MTH603 Mid Term Past and Current Solved Paper Discussion


  • Cyberian's Gold


  • Cyberian's Gold


  • Cyberian's Gold


  • Cyberian's Gold

    Question # 1 of 10 (Total Marks: 1)
    While solving a system of linear equations, which of the following approach is economical for the computer memory?
    Select correct option:
    Direct
    Iterative (Page 69)
    Analytical
    Graphical

    Question # 2 of 10 (Total Marks: 1)
    The basic idea of relaxation method is to reduce the largest residual to …
    Select correct option:
    One
    Two
    Zero (Page 83)
    None of the given choices

    Question # 3 of 10 (Total Marks: 1)
    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 (Page 104)
    last column
    last row
    first row

    Question # 4 of 10 (Total Marks: 1)
    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 Click here for detail
    FALSE

    Question # 5 of 10 (Total Marks: 1)
    A 3 x 3 identity matrix have three and different eigen values.
    Select correct option:
    TRUE Click here for detail
    FALSE

    Question # 6 of 10 (Total Marks: 1)
    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 # 7 of 10 (Total Marks: 1)
    Gauss - Jordan Method is similar to …
    Select correct option:
    Gauss–Seidel method
    Iteration’s method
    Relaxation Method
    Gaussian elimination method (Page 95)

    Question # 8 of 10 (Total Marks: 1)
    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 # 9 of 10 (Total Marks: 1)
    Gauss–Seidel method is also known as method of …
    Select correct option:
    Successive displacement (Page 263)
    Iterations
    False position
    None of the given choices

    Question # 10 of 10 (Total Marks: 1)
    Jacobi’s Method is a/an…
    Select correct option:
    Iterative method (Page 69)
    Direct method

    QUIZ.NO.1(2)

    Question # 1 of 10 (Total Marks: 1)
    The characteristics polynomial of a 3x 3 identity matrix is __________, if x is the eigen values of the
    given 3 x 3 identity matrix. where symbol ^ shows power.
    Select correct option:
    (x-1)^3
    (x+1)^3
    x^3-1
    x^3+1

    Question # 2 of 10 (Total Marks: 1)
    The 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 # 3 of 10 (Total Marks: 1)
    In … method, a system is reduced to an equivalent diagonal form using elementary
    transformations.
    Select correct option:
    Jacobi’s
    Gauss-Seidel
    Relaxation
    Gaussian elimination (Page 262)

    Question # 4 of 10 (Total Marks: 1)
    The linear equation: 2x+0y-2=0 has -------- solution/solutions.
    Select correct option:
    Unique (Page 48)
    no solution
    infinite many
    finite many

    Question # 5 of 10 (Total Marks: 1)
    Under elimination methods, we consider, Gaussian elimination and …methods.
    Select correct option:
    Gauss-Seidel
    Jacobi
    Gauss-Jordan elimination (Page 48)
    None of the given choices

    Question # 6 of 10 (Total Marks: 1)
    Which of the following method is not an iterative method?
    Select correct option:
    Jacobi’s method
    Gauss-Seidel method
    Relaxation methods
    Gauss-Jordan elimination method

    Question # 7 of 10 (Total Marks: 1)
    An eigenvector V is said to be normalized if the coordinate of largest magnitude is equal
    to zero.
    Select correct option:
    TRUE
    FALSE (Page 97)

    Question # 8 of 10 (Total Marks: 1)
    Exact solution of 2/3 is not exists.
    Select correct option:
    TRUE
    FALSE

    Question # 9 of 10 (Total Marks: 1)
    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 (Page 70)
    Divergent

    Question # 10 of 10 (Total Marks: 1)
    Gauss–Seidel method is similar to …
    Select correct option:
    Iteration’s method
    Regula-Falsi method
    Jacobi’s method
    None of the given choices (Page 263)

    QUIZ.NO.1(3)

    Question # 1 of 10 (Total Marks: 1)
    Sparse matrices arise in computing the numerical solution of …
    Select correct option:
    Ordinary differential equations
    Partial differential equations (Page 69)
    Linear differential equations
    Non-linear differential equations

    Question # 2 of 10 (Total Marks: 1)
    While solving by Gauss-Seidel method, which of the following is the first Iterative solution for the
    system; x-2y =1, x+4y=4 ?
    Select correct option:
    (1, 0.75)
    (0,0)
    (1,0)
    (0,1)

    Question # 3 of 10 (Total Marks: 1)
    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 # 4 of 10 (Total Marks: 1)
    Numerical methods for finding the solution of the system of equations are classified as direct and
    … methods
    Select correct option:
    Indirect
    Iterative (Page 48)
    Jacobi
    None of the given choices

    Question # 5 of 10 (Total Marks: 1)
    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 # 6 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)

    0= 1-2x-3y
    0= 4-3x -2y

    Question # 7 of 10 (Total Marks: 1)
    If the order of coefficient matrix corresponding to system of linear equations is 33 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’ = 13
    Order of ‘L’ = 3
    2, Order of ‘U’ = 2*3

    Order of ‘L’ = 33, Order of ‘U’ = 33
    Order of ‘L’ = 34, Order of ‘U’ = 43

    Question # 8 of 10 (Total Marks: 1)
    While solving the system; x–2y = 1, x+4y = 4 by Gauss-Seidel method, which of the following ordering
    is feasible to have good approximate solution?
    Select correct option:
    x+4y = 1, x-2y = 4
    x+2y = 1, x- 4y =4
    x+4y = 4, x–2y = 1
    no need to reordering

    Question # 9 of 10 (Total Marks: 1)
    Full pivoting, in fact, is more …than the partial pivoting.
    Select correct option:
    Easiest
    Complicated (Page 51)
    Question # 10 of 10 (Total Marks: 1)
    For the equation
    11fd5b6d-0b86-453d-83b2-64f970116bbc-image.png the root of the equation lies in the interval…

    ► (1, 3)
    ► (1, 2)
    ► (0, 1)
    ► (1, 2)

    QUIZ.NO.1(4)

    Question # 1 of 10 (Total Marks: 1)
    …lies in the category of iterative method.
    ► Bisection Method
    ► Regula Falsi Method
    ► Secant Method
    ► all of the given choices (Page 8)

    Question # 2 of 10 (Total Marks: 1)
    If n x n matrices A and B are similar, then they have the different eigenvalues (with the same
    multiplicities).
    True
    False

    Question # 3 of 10 (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.
    No Click here for detail
    At least one

    Question # 4 of 10 (Total Marks: 1)
    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 …
    b751921b-b3f6-45cd-9112-ad988bc16051-image.png

    Question # 5 of 10 (Total Marks: 1)
    To apply Simpson’s 3/8 rule, the number of intervals in the following must be
    ► 10
    ► 11
    ► 12
    ► 13

    Question # 6 of 10 (Total Marks: 1)
    The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric________ definite
    matrices A.
    Select correct option:
    Positive Click here for detail
    negative

    Question # 7 of 10 (Total Marks: 1)
    Differences methods find the ________ solution of the system.
    Select correct option:
    numerical
    Analytical

    Question # 8 of 10 (Total Marks: 1)
    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 # 9 of 10 (Total Marks: 1)
    Bisection and false position methods are also known as bracketing method and are always
    Divergent
    Convergent (Page 26)
    .67

    Question # 10 of 10 (Total Marks: 1)
    The Inverse of a matrix can only be found if the matrix is
    Singular
    None Singular: Every square non-singular matrix will have an inverse.
    Scalar
    Diagonal

    QUIZ.NO.1(5)

    Question # 1 of 10 (Total Marks: 1)
    In interpolation is used to represent the δ
    Forward difference Δ
    Central difference (Page 117)
    Backward difference

    Question # 2 of 10 (Total Marks: 1)
    The base of the decimal system is _______
    10
    0
    2
    8
    None of the above.

    Question # 3 of 10 (Total Marks: 1)
    Bisection method is … method
    ► Open Method
    ► Bracketing Method (page 26)

    Question # 4 of 10 (Total Marks: 1)
    A 3 x 3 identity matrix have three and __________eigen values.
    same
    different

    Question # 5 of 10 (Total Marks: 1)
    Eigenvalues of a symmetric matrix are all _______ .
    Real (page 104)
    complex
    zero
    positive

    Question # 6 of 10 (Total Marks: 1)
    The Jacobi iteration converges, if A is strictly diagonally dominant.
    TRUE (Page 69)
    FALSE

    Question # 7 of 10 (Total Marks: 1)
    Below are all the finite difference methods EXCEPT _________.
    jacobi’s method
    newton’s backward difference method
    Stirlling formula
    Forward difference method

    Question # 8 of 10 (Total Marks: 1)
    Two matrices with the same characteristic polynomial need not be similar.
    TRUE
    FALSE

    Question # 9 of 10 (Total Marks: 1) No.69
    The determinant of a diagonal matrix is the product of the diagonal elements.
    True
    False

    Question # 10 of 10 (Total Marks: 1)
    The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric positive definite matrices A.
    True
    False

    QUIZ.NO.1(6)

    Question # 1 of 10 (Total Marks: 1)
    The determinant of a _______ matrix is the product of the diagonal elements.
    Diagonal Page No.70
    Upper triangular
    Lower triangular
    Scalar

    Question # 2 of 10 (Total Marks: 1)
    For differences methods we require the set of values.
    True
    False

    Question # 3 of 10 (Total Marks: 1)
    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 # 4 of 10 (Total Marks: 1)
    Central difference method seems to be giving a better approximation, however it requires more computations.
    True
    False

    Question # 5 of 10 (Total Marks: 1)
    Iterative algorithms can be more rapid than direct methods.
    True
    False

    Question # 6 of 10 (Total Marks: 1)
    Central Difference method is the finite difference method.
    True
    False

    Question # 1 of 10 (Total Marks: 1)
    Back substitution procedure is used in …
    Select correct option:
    Gaussian Elimination Method
    Jacobi’s method
    Gauss-Seidel method
    None of the given choices

    Question # 7 of 10 (Total Marks: 1)
    The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its main diagonal.
    True
    False

    Question # 8 of 10 (Total Marks: 1)
    Power method is applicable if the eigen vectors corresponding to eigen values are linearly independent.
    True (Page102)
    False

    Question # 9 of 10 (Total Marks: 1)
    Power method is applicable if the eigen values are ______________.
    realanddistinct (Page102)
    real and equal
    positive and distinct
    negative and distinct

    Question # 10 of 10 (Total Marks: 1)
    Simpson’s rule is a numerical method that approximates the value of a definite integral by using polynomials.
    Quadratic (Page174)
    Linear
    Cubic
    Quartic

    QUIZ.NO.1(7)

    Question # 1 of 10 (Total Marks: 1)
    .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 Click here for detail
    False

    Question # 2 of 10 (Total Marks: 1)
    The predictor-corrector method an implicit method. (multi-step methods)
    True (Page 212)
    False

    Question # 3 of 10 (Total Marks: 1)
    Generally, Adams methods are superior if output at many points is needed.
    True
    False

    Question # 4 of 10 (Total Marks: 1)
    The Trapezoidal rule is a numerical method that approximates the value of a.______________.
    Indefinite integral
    Definiteintegral (Page176)
    Improper integral
    Function

    Question # 5 of 10 (Total Marks: 1)
    The need of numerical integration arises for evaluating the definite integral of a function that has no
    explicit ____________ or whose anti derivative is not easy to obtain.
    Antiderivative
    Derivatives.

    Question # 6 of 10 (Total Marks: 1)
    An indefinite integral may _________ in the sense that the limit defining it may not exist.
    diverge
    Converge

    Question # 7 of 10 (Total Marks: 1)
    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 Click here for detail
    FALSE
    Question # 8 of 10 (Total Marks: 1)
    Euler’s Method numerically computes the approximate derivative of a function.
    TRUE
    FALSE
    Question # 9 of 10 (Total Marks: 1)
    Euler’s Method numerically computes the approximate ________ of a function.
    Antiderivative
    Derivative
    Error
    Value
    Question # 10 of 10 (Total Marks: 1)
    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 Click here for detail
    Zero

    QUIZ.NO.1(8)

    Question # 1 of 10 (Total Marks: 1)
    The Jacobi iteration ______, if A is strictly diagonally dominant.
    converges
    Diverges
    Question # 2 of 10 (Total Marks: 1)
    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 # 3 of 10 (Total Marks: 1)
    The absolute value of a determinant (|detA|) is the product of the absolute values of the eigenvalues of

    13

    matrix A
    TRUE
    FALSE
    Question # 4 of 10 (Total Marks: 1)
    Eigenvectors of a symmetric matrix are orthogonal, but only for distinct eigenvalues.
    TRUE
    FALSE
    Question # 5 of 10 (Total Marks: 1)
    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
    Av + xv=0
    Av = Ax1
    Av = λv
    Question # 6 of 10 (Total Marks: 1)
    In Jacobi’s Method, the rate of convergence is quite ______ compared with other methods.
    Slow Click here for detail
    Fast
    Question # 7 of 10 (Total Marks: 1)
    Numerical solution of 2/3 up to four decimal places is ________.
    0.667
    0.6666
    0.6667
    0.666671.
    Question # 8 of 10 (Total Marks: 1)
    Symbol used for forward differences is
    ∆ (Page 12)
    δ
    μ
    Question # 9 of 10 (Total Marks: 1)
    The relationship between central difference operator and the shift operator is given by
    δ =Ε−Ε-1
    δ = Ε+Ε-1
    δ = Ε1/2+Ε1/2
    δ = E1/2 −Ε1/2
    1 1
    E E 2 2 

     

    (Page 152)
    Question # 10 of 10 (Total Marks: 1)

    14

    Muller’s method requires --------starting points
    1
    2
    3 (Page 41)

    QUIZ.NO.1(9)

    Question # 1 of 10 (Total Marks: 1)
    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 # 2 of 10 (Total Marks: 1)
    Two matrices with the _______ characteristic polynomial need not be similar.
    Select correct option:
    same
    different
    Question # 3 of 10 (Total Marks: 1)
    In … method, the elements above and below the diagonal are simultaneously made zero.
    Select correct option:
    Jacobi’s
    Gauss-Seidel
    Gauss–Jordon Elimination (Page 59)
    Relaxation
    Question # 4 of 10 (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 # 5 of 10 (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

    15

    None of the given choices
    Question # 6 of 10 (Total Marks: 1)
    Sparse matrix is a matrix with …
    Select correct option:
    Some elements are zero
    Many elements are zero (page 69)
    Some elements are one
    Many elements are one

    MTH603 – 2

    ND QUIZ FILE (24-11-2011)

    EDIT BY MUHAMMAD AWAIS AND MUHAMMAD MOAAZ SIDDIQ

    QUIZ.NO.2(1)
    Question # 1 of 10 ( Start time: 11:18:07 PM ) Total Marks: 1
    How many Eigen vectors will exist corresponding to the function; Exp(ax) = e^ax, when the matrix
    operator is of differentiation?
    Select correct option:
    Infinite many
    Finite Multiple
    None
    Question # 2 of 10 ( Start time: 11:19:00 PM ) Total Marks: 1
    Which of the following rearrangement make strictly diagonal dominant, the system of linear
    equations; x-3y+z= –2, –6x+4y+11z=1, 5x–2y–2z=9?
    Select correct option:
    5x–2y–2z=9, x–3y+z= –2, –6x+4y+11z=1
    –6x+4y+11z=1, x–3y+z= –2, 5x–2y–2z=9
    5x–2y–2z=9, –6x+4y+11z=1, x–3y+z= –2
    No need to rearrange as system is already in diagonal dominant form.
    Question # 3 of 10 ( Start time: 11:22:12 PM ) Total Marks: 1
    Which of the following is the meaning of partial pivoting while employing the row transformations?
    Select correct option:
    Making the largest element as pivot (Page 50)
    Making the smallest element as pivot
    Making any element as pivot
    Making zero elements as pivot

    16

    Question # 4 of 10 ( Start time: 11:53:06 PM ) Total Marks: 1
    Differences methods are iterative methods.
    Select correct option:
    TRUE
    FALSE

    Question # 5 of 10 ( Start time: 11:55:28 PM ) Total Marks: 1
    Eigenvalues of a _________ matrix are all real.
    Select correct option:
    symmetric
    antisymmetric
    rectangular
    triangular
    Question # 6 of 10 ( Start time: 11:32:38 PM ) Total Marks: 1
    If a system of equations has a property that each of the equation possesses one large coefficient and
    the larger coefficients in the equations correspond to different unknowns in different equations,
    then which of the following iterative method id preferred to apply?
    Select correct option:
    Gauss-Seidel method
    Gauss-Jordon method
    Gauss elimination method
    Crout’s method
    Question # 7 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 (Page 48)
    Question # 8 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)

    17

    Question # 9 of 10 ( Start time: 11:37:49 PM ) Total Marks: 1
    While using Relaxation method, which of the following is increment ‘dxi’corresponding to the
    largest Residual for 1st iteration on the system; 2x+3y = 1, 3x +2y = - 4 ?
    Select correct option:
    -2
    2
    3
    4
    Question # 10 of 10 ( Start time: 11:40:42 PM)Total Marks: 1
    If system of equations is inconsistent then its means that it has …
    Select correct option:
    No Solutions
    Many solutions
    Infinite Many solutions
    None of the given choices

    QUIZ.NO.2(2)
    Question # 1 of 10 ( Start time: 11:47:15 PM)Total Marks: 1
    Relaxation Method is a/an …
    Select correct option:
    Direct method
    Iterative method
    Question # 2 of 10 ( Start time: 11:33:36 PM ) Total Marks: 1
    How many Eigen values will exist corresponding to the function; Exp(ax) = e^ax, when the matrix
    operator is of differentiation?
    Select correct option:
    Finite Multiple
    Infinite many
    Unique
    None

    Question # 3 of 10 ( Start time: 11:36:46 PM ) Total Marks: 1
    The eigenvectors of a square matrix are the non-zero vectors that, after being multiplied by the
    matrix, remain … to the original vector.
    Select correct option:
    Perpendicular
    Parallel
    Diagonal

    18

    None of the given choices
    Question # 4 of 10 ( Start time: 11:38:16 PM ) Total Marks: 1
    In Jacobi’s method after finding D1, the sum of the diagonal elements of D1 should be … to
    the sum of the diagonal elements of the original matrix A.
    Select correct option:
    Greater than
    Less than
    Same (Page 106)
    Different
    Question # 5 of 10 (Total Marks: 1)
    In the context of Jacobi’s method for finding Eigen values and Eigen vectors of a real symmetric
    matrix of order 2*2, if |-5| be its largest off-diagonal and its two equal diagonal values are ‘3’ then
    which of the following will be its corresponding argument value ‘theta’ of Orthogonal Matrix?
    Select correct option:
    Pi/3
    Pi/6
    Pi/2
    Pi/4
    Question # 6 of 10 (Total Marks: 1)
    If f (x) contains trigonometric, exponential or logarithmic functions then this equation is known as
    Transcendental Equation (Page 6)
    Algebraic
    Polynomial
    Linear
    Question # 7 of 10 (Total Marks: 1)
    In interpolation is used to represent the d
    Forward difference ?
    Central difference
    Backward difference
    Question # 8 of 10 (Total Marks: 1)
    The Power method can be used only to find the eigen value of A that is largest in absolute value we call
    this eigen value the dominant eigen value of A.
    True
    False
    Question # 9 of 10 (Total Marks: 1)
    Power method is applicable if the eigen vectors corresponding to eigen values are linearly ----.
    Select correct option:
    independent
    dependent



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