true about the system?

Select correct option:

 

System may have unique solutions

System has no solution

System may have multiple numbers of finite solutions

System may have infinite many solutions

 

Question:    Numerical methods for finding the solution of the system of equations are classified as direct and ………… methods

Select correct option:

 

Indirect

Iterative

Jacobi

None of the given choices

 

 

Question : If the Relaxation method is applied on the system; 2x+3y = 1, 3x +2y = - 4, then largest residual in 1st iteration will reduce to -------.

Select correct option:

zero

4

-1

-1

Question :   While using Relaxation method, which of the following is the Residuals for 1st iteration on the system; 2x+3y = 1, 3x +2y =4 ?

Select correct option:

(2,3)

(3,-2)

(-2,3)

(1,4)

Question : If the order of coefficient matrix corresponding to system of linear equations is 3*3 then which of the following will be the orders of its decomposed matrices; ‘L’ and ‘U’?

Select correct option:

Order of ‘L’ = 3*1, Order of ‘U’ = 1*3

Order of ‘L’ = 3*2, Order of ‘U’ = 2*3

Order of ‘L’ = 3*3, Order of ‘U’ = 3*3

Order of ‘L’ = 3*4, Order of ‘U’ = 4*3

 

Question : While solving the system; x–2y = 1, x+4y = 4 by Gauss-Seidel method, which of the following ordering is feasible to have good approximate solution?

Select correct option:

x+4y = 1, x-2y = 4

x+2y = 1, x- 4y =4

x+4y = 4, x–2y = 1

no need to reordering

 

Question : Full pivoting, in fact, is more ……………than the partial pivoting.

Select correct option:

 

Easiest

Complicated

 

 

Question : Gauss–Seidel method is also known as method of …………….

Select correct option:

Successive displacement

Iterations

False position

None of the given choices

 Question : For the equation, the root of the equation lies in the interval......

 

 

       ► (1, 3)

       ► (1, 2)

       ► (0, 1)

       ► (1, 2)

 

Question :-............lies in the category of iterative method.

 

       ► Bisection Method

       ► Regula Falsi Method

       ► Secant Method

       ► all of the given choices

 

 

Question : Power method is applicable if the eigen vectors corresponding to eigen values are linearly independent.

True

1. false

 

Question:  A 3 x 3 identity matrix have three and different eigen values.

1. True

False

Question : If n x n matrices A and B are similar, then they have the different eigenvalues (with the same multiplicities).

1. True

False

Question : The Jacobi’s method is a method of solving a matrix equation on a matrix that has ____zeros along its main diagonal.

No

1. At least one

Question : An eigenvector V is said to be normalized if the coordinate of largest magnitude is

equal to ______.

Unity

1. zero

 

 Question : If the root of the given equation lies  between a and b, then the first approximation to the root  of the equation by bisection method is ……

 

 

 

 

       ►

       ►

       ►

       ► None of the given choices

 

Question : To apply Simpson’s 3/8 rule, the number of intervals in the following must be

 

       ► 10

       ► 11  

       ► 12

       ► 13

 

Question : The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric________ definite matrices A.

Select correct option:

positive

negative

Question : Differences methods find the ________ solution of the system.

Select correct option:

numerical

Analytical

Question : To apply Simpson’s 1/3 rule, the number of intervals in the following must be

 

       ► 2   (Simpson''s 1/3 rule must use an even number of elements')

       ► 3

       ► 5

       ► 7

Question : The Power method can be used only to find the eigenvalue of A that is largest in absolute value we call this eigenvalue the dominant eigenvalue of A.

Select correct option:

 

          TRUE

          FALSE

 

Question : The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its ________.

Select correct option:

 

          main diagonal

          last column

          last row

          first row    

 

 

Question : Bisection and false position methods are also known as bracketing method and are always

Divergent

Convergent   

Page No.67

Question  : The Inverse of a matrix can only be found if the matrix is

Singular

Every square non-singular matrix will have an inverse.

Scalar

Diagonal

Question : In interpolation is used to represent the δ

 

Forward difference Δ

Central difference

Backward difference

 

Question : The base of the decimal system is _______

10

0

2

8

None of the above.

 

Question  : Bisection method is ……………….. method

► Open Method

► Bracketing Method

Question : Exact solution of 2/3 is not exists.

TRUE

FALSE

Question : The Jacobi’s method is a method of solving a matrix equation on a matrix that has ____zeros along its main diagonal.

No 

atleast one

 

 

Question: A 3 x 3 identity matrix have three and __________eigen values.

same

different

Question : Eigenvalues of a symmetric matrix are all _______ .

real

complex

zero

positive

Question : The Jacobi iteration converges, if A is strictly diagonally dominant.

TRUE

FALSE

Question : Below are all the finite difference methods EXCEPT _________.

jacobi’s method

newton's backward difference method

Stirlling formula

Forward difference method

Question:  If n x n matrices A and B are similar, then they have the same eigenvalues (with the same multiplicities).

TRUE

FALSE

Question : If A is a nxn triangular matrix (upper triangular, lower triangular) or diagonal matrix , the eigenvalues of A are the diagonal entries of A.

TRUE

FALSE

Question: The characteristics polynomial of a 3x 3 identity matrix is __________, if x is the eigen values of the given 3 x 3 identity matrix. where symbol ^ shows power.

(x-1)^3

(x+1)^3

x^3-1

x^3+1

Question : Two matrices with the same characteristic polynomial need not be similar.

TRUE

FALSE

Page No.69

Question : The determinant of a diagonal matrix is the product of the diagonal elements.

True

1. False

Qusetion : The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric positive definite matrices A.

True

1. False

Question : The determinant of a _______ matrix is the product of the diagonal elements.

Page No.70

Diagonal

1. Upper triangular

2. Lower triangular

3. Scalar

Question : For differences methods we require the set of values.

True

 False

 

Question : If x is an eigen value corresponding to eigen value of V of a matrix A. If a is any constant, then x – a is an eigen value corresponding to eigen vector V is an of the matrix A - a I.

True

 False

Question : Central difference method seems to be giving a better approximation, however it requires more computations.

Page No.71

 True

False

Question : Iterative algorithms can be more rapid than direct methods.

True

1. False

Question : Central Difference method is the finite difference method.

True

1. False

 

 

Question : Back substitution procedure is used in …………….

Select correct option:

Gaussian Elimination Method

Jacobi’s method

Gauss-Seidel method

None of the given choices

Question : The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its main diagonal.

 

True

False1.

 

Question: The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its ________.

main diagonal

last column

last row

first row

Question : .An eigenvector V is said to be normalized if the coordinate of largest magnitude is equalto ______.

Unity

Zero

Question : An eigenvector V is said to be normalized if the coordinate of largest magnitude is equalto zero.

 

TRUE

FALSE

Question : .The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric positive definite matrices A.

 

True

False

 

Question : The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric_____ definite matrices A.

 

Pos I t ive

 Negative

Question : .The determinant of a diagonal matrix is the product of the diagonal elements.

 

True

False1

Question : Power method is applicable if the eigen vectors corresponding to eigen values are linearly independent.

 

True

False

Question : Power method is applicable if the eigen values are ______________.

 

real and distinct

real and equal

 positive and distinct

negative and distinct

 

 

Question : Simpson’s rule is a numerical method that approximates the value of a definite integral by using polynomials.

 

Quadratic

Linear 

Cubic

Quartic

 

Question : .In Simpson’s Rule, we use parabolas to approximating each part of the curve. This proves to be very efficient as compared to Trapezoidal rule.

 

True

False

Question : The predictor-corrector method an implicit method. (multi-step methods)

 

True

False

Question : Generally, Adams methods are superior if output at many points is needed.

 

True

False

 

Question : The Trapezoidal rule is a numerical method that approximates the value of a.______________.

 

Indefinite integral

Definite integral

Improper integral

Function

Question : The need of numerical integration arises for evaluating the definite integral of a function that has no explicit ____________ or whose antiderivative is not easy to obtain.

 

Anti deri vat ive

Derivatives.

Question : .An indefinite integral may _________ in the sense that the limit defining it may not exist.

 

diverge

Converge

Question : An improper integral is the limit of a definite integral as an endpoint of the interval of integration approaches either a specified real number or  ∞ or -∞ or, in some cases, as both endpoints approach limits.

 

TRUE

FALSE

Question : Euler's Method numerically computes the approximate derivative of a function.

 

TRUE

FALSE

Question :.Euler's Method numerically computes the approximate ________ of a function.

 

Antiderivative

Derivative

Error 

Value

Question: If we wanted to find the value of a definite integral with an infinite limit, we can instead replace the infinite limit with a variable, and then take the limit as this variable goes to _________.

Chose the correct option :

Constant

Finite

Infinity

Zero

 

Question : Euler's Method numerically computes the approximate derivative of a function.

TRUE

FALSE

 

 

Question: .The Jacobi iteration ______, if A is strictly diagonally dominant.

 

converges

Diverges

Question :.Two matrices with the same characteristic polynomial need not be similar.

 

TRUE

fALSE

Question :.Differences methods find the ________ solution of the system.

Nu me rical

Analytica

Question : .By using determinants, we can easily check that the solution of the given system of linear equation exits and it is unique.

 

TRUE

FALSE

Question : The absolute value of a determinant (|detA|) is the product of the absolute values of the eigen values of matrix A

 

TRUE

FALSE

 

Question : Eigenvectors of a symmetric matrix are orthogonal, but only for distinct eigenvalues.

 

TRUE

FALSE

 

.

Question : Let A be an n ×n matrix. The number x is an eigenvalue of A if there exists a non-zerovector v such that _______.

 

Av = xv 

Ax = xv     not shore

Av + xv=0

Av = Ax1

Question : In Jacobi’s Method, the rate of convergence is quite ______ compared with other methods.

 

slow

Fast

 

Question : .Numerical solution of 2/3 up to four decimal places is ________.

 

0.667

0.6666

0.6667

0.666671.

Question : Symbol used for forward differences is

 

∆   Correct

δ 

 µ 

Question : .The relationship between central difference operator and the shift operator is given by

 

δ =Ε−Ε-1

 

δ = Ε+Ε-1

 

δ = Ε1/2+Ε1/2

 

δ = E1/2 −Ε1/2 

Question : Muller’s method requires --------starting points

 

1

 

2

 

3

Question : By using determinants, we can easily check that the solution of the given system of linear equation ______ and it is ______.

 

Select correct option:

exits, unique

exists, consistent

trivial, unique

nontrivial, inconsistent

Question : Two matrices with the _______ characteristic polynomial need not be similar.

 

Select correct option:

same

different

 

 

Question :  In ……………… method, the elements above and below the diagonal are simultaneously made zero.

 

Select correct option:

Jacobi’s

Gauss-Seidel

Gauss–Jordon Elimination

Relaxation

 

Question : Which of the following is equivalent form of the system of equations in matrix form; AX=B ?

 

Select correct option:

XA = B

X = B(Inverse of A)

X =(Inverse of A)B

BX = A

Question : If the determinant of a matrix A is not equal to zero then the system of equations will have……….

 

Select correct option:

a unique solution

many solutions

infinite many solutions

None of the given choices

Question :  Sparse matrix is a matrix with ……….

 

Select correct option:

Some elements are zero

Many elements are zero

Some elements are one

Many elements are one

 

Question : An eigenvector V is said to be normalized if the coordinate of largest magnitude is equal to zero.

Select correct option:

 

              TRUE

              FALSE

 

Question # 1 of 10 ( Start time: 11:14:39 PM ) Total Marks: 1

The Jacobi iteration ______, if A is strictly diagonally dominant.

 

Select correct option:

converges

diverges

 

 

Question # 2 of 10 ( Start time: 11:16:04 PM ) Total Marks: 1

The Jacobi’s method is a method of solving a matrix equation on a matrix that has ____ zeros along its main diagonal.

 

Select correct option:

No

atleast one

 

 

Question # 3 of 10 ( Start time: 11:17:14 PM ) Total Marks: 1

Power method is applicable if the eigen vectors corresponding to eigen values are linearly _______.

 

Select correct option:

independent

dependent

 

 

Question # 4 of 10 ( Start time: 11:17:42 PM ) Total Marks: 1

Power method is applicable if the eigen values are ______________.

 

Select correct option:

real and distinct

real and equal

positive and distinct

negative and distinct

 

 

 

Question # 7 of 10 ( Start time: 11:19:55 PM ) Total Marks: 1

The determinant of a diagonal matrix is the product of the diagonal elements.

 

Select correct option:

TRUE

FALSE

 

 

Question # 8 of 10 ( Start time: 11:21:14 PM ) Total Marks: 1

For differences methods we require the set of values.

 

Select correct option:

TRUE

FALSE

 

 

Question # 10 of 10 ( Start time: 11:23:55 PM ) Total Marks: 1

Two matrices with the _______ characteristic polynomial need not be similar.

 

Select correct option:

Same

different

 

 

Question # 1 of 10  Total Marks: 1

While using Relaxation method, which of the following is the Residuals for 1st iteration on the system; 2x+3y = 1, 3x +2y =4 ?

 

Select correct option:

(2,3)

(3,-2)

(-2,3)

(1,4)

 

 

Question # 2 of 10 ( Start time: 11:14:32 PM ) Total Marks: 1

Sparse matrices arise in computing the numerical solution of …………….

 

Select correct option:

Ordinary differential equations

Partial differential equations

Linear differential equations

Non-linear differential equations

 

 

Question # 3 of 10 ( Start time: 11:15:18 PM ) Total Marks: 1

In ……………… method, the elements above and below the diagonal are simultaneously made zero.

 

Select correct option:

Jacobi’s

Gauss-Seidel

Gauss–Jordon Elimination

Relaxation

 

 

 

 

Question # 5 of 10 ( Start time: 11:17:54 PM ) Total Marks: 1

Which of the following is equivalent form of the system of equations in matrix form; AX=B ?

 

Select correct option:

XA = B

 X = B(Inverse of A)

X =(Inverse of A)B

BX = A

 

 

 

Question # 7 of 10 ( Start time: 11:20:24 PM ) Total Marks: 1

If the determinant of a matrix A is not equal to zero then the system of equations will have……….

 

Select correct option:

A unique solution

many solutions

infinite many solutions

None of the given choices

 

 

Question # 8 of 10 ( Start time: 11:21:37 PM ) Total Marks: 1

Sparse matrix is a matrix with ……….

 

Select correct option:

Some elements are zero

Many elements are zero

Some elements are one

Many elements are one

 

 

 

 

Question # 4 of 10 ( Start time: 11:31:21 PM ) Total Marks: 1

Back substitution procedure is used in …………….

 

Select correct option:

Gaussian Elimination Method

Jacobi’s method

Gauss-Seidel method

None of the given choices

 

Question # 5 of 10 ( Start time: 11:32:12 PM ) Total Marks: 1

The linear equation: 2x+0y-2=0 has -------- solution/solutions.

 

Select correct option:

unique

no solution

infinite many

finite many

 

 

Question # 8 of 10 ( Start time: 11:35:30 PM ) Total Marks: 1

For a system of linear equations, the corresponding coefficient matrix has the value of determinant; |A| = 0, then which of the following is true?

 

Select correct option:

The system has unique solution

The system has finite multiple solutions

The system has infinite may solutions

The system has no solution

 

 

Question # 9 of 10 ( Start time: 11:36:21 PM ) Total Marks: 1

For the system; 2x+3y = 1, 3x +2y = - 4, if the iterative solution is (0,0) and ‘dxi = 2’ is the increment in ‘y’ then which of the following will be taken as next iterative solution?

 

Select correct option:

(2,0)

(0,3)

(0,2)

(1,-4)

 

 

 

Question # 2 of 10 ( Start time: 11:42:14 PM)Total Marks: 1

Which of the following method is not an iterative?

 

Select correct option:

Gauss–Seidel method

Iteration’s method

Relaxation Method

Gauss Jordan method

 

 

Question # 3 of 10 ( Start time: 11:43:46 PM)Total Marks: 1

Sparse matrix is a matrix with ……….

 

Select correct option:

Some elements are zero

Many elements are zero

Some elements are one

Many elements are one

 

 

Question # 4 of 10 ( Start time: 11:44:33 PM)Total Marks: 1

While using Relaxation method, which of the following is the Residuals for 1st iteration on the system; 2x+3y = 1, 3x +2y =4

 

Select correct option:

(2,3)

(3,-2)

(-2,3)

(1,4)

 

 

 

Question # 6 of 10 ( Start time: 11:47:15 PM)Total Marks: 1

Relaxation Method is a/an ……….

 

Select correct option:

 

Direct method

Iterative method

 

 

Question # 9 of 10 ( Start time: 11:50:33 PM)Total Marks: 1

Full pivoting, in fact, is more ……………than the partial pivoting.

 

Select correct option:

Easiest

Complicated

 

 

Question # 10 of 10 ( Start time: 11:51:55 PM)Total Marks: 1

Gauss–Seidel method is also known as method of …………….

 

Select correct option:

Successive displacement

Iterations

False position

None of the given choices

 

Question # 2 of 10 ( Start time: 11:31:28 PM ) Total Marks: 1

Iterative algorithms can be more rapid than direct methods.

 

Select correct option:

FALSE

TRUE

 

 

 

 

 

Question # 3 of 10 ( Start time: 11:32:02 PM ) Total Marks: 1

Below are all the finite difference methods EXCEPT _________.

 

Select correct option:

jacobi’s method

newton's backward difference method

Stirlling formula

Forward difference method

 

Question # 2 of 10  Total Marks: 1

Sparse matrices arise in computing the numerical solution of …………….

 

Select correct option:

Ordinary differential equations

Partial differential equations

Linear differential equations

Non-linear differential equations

 

Question # 9 of 10

If x is an eigen value corresponding to eigen value of V of a matrix A. If a is any constant, then x – a is an eigen value corresponding to eigen vector V is an of the matrix A - a I.

 

Select correct option:

TRUE

FALSE

 

Question # 10 of 10

An eigenvector V is said to be normalized if the coordinate of largest magnitude is equal to zero.

 

Select correct option:

TRUE

FALSE

 

Question No: 1    ( Marks: 1 )    - Please choose one

 Symbol used for forward differences is

 

 

       ►

 

       ►

       ►

 

       ►

 

   

Question No: 2    ( Marks: 1 )    - Please choose one

 The relationship between central difference operator and the shift operator is given by

 

       ►

       ►

       ►

       ►

   

Question No: 3    ( Marks: 1 )    - Please choose one

  Muller’s method requires --------starting points

 

 

       ► 1

       ► 2

       ► 3

       ► 4

   

Question No: 4    ( Marks: 1 )    - Please choose one

 If   S is an identity    matrix, then

 

       ►

       ►

       ►

       ►

   

Question No: 5    ( Marks: 1 )    - Please choose one

 If we retain r+1 terms in Newton’s forward difference formula, we obtain a polynomial of degree ---- agreeing with  at

 

       ► r+2

       ► r+1

       ► r

       ► r-1

   

Question No: 6    ( Marks: 1 )    - Please choose one

 P in Newton’s forward difference formula is defined as

 

       ►

 

       ►

       ►

       ►

   

Question No: 7    ( Marks: 1 )    - Please choose one

 Octal number system has the base ---------------

 

       ► 2

       ► 8

       ► 10

       ► 16

   

Question No: 8    ( Marks: 1 )    - Please choose one

 Newton’s divided difference interpolation formula is used when the values of the independent variable are

 

       ► Equally spaced

 

       ► Not equally spaced

 

       ► Constant

       ► None of the above

   

Question No: 9    ( Marks: 1 )    - Please choose one

 Given the following data

 

0

1

2

4

1

1

2

5

 

Value of is

 

       ► 1.5

 

       ► 3

       ► 2

 

       ► 1

    

Question No: 10    ( Marks: 1 )    - Please choose one

 If is approximated by a polynomial  of degree n then the error is given by

       ►

      

       ►

       ►

   

Question No: 11    ( Marks: 1 )    - Please choose one

 Let  denotes the closed interval spanned by . Then vanishes ------times in the interval .

 

       ► n-1

       ► n+2

       ► n

       ► n+1

   

Question No: 12    ( Marks: 1 )    - Please choose one

 Differential operator in terms of forward difference operator is given by

 

       ►

       ►

      

       ►

   

Question No: 13    ( Marks: 1 )    - Please choose one

 Finding the first derivative of at =0.4 from the following table:

 

 

0.1

0.2

0.3

0.4

 

1.10517

1.22140

1.34986

1.49182

 

Differential operator in terms of ----------------will be used.

 

 

 

 

       ► Forward difference operator

       ► Backward difference operator

       ► Central difference operator

       ►  None of the given choices

   

Question No: 14    ( Marks: 1 )    - Please choose one

 

For the given table of values

0.1

0.2

0.3

0.4

0.5

0.6

0.425

0.475

0.400

0.452

0.525

0.575

 

, using two-point equation will be calculated as.............

 

 

 

       ► -0.5

       ► 0.5

       ► 0.75

       ► -0.75

   

Question No: 15    ( Marks: 1 )    - Please choose one

 In Simpson’s 1/3 rule, is of the form

 

       ►

       ►

       ►

       ►

   

Question No: 16    ( Marks: 1 )    - Please choose one

 While integrating , , width of the interval, is found by the formula-----.

 

      

       ►

       ►

       ► None of the given choices

 

   

Question No: 17    ( Marks: 1 )    - Please choose one

 To apply Simpson’s 1/3 rule, valid number of intervals are.....

 

       ► 7

       ► 8

       ► 5

       ► 3

   

Question No: 18    ( Marks: 1 )    - Please choose one

 For the given table of values

02

0.3

0.4

0.5

0.6

0.7

0.425

0.475

0.400

0.452

0.525

0.575

 

, using three-point equation will be calculated as ……

 

       ► 17.5

       ► 12.5

       ► 7.5

       ► -12.5

   

Question No: 19    ( Marks: 1 )    - Please choose one

 To apply Simpson’s 1/3 rule, the number of intervals in the following must be

 

       ► 2

       ► 3

       ► 5

       ► 7

   

Question No: 20    ( Marks: 1 )    - Please choose one

 To apply Simpson’s 3/8 rule, the number of intervals in the following must be

 

       ► 10

       ► 11       

       ► 12

       ► 13

   

Question No: 21    ( Marks: 1 )    - Please choose one

 If the root of the given equation lies  between a and b, then the first approximation to the root  of the equation by bisection method is ……

 

 

 

 

      

       ►

       ►

       ► None of the given choices

   

Question No: 22    ( Marks: 1 )    - Please choose one

 

............lies in the category of iterative method.

 

       ► Bisection Method

       ► Regula Falsi Method

       ► Secant Method

       ► All the given choices

   

Question No: 23    ( Marks: 1 )    - Please choose one

 For the equation, the root of the equation lies in the interval......

 

 

       ► (1, 3)

       ► (1, 2)

       ► (0, 1)

       ► (1, 2)

   

Question No: 24    ( Marks: 1 )    - Please choose one

 Rate of change of any quantity with respect to another can be modeled by

 

       ► An ordinary differential equation

       ► A partial differential equation

 

       ► A polynomial equation

 

       ►  None of the given choices

 

   

Question No: 25    ( Marks: 1 )    - Please choose one

 If

Then the integral of this equation is a curve in

 

       ► None of the given choices

 

       ► xt-plane

       ► yt-plane

       ► xy-plane

   

Question No: 26    ( Marks: 1 )    - Please choose one

  In solving the differential equation

                 

,   By Euler’s method  is calculated as

 

       ► 1.44

       ► 1.11

       ► 1.22

       ► 1.33

   

Question No: 27    ( Marks: 1 )    - Please choose one

 In second order Runge-Kutta method

 is given by

 

       ►

       ►

       ►

       ► None of the given choices

 

   

Question No: 28    ( Marks: 1 )    - Please choose one

 In fourth order Runge-Kutta method,   is given by

 

      

       ►

       ►

       ►

   

Question No: 29    ( Marks: 1 )    - Please choose one

 In fourth order Runge-Kutta method,  is given by

 

       ►

       ►

      

       ► None of the given choices

 

   

Question No: 30    ( Marks: 1 )    - Please choose one

 Adam-Moulton P-C method is derived by employing

 

       ► Newton’s backward difference interpolation formula

       ► Newton’s forward difference interpolation formula

       ► Newton’s divided difference interpolation formula

       ► None of the given choices

                                Mth603 Solved MCQS for Final Term Exam

                                             

                                Solved by Mermaid with reference of book

 

Exact solution of 2/3 is not exists.

TRUE

FALSE

 

The Jacobi’s method is

A method of solving a matrix equation on a matrix that has ____ zeros along its main diagonal.

 

 No

At least one

 

 

A 3 x 3 identity matrix have three and __________eigen values.

 Same

Different

 

 

 Eigenvalues of a symmetric matrix are all _______

 Real

Complex

Zero

Positive

 

The Jacobi iteration converges, if A is strictly diagonally dominant

TRUE

FALSE

 

Below are all the finite difference methods EXCEPT _________.

 

 Jacobi’s method

Newton’s backward difference method

Stirlling formula

Forward difference method

 

If n x n matrices A and B are similar, then they have the same eigenvalues (with the same multiplicities).

TRUE

FALSE

 

 

If A is a nxn triangular matrix (upper triangular, lower triangular) or diagonal matrix, the eigenvalues of A are the diagonal entries of A.

 

TRUE

FALSE

 

The characteristics polynomial of a 3x 3 Identity matrix is __________, if x is the Eigen values of the given 3 x 3 identity matrix. Where symbol ^ shows power.

 

(X-1)^3

(x+1)^3

 X^3-1

 X^3+1

 

 

Two matrices with the same characteristic polynomial need not be similar.

 

TRUE

FALSE

 

 

 

Bisection method is a

 

Bracketing method

Open method

 

Regula Falsi means

 

Method of Correct position

Method of unknown position

Method of false position

Method of known position

 

 

Eigenvalues of a symmetric matrix are all _________.

Select correct option:

 

            Real

            Zero

            Positive

            Negative

 

An eigenvector V is said to be normalized if the coordinate of largest magnitude is equal to zero.

Select correct option:

 

            TRUE

            FALSE

 

 

 

 

 

 

 

Exact solution of 2/3 is not exists.

Select correct option:

 

            TRUE

            FALSE

 

 

The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric ________ definite matrices A.

Select correct option:

 

            Positive

            Negative

 

 

 

 

Differences methods find the ________ solution of the system. 

Select correct option:

 

            Numerical

            Analytical

 

 

 

 

 

The Power method can be used only to find the eigenvalue of A that is largest in absolute value—we call this Eigenvalue the dominant eigenvalue of A.

Select correct option:

 

            TRUE

            FALSE

 

 

 

 

 

 

The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its ________.

Select correct option:

 

            Main diagonal

            Last column

            Last row

            First row    

 

 

 

 

 

 

 

If A is a nxn triangular matrix (upper triangular, lower triangular) or diagonal matrix , the eigenvalues of A are the diagonal entries of A. 

Select correct option:

 

            TRUE

            FALSE

 

 

 

 

A 3 x 3 identity matrix have three and different Eigen values.

Select correct option:

 

            TRUE

            FALSE

 

Newton Raphson method falls in the category of

 

Bracketing method

Open Method

Iterative Method

Indirect Method

 

 

Newton Raphson method is also known as

Tangent Method

Root method

Open Method

Iterative Method

 

Secant Method uses values for approximation

 

1

3

2

4

 

Secant Method is than bisection method for finding root

Slow

Faster

 

In Newton Raphson method

 

Root is bracketed

Root is not bracketed

 

Regula falsi method and bisection method are both

 

Convergent

Divergent

 

In bisection method the two points between which the root lies are

 

Similar to each other

Different

Not defined

Opposite

 

In which methods we do not need initial approximation to start

Indirect Method

Open Method

Direct Method

Iterative Method

 

Root may be

 

Complex

Real

Complex or real

None

 

In Regula falsi method we choose points that have signs

 

2 points opposite signs

3 points opposite signs

2 points similar signs

None of the given

 

In a bounded function values lie between

1 and -1

1 and 2

0 and 1

0 and -2

 

Newton Raphson method is a method which when it leads to division of number close to zero

Diverges

Converges

 

Which of the following method is modified form of Newton Raphson Method?

Regula falsi method

Bisection method

Secant method

Jacobi’s Method

 

Which 1 of the following is generalization of Secant method?

Muller’s Method

Jacobi’s Method

Bisection Method

N-R Method

Secant Method needs starting points

 

2

3

4

1

Near a simple root Muller’s Method converges than the secant method

 

Faster

Slower

 

If   S is an identity    matrix, then

 

        

        

        

           All are true

 

If we retain r+1 terms in Newton’s forward difference formula, we obtain a polynomial of degree ---- agreeing with  at

 

        r+2

        r+1

        R

        R-1

P in Newton’s forward difference formula is defined as

 

            

 

        

        

      

Octal numbers has the base

 

           10

             2

             8

            16

Newton’s divided difference interpolation formula is used when the values of the independent variable are

 

       Equally spaced

 

        Not equally spaced

 

        Constant

        None of the above

 

Given the following data

 

0

1

2

4

1

1

2

5

 

Value of is

 

      1.5

 

       3

       2

 

       1

 

If is approximated by a polynomial  of degree n then the error is given by

 

        

           

 

Let  denotes the closed interval spanned by . Then vanishes ------times in the interval .

 

        N-1

        N+2

        N

        N+1

 Differential operator in terms of forward difference operator is given by

 

        

        

        

        

 Finding the first derivative of at =0.4 from the following table:

 

 

0.1

0.2

0.3

0.4

 

1.10517

1.22140

1.34986

1.49182

 

Differential operator in terms of ----------------will be used.

 

 

 

 

       Forward difference operator

        Backward difference operator

        Central difference operator

       All of the given choices

                                              

 

For the given table of values

0.1

0.2

0.3

0.4

0.5

0.6

0.425

0.475

0.400

0.452

0.525

0.575

 

, using two-point equation will be calculated as.............

 

 

 

        -0.5

        0.5

        0.75

        -0.75

  

 In Simpson’s 1/3 rule, is of the form

 

        

       ►

       ►

       ►

   

 

 While integrating, , width of the interval, is found by the formula-----.

 

        

      

        

        None of the given choices

 

   

 

 To apply Simpson’s 1/3 rule, valid number of intervals are.....

 

        7

        8

        5

        3

   

 For the given table of values

0.1

0.2

0.3

0.4

0.5

0.6

0.425

0.475

0.400

0.452

0.525

0.575

 

, using three-point equation will be calculated as ……

 

      17.5

      12.5

       7.5

     -12.5

   

 To apply Simpson’s 1/3 rule, the number of intervals in the following must be

 

        2

        3

        5

        7

   

 To apply Simpson’s 3/8 rule, the number of intervals in the following must be

 

       10

       11

       12

       13

   

 

 If the root of the given equation lies between a and b, then the first approximation to the root of the equation by bisection method is ……

 

 

 

 

       

        

        

        None of the given choices

   

 

............lies in the category of iterative method.

 

        Bisection Method

        Regula Falsi Method

       Secant Method

        All of the given choices                                                                                                

 For the equation, the root of the equation lies in the interval......

 

 

        (1, 3)

        (1, 2)

        (0, 1)

        (1, 2)

   

 

 Rate of change of any quantity with respect to another can be modeled by

 

        An ordinary differential equation

        A partial differential equation

 

        A polynomial equation

 

       None of the given choices

 

  

 If

Then the integral of this equation is a curve in

 

        None of the given choices

 

        Xt-plane

        Yt-plane

       Xy-plane

   

 

  In solving the differential equation

                 

,   By Euler’s method  is calculated as

 

        1.44

       1.11

        1.22

        1.33

   

 In second order Runge-Kutta method

 is given by

 

        

        

        

        None of the given choices

 

   

 In fourth order Runge-Kutta method,   is given by

 

                                                                                                         

      

        

        

 In fourth order Runge-Kutta method,  is given by

 

        

        

        

       None of the given choices

 

 

Adam-Moulton P-C method is derived by employing

 

       Newton’s backward difference interpolation formula

       Newton’s forward difference interpolation formula

        Newton’s divided difference interpolation formula

        None of the given choices

 

The need of numerical integration arises for evaluating the definite integral of a function that has no explicit ____________ or whose antiderivative is not easy to obtain

 

Derivatives

Antiderivative

 

If then system will have a

Definite solution

Unique solution

Correct solution

No solution

 

If  then

There is a unique solution

There exists a complete solution

There exists no solution

None of the above options

 

Direct method consists of method

2

3

5

4

We consider Jacobi’s method Gauss Seidel Method and relaxation method as

Direct method

Iterative method

Open method

All of the above

 

In Gauss Elimination method Solution of equation is obtained in

3 stages

2 stages

4 stages

5 stages

 

Gauss Elimination method fails if any one of the pivot values becomes

Greater

Small

Zero

None of the given

 

Changing the order of the equation is known as

 

Pivoting

Interpretation

 

Full pivoting is than partial pivoting

Easy

More complicated

 

The following is the variation of Gauss Elimination method

 

Jacobi’s method

Gauss Jordan Elimination method

 

Courts reduction method is also known as Cholesky Reduction method

True

False

 

Jacobi’s method is also known as method of Simultaneous displacement

True

False

Gauss Seidel method is also known as method of Successive displacement

False

True

 In Jacobi’s method approximation calculated is used for

Nothing

Calculating the next approximation

Replaced by previous one

All above

 

In Gauss Seidel method approximation calculated is replaced by previous one

True

False

 

Relaxation method is derived by

South well

Not defined

 

Power method is applicable for only

Real metrics

Symmetric

 Unsymmetrical

Both symmetric and real

 

 

The process of eliminating value of y for intermediate value of x is know as interpolation

True

False

 

 

Question No: 31    ( Marks: 2 )

 If  and, then find using Richardson’s extrapolation limit.

 

   

Question No: 32    ( Marks: 2 )

 Evaluate the integral 

                                

Using Simpson’s 3/8 rule

   

Take h=

 

   

Question No: 33    ( Marks: 2 )

 Write a general formula for Modified Euler’s method of solving the given differential equation.

   

Question No: 34    ( Marks: 3 )

 Evaluate the integral 

                                 

Using Trapezoidal rule

Take h=1

   

Question No: 35    ( Marks: 3 )

 Evaluate the integral 

                                

Using Simpson’s 3/8 rule

Take h=1

 

 

   

Question No: 36    ( Marks: 3 )

 Write a formula for finding the value of in Fourth-order R-K method.

   

Question No: 37    ( Marks: 5 )

 Find Newton’s forward difference table from the following data.

 

0.0

0.1

0.2

0.3

0.4

1

0.9048

0.8187

0.7408

0.6703

 

 

   

Question No: 38    ( Marks: 5 )

 Evaluate the integral 

                                

Using Simpson’s 3/8 rule

   

Take h=1

 

   

Question No: 39    ( Marks: 5 )

 Use Runge-Kutta Method of order four to find the values of

 for the initial value problem

 

 taking

 

thanks alot admin

nice

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