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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 1.2214 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 0.4 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 0.4 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.

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 ______________.

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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.

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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 1.2214 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 0.4 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

 2 0.3 0.4 0.5 0.6 0.7 0.425 0.475 0.4 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 1.2214 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 0.4 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 0.4 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 0.1 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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