Sunday, 27 December 2020

MTH603-Numerical Analysis Quiz MCQs Lecture 1-22 Midterm Objective Questions | SUPERSTARWEBTECH



MTH603-Numerical Analysis Quiz MCQS #Objective #Questions #MidTerm

1. If n x n matrices A and B are similar, then they have the ___ eigenvalues (with the same multiplicities)
  • same ✔
  • different
2. If the product of two matrices is an identity matrices that is AB = I, then which of the following is true?
  • A is transpose of B
  • A is inverse of B ✔
  • A is singular
  • B is singular
3. Iterative algorithms can be more rapid than direct methods.
  • False 
  • True ✔
4. 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
5. Which of the following systems of linear equations has a strictly diagonally dominant coefficient matrix?
  • -2x+7x+2x=5, 6x-2x+3x=1, x+x-5x=-13
  • -2x+7x+2x=5, 6x-2x+3x=1, x+x-5x=-13
  • x+x-5x=-13, 6x-2x+3x=1, -2x+7x+2x=5
  • 6x-2x+3x=1, -2x+7x+2x=5, x+x-5x=-13 
6. 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 then which of the following will be its corresponding off-diagonal values of Orthogonal Matrix?
  • Cos(theta), -Cos(theta) 
  • Sin(theta), Cos(theta)
  • Sin(theta), -Sin(theta)
  • -Sin(theta), Cos(theta)
7. While using power method, from the resultant normalize vector
8. Every non-zero vector x is an eigenvector of the identity matrix with Eigen value___
  • one
  • two
  • three
  • four
9. Which of the following systems of linear equations has a strictly diagonally coefficient matrix?
  • -x+12x+5x=8, 9x+5x-3x=12, 2x-4x+7x=-15
  • 9x+5x-3x=12, -x+12x+5x=8, 2x-4x+7x=-15
  • 2x-4x+7x=-15, -x+12x+5x=8, 9x+5x-3x=12
  • 9x+5x-3x=12, 2x-4x+7x=-15, -x+12x+5x=8
10. Let[A] be a 3 x 3 real symmetric matrix with |a| be numerically the largest off-diagonal element of A, then we can construct orthogonal matrix S1 by Jacobi's method as
11. If the pivot element happens to be zero, then the i-th column elements are searched for the numerically ___ element
  • Smallest
  • Largest ✔
12. Exact solution of 2/3 is not exists
  • True ✔
  • False
13. A and its transpose matrix have ___ eigenvalues
  • same ✔
  • different
14. If n x n matrices A and B are similar, then they have the different eigenvalues (with the same multiplicities)
  • True ✔
  • False
15. Power method is applicable if the eigen values are real and distinct
  • True ✔
  • False
16. By using determinants, we can easily check that the solution of the given system of linear equation ___ and it is ___
  • exists, unique ✔
  • exists, consistent
  • trivial, unique
  • nontrivial, inconsistent
17. Power method is applicable if the eigen vectors corresponding to eigen values are linearly ___
  • independent ✔
  • dependent
18. When the condition of diagonal dominance becomes true in Jacobi's Method. Then its means that the method is ___
  • Stable
  • Unstable
  • Convergent ✔
  • Divergent
19. While using Jacobi method for the matrix

A = [11/41/3]
1/41/31/2
1/31/21/5
 the value of 'theta Θ' can be found as 
  • tan 2Θ = 2a13/a11-a33
20. While using Jacobi method for the matrix
A = [11/41/2]
1/41/31/4
1/21/41/5
and 'theta Θ=0.4480' the orthogonal matrix S1 will be given by
  • S1 = [cos 0.44800-sin 0.4480]
    010
    sin 0.44800cos 0.4480
21. Full pivoting, in fact, is more ___ than the partial pivoting
  • Easiest
  • Complicated ✔
22. While using the Gauss-Seidel Method for finding the solution of the system of equation, the following system
x + 2y + 2z = 3
x + 3y + 3z = 2
x + y + 5z = 2
  • x = 3 - 2y - 2z, y = 2/3 - x/3 - z, z = 2/5 - x/5 - y/5
23. By using determinants, we can easily check that the solution of the given system of linear equation exists and it is unique
  • True ✔
  • False 
24. While using Jacobi method for the matrix
A = [11/41/3]
1/41/31/2
1/31/21/5
and 'theta Θ= 0.7191' the orthogonal matrix S1 will be given by
  • S1 = [cos 0.71910-sin 0.7191]
    010
    sin 0.71910cos 0.7191
25. The linear equation x + y = 1 has ___ solution/solutions
  • no solution
  • unique ✔
  • infinite many
  • finite many
26. For a system of linear equations, the corresponding coefficient matrix has the value of determinant; |A|=-3, then which of the following is true?
  • The system has unique solution ✔
  • The system has finite multiple solutions
  • The system has infinite many solutions
  • The system has no solution
27. In Gauss-Jacobi's method, the corresponding elements of xi(r+1) replaces those of xir as soon as they become available
  • True
  • False ✔
28. An augmented matrix may also be used to find the inverse of a matrix by combining it with the ___ matrix
  • Inverse
  • Square
  • Identity ✔
  • None
29. Power method is applicable it the eigen vectors corresponding to eigen values are linearly independent
  • True ✔
  • False
30. While using the relaxation method for finding the solution of the below given system, which of the following increment will be introduced?
6x1 - 2x2 + 3x3 = 1
-2x1 + 7x2 + 2x3 = 5
x1 + x2 - 5x3 = -13
  • dx3 = R3/a33
31. Let |A| be a 3 x 3 real symmetric matrix with |a23| be the numerically largest off-diagonal element then using Jacobi's method the value of theta can be found by
  • tan 2 Θ = 2a23/a22-a33 
32. The linear equation; 0x+0y=2 has ___ solution/solutions
  • unique
  • no solution ✔
  • infinite many
  • finite many
33. The root of the equation xex-5=0 is bounded in the interval
  • [-2, 1]
  • [-1, 1]
  • [0, 1] ✔
  • [1, 2]
34. Which of the following is a forward difference table for the given values of x and y?
x   0.1   0.5   0.9
y   0.003   0.148   0.370
  • xyΔyΔ2y
    0.10.0030.1450.077
    0.50.1480.222
    0.90.37
35. In ___ method, a system is reduced to an equivalent diagonal form using elementary transformations
  • Jacobi's 
  • Gauss-Seidel
  • Relaxation
  • Gaussian elimination ✔
36. 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
  • None
37. A 3 x 3 identity matrix have three and ___ eigen values
  • same ✔
  • different
38. Numerical methods for finding the solution of the system of equations are classified as direct and ___ methods
  • Indirect
  • Iterative ✔
  • Jacobi
  • None
39. Which of the following is a forward difference table for the given values of x and y?
x   0.1   0.7   1.3
y   0.003   0.248   0.697

  • xyΔyΔ2y
    0.10.0030.2450.204
    0.70.2480.449
    1.30.697
40. 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) ✔