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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.
(X1)^3
(x+1)^3
X^31
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 GaussSeidel 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
NR 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
R1
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 .
N1
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 twopoint 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 threepoint 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
Xtplane
Ytplane
Xyplane
In solving the differential equation
, By Euler’s method is calculated as
1.44
1.11
1.22
1.33
In second order RungeKutta method
is given by
None of the given choices
In fourth order RungeKutta method, is given by
In fourth order RungeKutta method, is given by
None of the given choices
AdamMoulton PC 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 subintervals. Where n is divisible by.....
3
4
5
None
1Generally, Adams methods are superior if output at many points is needed.
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 ____________.
3 The first lngrange polynomial with equally spaced nodes produced the formula for __________.
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.
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
6 The Euler method is numerically unstable because of ________ convergence of error.
7 Adams – Bashforth is a multistep method.
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.
9 In Runge – Kutta Method, we do not need to calculate higher order derivatives and find greater accuracy.
10An indefinite integral may _________ in the sense that the limit defining it may not exist.
11The 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.
12An 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.
13Euler's Method numerically computes the approximate derivative of a function.
14If 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 _________.
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:
(x1)^3
(x+1)^3
x^31
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
GaussSeidel
Relaxation
Gaussian elimination
Question : The linear equation: 2x+0y2=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:
GaussSeidel
Jacobi
GaussJordan elimination
None of the given choices
Question : Which of the following method is not an iterative method?
Select correct option:
Jacobi’s method
GaussSeidel method
Relaxation methods
GaussJordan 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
RegulaFalsi 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
Nonlinear differential equations
Question : While solving by GaussSeidel method, which of the following is the first Iterative solution for the system; x2y =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 GaussSeidel method, which of the following ordering is feasible to have good approximate solution?
Select correct option:
x+4y = 1, x2y = 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 GaussSeidel 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 nonsingular 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.
(x1)^3
(x+1)^3
x^31
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 GaussSeidel 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
GaussSeidel 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 GaussSeidel method is applicable to strictly diagonally dominant or symmetric positive definite matrices A.
True
False
Question : The GaussSeidel 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 predictorcorrector method an implicit method. (multistep 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 nonzerovector 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 = _{Ε}1/2+_{Ε}^{1/2}
δ = E^{1/2} −Ε^{1/2 }
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
GaussSeidel
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
Nonlinear 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
GaussSeidel
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
GaussSeidel method
None of the given choices
Question # 5 of 10 ( Start time: 11:32:12 PM ) Total Marks: 1
The linear equation: 2x+0y2=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
Nonlinear 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
► r1
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 .
► n1
► 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 twopoint 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 threepoint 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
► xtplane
► ytplane
► xyplane
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 RungeKutta method
is given by
►
►
►
► None of the given choices
Question No: 28 ( Marks: 1 )  Please choose one
In fourth order RungeKutta method, is given by
►
►
►
►
Question No: 29 ( Marks: 1 )  Please choose one
In fourth order RungeKutta method, is given by
►
►
►
► None of the given choices
Question No: 30 ( Marks: 1 )  Please choose one
AdamMoulton PC 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.
(X1)^3
(x+1)^3
X^31
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 GaussSeidel 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
NR 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
R1
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 .
N1
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 twopoint 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 threepoint 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
Xtplane
Ytplane
Xyplane
In solving the differential equation
, By Euler’s method is calculated as
1.44
1.11
1.22
1.33
In second order RungeKutta method
is given by
None of the given choices
In fourth order RungeKutta method, is given by
In fourth order RungeKutta method, is given by
None of the given choices
AdamMoulton PC 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 Fourthorder RK 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 RungeKutta Method of order four to find the values of
for the initial value problem
taking
nice
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