Mth603 Solved MCQS For Final Term Exam: True False

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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.
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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.
TRUE
FALSE

TRUE
FALSE
The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric

________ definite matrices A.
Positive
Negative
Differences methods find the ________ solution of the system.

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

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

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
S 1  S
St  S
S 1  S t
All are true
If we retain r+1 terms in Newton’s forward difference formula, we obtain a

polynomial of degree ---- agreeing with y x at x0, x1 ,..., xr
r+2
r+1
R
R-1
P in Newton’s forward difference formula is defined as
x  x0
p( )
h
x  x0
p( )
h
x  xn
p( )
h
x  xn
p( )
h
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
x 0 1 2 4
f ( x) 1 1 2 5
Value of f (2, 4) is
1.5
3
2
If y ( x) is approximated by a polynomial pn ( x) of degree n then the error is

given by
 ( x)  y ( x)  Pn ( x)
 ( x)  y ( x)  Pn ( x)
 ( x)  y ( x)  Pn ( x)
 ( x)  Pn ( x)  y ( x)
Let I denotes the closed interval spanned by x0 , x1 , x2 , x3 , x4 , x5 , x6 , x7 , x . Then

F ( x) vanishes ------times in the interval I .
N-1
N+2
N
N+1
Differential operator in terms of forward difference operator is given by
1  2 3  4 5
D (      ...)
h 2! 3! 4! 5!
1  2 3  4 5
D (      ...)
h 2 3 4 5
1  2 3 4 5
D (      ...)
h 2 3 4 5
1  2 3  4 5
D (      ...)
h 2! 3! 4! 5!
Finding the first derivative of f ( x) at x =0.4 from the following table:
x 0.1 0.2 0.3 0.4

f ( x) 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

x 0.1 0.2 0.3 0.4 0.5 0.6
f ( x) 0.425 0.475 0.400 0.452 0.525 0.575
f / (0.1) , using two-point equation will be calculated as.............
-0.5
0.5
0.75
-0.75
In Simpson’s 1/3 rule, f ( x) is of the form
ax  b
► ax 2  bx  c
► ax 3  bx 2  cx  d
► ax 4  bx3  cx 2  dx  e
While integrating I   f ( x)dx , h , width of the interval, is found by the

a
formula-----.
ba
n
ba
n
a b
n
None of the given choices
To apply Simpson’s 1/3 rule, valid number of intervals are.....
7
8
5
3

x 0.1 0.2 0.3 0.4 0.5 0.6
f ( x) 0.425 0.475 0.400 0.452 0.525 0.575
f / / (0.2) , 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
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 ……
( a  b)
2
( a  b)
2
(b  a)
2
............lies in the category of iterative method.
Bisection Method
Regula Falsi Method
Secant Method
For the equation x 3  3x  1  0 , 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
If
dy
 f ( x, y )
dx
Then the integral of this equation is a curve in
Xt-plane
Yt-plane
Xy-plane
In solving the differential equation

y /  x  y ; y (0.1)  1.1
h  0.1 , By Euler’s method y (0.2) is calculated as
1.44
1.11
1.22
1.33
In second order Runge-Kutta method

k1 is given by
k1  hf ( xn , yn )
k1  2hf ( xn , yn )
k1  3hf ( xn , yn )
In fourth order Runge-Kutta method, k2 is given by
h k
k2  hf ( xn  , yn  1 )
2 2
h k
k2  hf ( xn  , yn  1 )
3 3
h k
k2  hf ( xn  , yn  1 )
3 3
h k1
k2  hf ( xn  , yn  )
2 2
k3  hf ( xn  2h, yn  2k3 )
k3  hf ( xn  h, yn  k3 )
k3  hf ( xn  h, yn  k3 )
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
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 A  0 then system will have a

Definite solution
Unique solution
Correct solution
No solution
If A  0 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?
Direct
Iterative
Analytical
Graphical
Question :The basic idea of relaxation method is to reduce the largest

residual to ………….
One
Two
Zero
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: 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 : A 3 x 3 identity matrix have three and different
eigen values.
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?
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 ……….

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 ?
-4
3
2
1
Question : Gauss–Seidel method is also known as method of …………….

Successive displacement
Iterations
False position
Question : Jacobi’s Method is a/an………………

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.
(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.
TRUE
FALSE
Question: In …………… method, a system is reduced to an equivalent

diagonal form using elementary transformations.
Jacobi’s
Gauss-Seidel
Relaxation
Gaussian elimination
Question : The linear equation: 2x+0y-2=0 has -------- solution/solutions.

unique
no solution
infinite many
finite many
Question : Under elimination methods, we consider, Gaussian elimination

and ……………methods.
Gauss-Seidel
Jacobi
Gauss-Jordan elimination
Question : Which of the following method is not an iterative method?

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

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 …………….
Stable
Unstable
Convergent
Divergent
Question : Gauss–Seidel method is similar to ……….

Regula-Falsi method
Jacobi’s method
Question : Sparse matrices arise in computing the numerical solution of

…………….
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 ?
(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?
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
Indirect
Iterative
Jacobi
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 -------.
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 ?
(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’?
Order of ‘L’ = 3*1, Order of ‘U’ = 1*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?

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

Iterations
False position
Question : For the equation x3  3x  1  0 , 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
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 ……
( a  b)
► 2
( a  b)
► 2
(b  a)
► 2
► 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.
positive
negative
Question : Differences methods find the ________ solution of
the system.
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.
TRUE
FALSE
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 : 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
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 …………….

Gaussian Elimination Method
Jacobi’s method
Gauss-Seidel method
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
h a s n o 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
i s e q u a l to ______.
Unity
Zero
Question : An eigenvector V is said to be
normalized if the coordinate of largest magnitude
i s e q u a l to zero.
TRUE
FALSE
Question : .The Gauss-Seidel method is applicable

t o s t r i c t l y d i a g o n a l l y d o m i n a n t o r s y m m e t r i c positive
definite matrices A.
True
False
Question : The Gauss-Seidel method is applicable to strictly

diagonally dominant or symmetric _____ definite matrices A.
Pos I t ive
Negative
Question : .The determinant of a diagonal matrix
is the product of the diagonal elements.
True
False1
Question : Power method is applicable if the eigen vectors corresponding to
eigen values are linearly independent.
True
False
Question : Power method is applicable if the eigen values are
______________.
real and distinct

real and equal
positive and distinct
negative and distinct
Question : Simpson’s rule is a numerical method that

approximates the value of a definite integral by using polynomials.
Quadratic
Linear
Cubic
Quartic
Question : .In Simpson’s Rule, we use parabolas

to approximating each part of the curve. This
p r o v e s 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: I f w e w a n t e d t o f i n d t h e v a l u e o f a d e f i n i t e
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 :. T w o m a t r i c e s w i t h t h e s a m e c h a r a c t e r i s t i c
polynomial need not be similar.
TRUE
fALSE
Question :. D i f f e r e n c e s m e t h o d s f i n d t h e _ _ _ _ _ _ _ _
solution of the system.
Nu me rical
Analytica
Question : . B y u s i n g d e t e r m i n a n t s , w e c a n e a s i l y c h e c k
t h a t t h e s o l u t i o n o f t h e g i v e n s y s t e m o f l i n e a r 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-zero vector 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
o t h e r 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

1 / 2
δ = Ε 1 / 2 + Ε

δ = E 1 / 2 − Ε 1 / 2
Question : Muller’s method requires
--------starting points
Question : By using determinants, we can easily check that the solution of

the given system of linear equation ______ and it is ______.

exits, unique
exists, consistent
trivial, unique
nontrivial, inconsistent
Question : Two matrices with the _______ characteristic polynomial need
not be similar.

same
different
Question : In ……………… method, the elements above and below the

diagonal are simultaneously made zero.

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 ?

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……….

a unique solution
many solutions
infinite many solutions
Question : Sparse matrix is a matrix with ……….

Some elements are zero
Many elements are zero
Some elements are one
Many elements are one

coordinate of largest magnitude is equal to zero.

TRUE
FALSE

Question # 1 of 10 ( Start time: 11:14:39 PM ) Total Marks: 1
The Jacobi iteration ______, if A is strictly diagonally dominant.

converges
diverges

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

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

independent
dependent

Power method is applicable if the eigen values are ______________.

real and distinct
real and equal
positive and distinct
negative and distinct

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

TRUE
FALSE

For differences methods we require the set of values.

TRUE
FALSE

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

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 ?

(2,3)
(3,-2)
(-2,3)
(1,4)

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


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

Jacobi’s
Gauss-Seidel
Gauss–Jordon Elimination
Relaxation

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

XA = B
X = B(Inverse of A)
X =(Inverse of A)B
BX = A

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

A unique solution
many solutions
infinite many solutions

Sparse matrix is a matrix with ……….


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

Gaussian Elimination Method
Jacobi’s method
Gauss-Seidel method

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

unique
no solution
infinite many
finite many

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

The system has unique solution
The system has finite multiple solutions
The system has infinite may solutions
The system has no solution

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?

(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?

Gauss–Seidel method
Relaxation Method
Gauss Jordan method

Sparse matrix is a matrix with ……….


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

(2,3)
(3,-2)
(-2,3)
(1,4)

Relaxation Method is a/an ……….
Direct method
Iterative method

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

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

Iterations
False position

Iterative algorithms can be more rapid than direct methods.

FALSE
TRUE


jacobi’s method
newton's backward difference method
Stirlling formula
Question # 2 of 10 Total Marks: 1

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

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.

TRUE
FALSE
Question # 10 of 10
An eigenvector V is said to be normalized if the coordinate of largest
magnitude is equal to zero.

TRUE
FALSE
Question No: 1 ( Marks: 1 ) - Please choose one
Symbol used for forward differences is
►
►
►
► 
The relationship between central difference operator and the shift operator is
given by
►   
1
►  
1
1 1

►   
2 2
1 1

►   2   2
Muller’s method requires --------starting points
►1
►2
►3
►4

1
► S S
► S S
t
► All are true

1
► S S
t

x x ,..., xr
polynomial of degree ---- agreeing with yx at 0, 1
► r+2
► r+1
►r
► r-1
x  x0
p( )
► h
x  x0
p( )
► h
x  xn
p( )
► h
x  xn
p( )
► h
Octal number system has the base ---------------
►2
►8
► 10
► 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
x 0 1 2 4
f ( x) 1 1 2 5
► 1.5
►3
►2
►1
If y ( x) is approximated by a polynomial pn ( x) of degree n then the error is given

by
►  ( x )  y ( x)  Pn ( x)
►
 ( x)  y ( x)  Pn ( x)
►  ( x )  Pn ( x)  y ( x)
►  ( x )  y ( x)  Pn ( x)
► n-1
► n+2
►n
► n+1
1  2 3  4 5
D (      ...)
► h 2! 3! 4! 5!
1  2 3  4 5
D (      ...)
► h 2 3 4 5
1  2 3  4 5
D (      ...)
► h 2 3 4 5
1  2 3  4 5
D (      ...)
► h 2! 3! 4! 5!
x 0.1 0.2 0.3 0.4

f ( x) 1.10517 1.22140 1.34986 1.49182
► Forward difference operator

► Backward difference operator
► Central difference operator

x 0.1 0.2 0.3 0.4 0.5 0.6
f ( x) 0.425 0.475 0.400 0.452 0.525 0.575
► -0.5
► 0.5
► 0.75
► -0.75
In Simpson’s 1/3 rule,

f ( x ) is of the form
► ax  b
► ax  bx  c
2
► ax  bx  cx  d
3 2
► ax  bx  cx  dx  e
4 3 2
b
I   f ( x)dx
While integrating a , h , width of the interval, is found by the
formula-----.
ba
► n
ba
► n
ab
► n
►7
►8
►5
►3

x 02 0.3 0.4 0.5 0.6 0.7
f ( x) 0.425 0.475 0.400 0.452 0.525 0.575
► 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
( a  b)
► 2
( a  b)
► 2
(b  a)
► 2
► Bisection Method
► Regula Falsi Method
► Secant Method
► All the given choices
For the equation x  3 x  1  0 , the root of the equation lies in the interval......
3
► (1, 3)
► (1, 2)
► (0, 1)
► (1, 2)
► An ordinary differential equation

► A partial differential equation
► A polynomial equation
If
dy
 f ( x, y )
dx
► xt-plane
► yt-plane
► xy-plane

y /  x  y ; y (0.1)  1.1
► 1.44
► 1.11
► 1.22
► 1.33

k1 is given by
► k1  hf ( xn , yn )
► k1  2hf ( xn , yn )
► k1  3hf ( xn , yn )
h k
k2  hf ( xn  , yn  1 )
► 2 2
h k
k2  hf ( xn  , yn  1 )
► 3 3
h k
k2  hf ( xn  , yn  1 )
► 3 3
h k
k2  hf ( xn  , yn  1 )
► 2 2
► k3  hf ( xn  2h, yn  2k3 )
► k3  hf ( xn  h, yn  k3 )
► k3  hf ( xn  h, yn  k3 )
► Newton’s backward difference interpolation formula

► Newton’s forward difference interpolation formula
► Newton’s divided difference interpolation formula
Mth603 Solved MCQS for Final Term Exam
Solved by Mermaid with reference of book

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
Jacobi’s method
Newton’s backward difference method
Stirlling formula
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 _________.

Real
Zero
Positive
Negative
An eigenvector V is said to be normalized if the coordinate of largest magnitude is equal to

zero.
TRUE
FALSE

TRUE
FALSE
The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric

________ definite matrices A.
Positive
Negative
Differences methods find the ________ solution of the system.

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

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
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 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
S 1  S
St  S
S 1  S t
All are true

polynomial of degree ---- agreeing with y x at x0, x1 ,..., xr
r+2
r+1
R
R-1
x  x0
p( )
h
x  x0
p( )
h
x  xn
p( )
h
x  xn
p( )
h
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
x 0 1 2 4
f ( x) 1 1 2 5
1.5
3
2
If y ( x) is approximated by a polynomial pn ( x) of degree n then the error is

given by
 ( x)  y ( x)  Pn ( x)
 ( x)  y ( x)  Pn ( x)
 ( x)  y ( x)  Pn ( x)
 ( x)  Pn ( x)  y ( x)

N-1
N+2
N
N+1
1  2 3  4 5
D (      ...)
h 2! 3! 4! 5!
1  2 3  4 5
D (      ...)
h 2 3 4 5
1  2 3 4 5
D (      ...)
h 2 3 4 5
1  2 3  4 5
D (      ...)
h 2! 3! 4! 5!
x 0.1 0.2 0.3 0.4

f ( x) 1.10517 1.22140 1.34986 1.49182
Forward difference operator

Backward difference operator
Central difference operator

x 0.1 0.2 0.3 0.4 0.5 0.6
f ( x) 0.425 0.475 0.400 0.452 0.525 0.575
-0.5
0.5
0.75
-0.75
In Simpson’s 1/3 rule, f ( x) is of the form
ax  b
► ax 2  bx  c
► ax 3  bx 2  cx  d
► ax 4  bx3  cx 2  dx  e
While integrating I   f ( x)dx , h , width of the interval, is found by the

a
formula-----.
ba
n
ba
n
a b
n
7
8
5
3

x 0.1 0.2 0.3 0.4 0.5 0.6
f ( x) 0.425 0.475 0.400 0.452 0.525 0.575
17.5
12.5
7.5
-12.5
be
2
3
5
7
be
10
11
12
13
( a  b)
2
( a  b)
2
(b  a)
2
Bisection Method
Regula Falsi Method
Secant Method
For the equation x 3  3x  1  0 , the root of the equation lies in the interval......
(1, 3)
(1, 2)
(0, 1)
(1, 2)
An ordinary differential equation

A partial differential equation
A polynomial equation
If
dy
 f ( x, y )
dx
Xt-plane
Yt-plane
Xy-plane

y /  x  y ; y (0.1)  1.1
1.44
1.11
1.22
1.33

k1 is given by
k1  hf ( xn , yn )
k1  2hf ( xn , yn )
k1  3hf ( xn , yn )
h k
k2  hf ( xn  , yn  1 )
2 2
h k
k2  hf ( xn  , yn  1 )
3 3
h k
k2  hf ( xn  , yn  1 )
3 3
h k1
k2  hf ( xn  , yn  )
2 2
k3  hf ( xn  2h, yn  2k3 )
k3  hf ( xn  h, yn  k3 )
k3  hf ( xn  h, yn  k3 )
Newton’s backward difference interpolation formula

Newton’s forward difference interpolation formula
Newton’s divided difference interpolation formula
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 A  0 then system will have a

Definite solution
Unique solution
Correct solution
No solution
If A  0 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 )
h h
F ( )  257.1379 F1 ( )
If F (h)  256.2354 and 2 , then find 2 using Richardson’s
extrapolation limit.
Evaluate the integral


2
 (cos x  2)dx
0
Using Simpson’s 3/8 rule

Take h= 4
Write a general formula for Modified Euler’s method of solving the given
differential equation.

4
 x dx
2
Using Trapezoidal rule

Take h=1

5
 (log x  2)dx
3

Take h=1
Write a formula for finding the value of k3 in Fourth-order R-K method.
Find Newton’s forward difference table from the following data.
x 0.0 0.1 0.2 0.3 0.4

f ( x) 1 0.9048 0.8187 0.7408 0.6703

3
 (x  x)dx
2
Take h=1
Use Runge-Kutta Method of order four to find the values of

k1 , k2 , k3 and k4 for the initial value problem
1
y/  (2 x3  y ), y (1)  2 taking h  0.1
2

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Mth603 Solved MCQS for Final Term Exam

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

Eigenvalues of a symmetric matrix are all _______ .

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

Below are all the finite difference methods EXCEPT _________.

If A is a nxn triangular matrix (upper triangular, lower triangular) or diagonal

The characteristics polynomial of a 3x 3 Identity matrix is __________, if x is the

Regula Falsi means

Method of Correct position

Eigenvalues of a symmetric matrix are all _________.

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

Exact solution of 2/3 is not exists.

The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric

Differences methods find the ________ solution of the system.

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

Newton Raphson method falls in the category of

Newton Raphson method is also known as

Secant Method uses values for approximation

Secant Method is than bisection method for finding root

In Newton Raphson method

Regula falsi method and bisection method are both

Similar to each other

In which methods we do not need initial approximation to start

In Regula falsi method we choose points that have signs

2 points opposite signs

In a bounded function values lie between

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

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

Which 1 of the following is generalization of Secant method?

Secant Method needs starting points

If S is an identity matrix, then

If we retain r+1 terms in Newton’s forward difference formula, we obtain a

Not equally spaced

Given the following data

If y ( x) is approximated by a polynomial pn ( x) of degree n then the error is

Let I denotes the closed interval spanned by x0 , x1 , x2 , x3 , x4 , x5 , x6 , x7 , x . Then

Differential operator in terms of forward difference operator is given by

Finding the first derivative of f ( x) at x =0.4 from the following table:

x 0.1 0.2 0.3 0.4

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

Forward difference operator

For the given table of values

f / (0.1) , using two-point equation will be calculated as.............

In Simpson’s 1/3 rule, f ( x) is of the form

While integrating I   f ( x)dx , h , width of the interval, is found by the

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

For the given table of values

f / / (0.2) , using three-point equation will be calculated as ……

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

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

An ordinary differential equation

None of the given choices

None of the given choices

In solving the differential equation

In second order Runge-Kutta method

In fourth order Runge-Kutta method, k2 is given by

In fourth order Runge-Kutta method, k4 is given by

Adam-Moulton P-C method is derived by employing