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Worksheets

Numerical Methods & Data Analysis — Worksheet Extraction

Total questions: 135

Worksheet time: 1hrs 8mins

Name
Class
Date
1.

Resolve the following problems: What is the primary purpose of regression analysis?

a)

To sort data values

b)

To calculate probabilities

c)

To predict or estimate one variable based on another

d)

To test for independence between variables

2.

Resolve the following problems: What is the primary purpose of a histogram?

a)

To display data trends over time

b)

To show the relationship between two variables

c)

To represent the frequency distribution of data

d)

To compare categories of data

3.

Resolve the following problems: Which of the following methods is specifically designed for solving systems of linear equations using an iterative approach and updates all variables simultaneously using values from the previous iteration?

a)

Gauss-Seidel

b)

Newton-Raphson

c)

Jacobi

d)

Bisection Method

4.

Resolve the following problems: What is the key requirement for the bisection method to work in finding a root of a function f(x)?

a)

The function must be linear.

b)

The function must be differentiable.

c)

The function must change sign over the interval.

d)

The function must have a maximum or minimum in the interval.

5.

Resolve the following problems: For the Gauss-Seidel method to converge when solving a system of linear equations, what condition must the coefficient matrix satisfy?

a)

Symmetric

b)

Positive definite

c)

Diagonally dominant

d)

Sparse

6.

Resolve the following problems: What type of data is best represented using a bar chart?

a)

Continuous numerical data

b)

Discrete categorical data

c)

Time-series data

d)

Frequency distribution of continuous variables

7.

Resolve the following problems: The aim of elimination steps in Gauss elimination method is to reduce the coefficient matrix to ________.

a)

A diagonal

b)

identity

c)

lower triangular

d)

upper triangular

8.

Resolve the following problems: Which of the following is NOT a root-finding method?

a)

Bisection

b)

Newton-Raphson

c)

Gauss-Seidel

d)

Secant

9.

Resolve the following problems: Which of the following is the main difference between the Jacobi Method and the Gauss-Seidel Method when solving systems of linear equations?

a)

The Jacobi Method updates all variables using the previous iteration values, while the Gauss-Seidel Method updates variables immediately after computing each value.

b)

The Gauss-Seidel Method requires more iterations than the Jacobi Method for convergence.

c)

The Jacobi Method is used for solving nonlinear systems, while the Gauss-Seidel Method is only for linear systems.

d)

The Gauss-Seidel Method requires the matrix to be diagonally dominant, while the Jacobi Method does not.

10.

Resolve the following problems: What is the fundamental requirement for the Newton-Raphson Method to successfully find a root of a function?

a)

The function must be linear.

b)

The derivative of the function must be zero at the root.

c)

The function must be continuous and differentiable near the root.

d)

The initial guess must be far from the root.

11.

Resolve the following problems: In numerical methods, the Jordan method is primarily used for:

a)

Solving systems of linear equations

b)

Finding roots of nonlinear equations

c)

Approximating definite integrals

d)

Eigenvalue analysis

12.

Resolve the following problems: Which of the following updates immediately?

a)

Gauss Jacobi

b)

Gauss Seidel

c)

Newton Raphson

d)

Bisection

13.

Resolve the following problems: How does the Jacobi method differ from the Gauss-Seidel method in solving systems of linear equations?

a)

Jacobi uses updated values immediately, while Gauss-Seidel uses old values only.

b)

Jacobi updates all variables simultaneously using previous iteration values.

c)

Jacobi requires the matrix to be symmetric, while Gauss-Seidel does not.

d)

Jacobi is faster and more stable than Gauss-Seidel in all cases.

14.

Resolve the following problems: What is the primary purpose of a scatter plot in electrical engineering data analysis?

a)

To display voltage versus time in a signal

b)

To show frequency domain representations

c)

To observe the relationship between two variables, such as current and voltage

d)

To solve complex circuit equations

15.

Resolve the following problems: Which best differentiates the Jacobi method from the Gauss-Seidel method?

a)

Jacobi updates all variables simultaneously using previous values; Gauss-Seidel uses the most recent values.

b)

Gauss-Seidel requires matrix inversion; Jacobi does not.

c)

Jacobi is faster than Gauss-Seidel in all cases.

d)

Gauss-Seidel can’t solve nonlinear systems.

16.

Resolve the following problems: What process does the Bisection Method perform when solving for the root of an equation?

a)

Halves the interval

b)

Doubles the interval

c)

Iterates the interval randomly

d)

None of the above

17.

Resolve the following problems: The Bisection Method is guaranteed to converge if:

a)

Function is continuous and f(a) and f(b) have opposite signs

b)

Function is discontinuous

c)

Function is differentiable only

d)

Any two points are selected randomly

18.

Resolve the following problems: Which of the following data is used in Bar Graphs?

a)

Categorical Data

b)

Quantitative Data

c)

Historical Data

d)

Both Categorical and Quantitative Data

19.

Resolve the following problems: In Pearson Correlation, what does a value of −1 indicate?

a)

Perfect positive linear correlation

b)

No correlation

c)

Perfect negative linear correlation

d)

Random relationship

20.

Resolve the following problems: In electrical circuit design, what does a scatter plot help reveal when analyzing two variables, such as input voltage and output current?

a)

The impedance of the circuit

b)

The time delay between signals

c)

The correlation between the two variables

d)

The total harmonic distortion

21.

Resolve the following problems: In electrical engineering, what is the main purpose of Fourier Analysis?

a)

To solve linear systems of equations

b)

To approximate a function using a series of sine and cosine terms

c)

To find the shortest path in a network

d)

To minimize electrical losses in transmission lines

22.

Resolve the following problems: What is the requirement for the Gauss-Seidel Method to guarantee convergence?

a)

The matrix must be positive definite

b)

The matrix must be sparse

c)

The matrix must be strictly diagonally dominant

d)

The system must have no free variables

23.

Resolve the following problems: What is the main requirement for the Newton-Raphson Method to work correctly?

a)

The function must be discontinuous

b)

The function must be differentiable and continuous near the root

c)

The matrix must be symmetric

d)

The function must be quadratic

24.

Resolve the following problems: What does Fourier Analysis primarily transform a signal into?

a)

Time domain

b)

Laplace domain

c)

Frequency domain

d)

Spatial domain

25.

Resolve the following problems: Which mathematical components are used in Fourier Series?

a)

Exponential and polynomial terms

b)

Sine and cosine terms

c)

Logarithmic and hyperbolic functions

d)

Step and impulse functions

26.

Resolve the following problems: In a line graph, the x-axis usually represents:

a)

Frequency

b)

Categories

c)

Time

d)

Percentages

27.

Resolve the following problems: In Fourier Analysis, a square wave is represented by:

a)

Infinite odd harmonics

b)

Even harmonics only

c)

A single sine wave

d)

Cosine terms only

28.

Resolve the following problems: Fourier Analysis is useful for analyzing:

a)

Random signals

b)

Periodic signals

c)

Discrete events

d)

Chemical reactions

29.

Resolve the following problems: For Newton-Raphson to work, the function must be:

a)

Discontinuous

b)

Nonlinear only

c)

Linear only

d)

Differentiable and continuous

30.

Resolve the following problems: The Newton-Raphson Method is used for:

a)

Matrix inversion

b)

Finding roots of equations

c)

Finding eigenvalues

d)

Solving systems of linear equations

31.

Resolve the following problems: What is the basic formula used in Newton-Raphson iteration?

a)

xn+1=xn + f(xn)f′(xn)x_{n+1}=x_n\,+\,\frac{f(x_n)}{f'(x_n)}

b)

xn+1=xn − f(xn)f′(xn)x_{n+1}=x_n\,-\,\frac{f(x_n)}{f'(x_n)}

c)

xn+1=xn×f(xn)f′(xn)x_{n+1}=x_n\times\frac{f(x_n)}{f'(x_n)}

d)

xn+1=f(xn)x_{n+1}=\sqrt{f(x_n)}

32.

Resolve the following problems: The Secant Method does NOT require:

a)

Derivative of the function

b)

Two initial approximations

c)

Evaluation of function values

d)

Iterative updates

33.

Resolve the following problems: Gauss-Seidel Method requires the coefficient matrix to be:

a)

Orthogonal

b)

Symmetric

c)

Strictly diagonally dominant

d)

Sparse

34.

Resolve the following problems: Jacobi's Method updates variables using:

a)

Latest available values

b)

Values from the previous iteration only

c)

Randomized values

d)

Midpoints of interval estimates

35.

Resolve the following problems: What does a Pearson correlation coefficient value of 0 indicate?

a)

Perfect positive linear relationship

b)

Perfect negative linear relationship

c)

No linear relationship between the variables

d)

Strong nonlinear relationship

36.

Which iterative method typically converges faster, Gauss-Seidel or Jacobi?

a)

Gauss-Seidel

b)

Jacobi

c)

Both converge equally fast

d)

Neither converges

37.

What does a Pearson Correlation coefficient indicate?

a)

No correlation

b)

Perfect positive linear correlation

c)

Perfect negative linear correlation

d)

Weak correlation

38.

What does a Pearson correlation coefficient of +1+1 indicate?

a)

No linear relationship between variables

b)

Perfect positive linear relationship

c)

Perfect negative linear relationship

d)

Weak positive correlation

39.

What does a Pearson correlation coefficient of −0.8-0.8 suggest?

a)

Strong negative linear relationship

b)

Weak negative linear relationship

c)

No correlation

d)

Strong positive linear relationship

40.

What does a Pearson correlation coefficient of 0.50.5 imply?

a)

No correlation

b)

Moderate positive correlation

c)

Moderate negative correlation

d)

Perfect positive correlation

41.

Which type of data is best displayed using a bar graph?

a)

Discrete categorical data

b)

Continuous numerical data

c)

Time-series data

d)

Probability distribution

42.

What is the primary purpose of a pie chart?

a)

To show relationships over time

b)

To compare parts of a whole

c)

To track changes between variables

d)

To display frequency distributions

43.

Which graph is most appropriate for displaying continuous numerical data grouped into intervals?

a)

Line Graph

b)

Histogram

c)

Bar Graph

d)

Pie Chart

44.

What does each "slice" in a pie chart represent?

a)

Frequency

b)

Part of the total percentage

c)

Time period

d)

Random events

45.

Which of the following graphs best shows trends over time?

a)

Pie Chart

b)

Histogram

c)

Bar Graph

d)

Line Graph

46.

Compared to the Newton-Raphson method, the Secant Method:

a)

Converges faster

b)

Converges slower

c)

Always fails

d)

Does not converge

47.

In a bar graph, bars should:

a)

Overlap to save space

b)

Touch each other

c)

Be separated by spaces

d)

Have random heights

48.

What kind of graph is best suited for showing how a quantity is broken down into percentages?

a)

Pie chart

b)

Bar graph

c)

Line graph

d)

Histogram

49.

Which graph uses "bins" to group data?

a)

Bar graph

b)

Line graph

c)

Histogram

d)

Pie chart

50.

If you want to emphasize the relative size of categories visually, which graph would you use?

a)

Histogram

b)

Pie chart

c)

Line graph

d)

Scatter plot

51.

Which graph is best for displaying cause and effect relationships?

a)

Pie chart

b)

Line graph

c)

Scatter plot

d)

Histogram

52.

In a bar graph, the height of each bar represents:

a)

The percentage change

b)

The cumulative frequency

c)

The mean of the data

d)

The value or frequency of the data

53.

A histogram differs from a bar graph because:

a)

Bars touch each other in a histogram

b)

Bars are separated in a histogram

c)

Histograms use discrete data

d)

Histograms only show percentages

54.

When dealing with categorical variables, which graph is inappropriate?

a)

Bar graph

b)

Pie chart

c)

Line graph

d)

None of the above

55.

Which visual tool is used to show the distribution of a dataset and allows for quick median and quartile observations?

a)

Box-and-whisker plot

b)

Scatter plot

c)

Line graph

d)

Histogram

56.

What is the main use of a scatter plot?

a)

Show parts of a whole

b)

Show correlation between two variables

c)

Display frequency distribution

d)

Track time trends

57.

Which graph would best show monthly sales over a year?

a)

Pie chart

b)

Line graph

c)

Bar graph

d)

Histogram

58.

A graph that displays data points without connecting lines to show relationships is called:

a)

Line graph

b)

Bar graph

c)

Histogram

d)

Scatter plot

59.

Which graph is best suited to compare quantities among different categories?

a)

Bar graph

b)

Line graph

c)

Scatter plot

d)

Histogram

60.

What type of graph would be best used to visualize test scores grouped into score ranges?

a)

Pie chart

b)

Histogram

c)

Line graph

d)

Scatter plot

61.

The Secant Method requires:

a)

Two initial guesses

b)

Derivative evaluation

c)

Symmetric matrix

d)

None of the above

62.

Which method converges faster in general?

a)

Bisection Method

b)

Newton-Raphson Method

c)

Gauss-Seidel Method

d)

Jacobi Method

63.

Which method generally converges slower, Jacobi or Gauss-Seidel?

a)

Gauss-Seidel

b)

Depends on the function

c)

Both are equally fast

d)

Jacobi

64.

In Gauss-Seidel Method, convergence is guaranteed if the coefficient matrix is:

a)

Sparse

b)

Diagonally dominant

c)

Symmetric

d)

Upper triangular

65.

Which iterative method uses the newest available value immediately after computation?

a)

Jacobi Method

b)

Newton-Raphson Method

c)

Bisection Method

d)

Gauss-Seidel Method

66.

In the Bisection Method, a necessary condition for the initial interval is:

a)

Both endpoints must be positive

b)

Derivatives must exist at endpoints

c)

Function values at endpoints must have opposite signs

d)

Both endpoints must be negative

67.

What is the main purpose of the Bisection Method?

a)

To approximate a function's derivative

b)

To find roots by halving intervals

c)

To solve a system of equations

d)

To minimize errors in integration

68.

In Jacobi Method, variables are updated:

a)

Sequentially

b)

Simultaneously using previous iteration values

c)

Randomly

d)

Based on maximum errors

69.

Which method has a quadratic rate of convergence under good conditions?

a)

Secant Method

b)

Bisection Method

c)

Newton-Raphson Method

d)

Gauss-Seidel Method

70.

Which method does NOT require derivative evaluation?

a)

Newton-Raphson

b)

Secant Method

c)

Both A and B

d)

None of the above

71.

What is the main weakness of the Secant Method?

a)

Requires derivative computation

b)

Only works for symmetric functions

c)

Too slow compared to Bisection

d)

May fail if guesses are poor

72.

The Bisection Method guarantees convergence if:

a)

The function is continuous and signs are opposite at endpoints

b)

The derivative is large

c)

The function is discrete

d)

Initial guesses are very close

73.

In Newton-Raphson Method, what happens if the derivative is zero at some iteration?

a)

The method speeds up

b)

The method stalls or fails

c)

The method resets to a new point

d)

The iteration doubles

74.

In numerical methods, what is an "iteration"?

a)

An exact solution

b)

Random guessing

c)

A single step closer to the solution

d)

Verification of final answer

75.

What is the general goal of iterative numerical methods?

a)

Solve exact solutions analytically

b)

Increase matrix size

c)

Reduce number of equations

d)

The function is continuous and signs are opposite at endpoints

76.

What is the convergence rate of the Newton-Raphson Method?

a)

Linear

b)

Quadratic

c)

Exponential

d)

Superlinear

77.

What is the convergence rate of the Secant Method?

a)

Linear

b)

Quadratic

c)

Superlinear

d)

Cubic

78.

If the initial guess is very poor, Newton-Raphson Method:

a)

Always converges

b)

May diverge

c)

May converge faster

d)

Guarantees a global solution

79.

Which method approximates the derivative using finite differences?

a)

Bisection Method

b)

Newton-Raphson Method

c)

Secant Method

d)

Gauss-Seidel Method

80.

Which of the following is TRUE about the Secant Method?

a)

It requires fewer initial assumptions than Newton-Raphson

b)

It needs two initial points

c)

It does not compute derivatives directly

d)

All of the above

81.

If Newton-Raphson oscillates between two points, the cause is likely:

a)

Very steep slope

b)

Very flat slope

c)

Derivative equals zero

d)

Discontinuity in function

82.

Which method is sensitive to choice of initial point, potentially failing if a poor initial guess is used?

a)

Bisection Method

b)

Secant Method

c)

Newton-Raphson Method

d)

Gauss-Seidel Method

83.

When is Newton-Raphson preferred over the Bisection Method?

a)

When the function is not continuous

b)

When guessing is not allowed

c)

For all non-linear equations regardless of behavior

d)

When a faster convergence is needed and derivative is available

84.

Which method is guaranteed to converge under correct starting conditions?

a)

Secant Method

b)

Bisection Method

c)

Newton-Raphson Method

d)

None

85.

The Secant Method replaces the true derivative with:

a)

Random values

b)

Tangent approximation

c)

Finite difference slope

d)

Analytical derivative

86.

Which method typically converges faster than Bisection but is not always guaranteed to converge?

a)

Simpson's

b)

Bisection

c)

Gauss-Seidel

d)

Newton-Raphson

87.

In which method is a poor initial guess most likely to cause failure?

a)

Newton-Raphson

b)

Secant

c)

Bisection

d)

Trapezoidal

88.

Which method can work without needing the derivative of the function?

a)

Newton-Raphson

b)

Secant

c)

None

d)

Both Bisection and Secant

89.

Which method converges at a superlinear rate, better than linear but not quite quadratic?

a)

Newton-Raphson

b)

Secant

c)

Bisection

d)

Jacobi

90.

Which method uses two previous points but does not require derivatives?

a)

Bisection

b)

Newton-Raphson

c)

Secant

d)

Simpson's Rule

91.

When the function's derivative is difficult to compute, which method is most practical?

a)

Bisection

b)

Secant

c)

Newton-Raphson

d)

None

92.

What is a key advantage of the Secant Method over Newton-Raphson?

a)

Does not require evaluation of derivatives

b)

Converges faster

c)

Solves linear systems better

d)

Works only on discrete functions

93.

What is the disadvantage of Newton-Raphson compared to Bisection?

a)

Slower convergence

b)

Higher computation cost for derivatives

c)

Requires no function evaluations

d)

Does not use any approximations

94.

Which method approximates the derivative using two previous points to find the next guess?

a)

Newton-Raphson Method

b)

Bisection Method

c)

Secant Method

d)

Fixed-Point Method

95.

Which method uses a tangent line at the current guess to approximate the root?

a)

Newton-Raphson Method

b)

Secant Method

c)

Bisection Method

d)

Gauss-Seidel Method

96.

Which method guarantees convergence if the function is continuous and the initial interval brackets a root?

a)

Newton-Raphson Method

b)

Secant Method

c)

Bisection Method

d)

Jacobi Method

97.

Which method is known for a simple concept but relatively slow convergence?

a)

Bisection Method

b)

Newton-Raphson Method

c)

Secant Method

d)

Gauss-Seidel Method

98.

Refers to a numerical method used for approximating the integral of a function between two limits, a and b.

a)

Newton-Raphson

b)

Gauss-Seidel

c)

Bisection

d)

Simpson's Rule

99.

The ____ method is a process for solving systems of linear equations and finding the inverse of a matrix by using elementary row operations to transform the augmented matrix into reduced row-echelon form.

a)

Simpson's Rule

b)

Gauss-Jordan

c)

Newton-Raphson

d)

Gauss-Seidel

100.

An iterative method for approximating the solution of a system of n linear equations in n variables.

a)

Simpson's Rule

b)

Gauss-Jordan

c)

Jacobi method

d)

Gauss-Seidel

101.

Which method requires the function to be differentiable for successful application?

a)

Newton-Raphson Method

b)

Bisection Method

c)

Secant Method

d)

None of the above

102.

What is Data Normalization?

a)

The process of creating multiple copies of data to ensure backup

b)

The process of organizing data in a structured format to eliminate redundancy and inconsistencies

c)

The method of encrypting data for security purposes

d)

The visualization of data in pie and bar graphs

103.

In database design, what is a "Primary Key"?

a)

A field that uniquely identifies each record in a table

b)

A field used for foreign reference

c)

A backup identifier

d)

A graphical representation of a table

104.

Which of the following is a violation of normalization principles?

a)

Unique primary keys

b)

Repeated groups in a table

c)

Removing null values

d)

Normalized foreign keys

105.

What does 2NF require in addition to 1NF?

a)

No repeated columns

b)

Elimination of transitive dependency

c)

No partial dependency on the primary key

d)

Introduction of surrogate keys

106.

A table is in 1NF if:

a)

It has no foreign keys

b)

It has composite primary keys

c)

It has no partial dependencies

d)

It has atomic (indivisible) values in each field

107.

Which form of normalization ensures that all attributes depend only on the primary key?

a)

First Normal Form (1NF)

b)

Second Normal Form (2NF)

c)

Third Normal Form (3NF)

d)

Boyce-Codd Normal Form (BCNF)

108.

Which normal form removes multi-valued attributes?

a)

1NF

b)

2NF

c)

3NF

d)

4NF

109.

What is a Foreign Key?

a)

A random identifier

b)

A backup key

c)

A hashed security code

d)

A primary key in another table used for linking records

110.

Which normal form deals with transitive dependencies?

a)

1NF

b)

2NF

c)

3NF

d)

BCNF

111.

Compared to Gauss-Seidel, the Newton-Raphson Method typically has:

a)

More iterations but less time per iteration

b)

Less iterations but more time per iteration

c)

The same number of iterations with faster computations

d)

Random convergence behavior

112.

What is denormalization?

a)

Organizing data into more tables

b)

Combining tables to improve read performance at the cost of redundancy

c)

Encrypting normalized tables

d)

Visualizing relationships graphically

113.

Which method generally requires the fewest iterations but more computation per iteration?

a)

Gauss-Seidel

b)

Jacobi

c)

Newton-Raphson

d)

Secant

114.

In the Bisection Method, the basic requirement is:

a)

Knowing the derivative

b)

Knowing two points with the function having opposite signs

c)

Diagonal dominance

d)

Superlinear convergence

115.

Which method updates variables immediately after computation during iteration?

a)

Newton-Raphson

b)

Jacobi

c)

Gauss-Seidel

d)

Secant

116.

Which method is typically slower because it uses previous iteration values for all updates?

a)

Gauss-Seidel

b)

Jacobi

c)

Newton-Raphson

d)

Secant

117.

Which method is best suited for solving large systems of linear equations, especially when the matrix is diagonally dominant?

a)

Newton-Raphson

b)

Secant

c)

Gauss-Seidel

d)

Jacobi

118.

If a system of linear equations is not diagonally dominant, which method might struggle to converge?

a)

Gauss-Seidel Method

b)

Newton-Raphson Method

c)

Secant Method

d)

Bisection Method

119.

Which method works best for solving systems of nonlinear equations by linearizing around a point?

a)

Bisection Method

b)

Secant Method

c)

Newton-Raphson Method

d)

Gauss-Seidel Method

120.

Which method approximates a root by assuming the function is approximately linear between two points?

a)

Secant

b)

Newton-Raphson

c)

Gauss-Seidel

d)

Jacobi

121.

Which method works best for solving systems of nonlinear equations by linearizing around a point?

a)

Bisection Method

b)

Secant Method

c)

Newton-Raphson Method

d)

Gauss-Seidel Method

122.

What is the main purpose of matrix deflation?

a)

To normalize a matrix for input-output transformation

b)

To reduce the size of a matrix by removing known eigenvalues

c)

To convert sparse matrices into diagonal form

d)

To estimate the trace of a matrix

123.

A 3×3 matrix can be reduced to a 2×2 matrix using which of the following methods?

a)

Gauss-Seidel Method

b)

Newton-Raphson Method

c)

Matrix Deflation

d)

Jacobi Iteration

124.

Which method is least sensitive to the choice of initial guesses?

a)

Newton-Raphson

b)

Bisection Method

c)

Secant Method

d)

Jacobi Method

125.

For a large sparse linear system, which iterative method is often preferred because of faster convergence when properly ordered?

a)

Jacobi

b)

Gauss-Seidel

c)

Secant

d)

Bisection

126.

After one eigenvalue is found using an iterative method, which process allows for finding the next eigenvalue?

a)

Matrix deflation

b)

Bisection method

c)

Gauss-Seidel method

d)

LU decomposition

127.

Which method is most commonly paired with matrix deflation to find successive eigenvalues?

a)

Newton-Raphson method

b)

Power method

c)

Bisection method

d)

Jacobi iteration

128.

What is the main purpose of matrix deflation?

a)

To normalize a matrix for input-output transformation

b)

To reduce the size of a matrix by removing known eigenvalues

c)

To convert sparse matrices into diagonal form

d)

To estimate the trace of a matrix

129.

Why is Bessel's correction applied when calculating sample variance?

a)

Because the standard deviation increases with sample size

b)

Because the mean of the sample is biased

c)

Because we are estimating population variance from a sample

d)

Because it only works for large sample sizes

130.

What is Bessel's correction used for in statistics?

a)

To increase the mean of a sample

b)

To correct bias in the sample variance

c)

To normalize a non-Gaussian distribution

d)

To estimate the median more accurately

131.

After one eigenvalue is found using an iterative method, which process allows for finding the next eigenvalue?

a)

Matrix deflation

b)

Bisection method

c)

Gauss-Seidel method

d)

LU decomposition

132.

In the Jacobi method, when will the method definitely converge?

a)

When the system is inconsistent

b)

When the coefficient matrix is symmetric

c)

When the matrix is strictly diagonally dominant

d)

When the initial guess is zero

133.

What happens if the Jacobi method is applied to a matrix with zeros along the diagonal?

a)

It always converges

b)

The method fails due to division by zero

c)

It becomes the Gauss-Seidel method

d)

The result is approximate

134.

Compared to Gauss-Seidel, Newton-Raphson method has ________.

a)

more iterations but less time per iteration

b)

equal performance always

c)

no convergence

d)

less iterations but more time per iteration

135.

In Bessel's correction, the denominator for sample variance becomes:

a)

n

b)

n + 1

c)

n − 1

d)

√n

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F1 QUESTION

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