CUSTOMER_CODE
SMUDE
DIVISION_CODE
SMUDE
EVENT_CODE
SMUAPR15
ASSESSMENT_CODE BCA3010_SMUAPR15
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
10677
QUESTION_TEXT
Define curve fitting. What are the methods of curve fitting.
SCHEME OF
EVALUATION
The process of finding the equation of the curve of best fit which
may be suitable for predicting the unknown values in known is
curve fitting. (2 Marks)
Methods:
i.Graphic method (1 Mark)
ii.Method of group average (1 Mark)
iii.Method of moments (1 Mark)
iv.Method of least squares (1 Mark)
Graphical method explanation (4 Marks)
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
10678
QUESTION_TEXT
Define interpolation and extrapolation. When the following
formulate are useful
i. Newton’s forward difference interpolation formula
ii. Newton’s backward difference interpolation formula
iii. Central difference formula
SCHEME OF
EVALUATION
For a given table of values (Xk, Yk), K=0, 1,2, 3…….n the process
of estimating value for Y, for any intermediate value of X is called
interpolation (2 Marks)
Computing Y for X, lying outside the table of values of X
extrapolation (2 Marks)
i.Interpolation near the beginning of set of tabular values (2 Marks)
ii.Near the end of the tabular values (2 Marks)
iii.Near middle of the table (2 Marks)
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
10680
QUESTION_TEXT
Define significant digits. State the rules and describe the notion
of significant digits
SCHEME OF
EVALUATION
The digits that are used to express a number (1 Mark)
Rule 1: (Numbers without decimal point) (2 Marks)
Rule 2: (Numbers with decimal point) (2 Marks)
Note:
1.All non zero digits are significant (1 Mark)
2.All zeros occurring between non zero digits are significant
digits (1 Mark)
3.Trailing zeros following a decimal point (1 Mark)
4.Zeros between decimal point and preceding a non zero digit are
not significant (1 Mark)
5.When the decimal point is not written trailing zeros are not
considered to be significant. (1 Mark)
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
10681
QUESTION_TEXT
Explain Inherent errors and numerical errors with their
component
SCHEME OF
EVALUATION
Inherent errors (2 Marks)
Data error (2 Marks)
Conversion error (2 Marks)
Numerical errors (2 Marks)
Truncation numerical error (2 Marks)
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
73416
QUESTION_TEXT
Explain six steps to apply Cramer’s Rule
SCHEME OF
EVALUATION
Step i. Write the given equations in order so
that
constant terms all on the right side
(1.5
Marks)
Step ii. Take = the determinant formed by
the
coefficients of x, y, z (1.5 Marks)
Step iii. Replace the first column of  by constant
terms
of the equations and denote as x
(1.5 Marks)
Step iv. Replace the second column of by
constant
terms of the equations and denote
as y (1.5 Marks)
Step v. Replace the third column of by
constant
terms of the equations and denote
as z (1.5 Marks)
Step vi. Write the solution
(3 marks)
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
125708
QUESTION_TEXT
Explain the power method.
In many engineering problems, it is required to compute the
numerically largest eigen value and the corresponding eigen vector.
In such cases, the following power method is quite convenient
which is also well suited for solid machine computation.
Method: (To find the largest eigen value and the corresponding eigen
vector).
Suppose A is the given square matrix.
Step 1: Choose the initial vector such that the largest element is
unity.
(choose initially an eigen vector X(0) = (1, 0, 0)t or (0, 1, 0)t or (0, 0, 1)t
etc)
SCHEME OF
EVALUATION
Step 2: This normalized (taking the largest component out as a
common factor) vector X(0) is pre-multiplied by the given matrix.
(evaluate the matrix product AX(0) which is written as (1) X(1) after
normalization).
Step 3: This gives the first approximation (1) to the eigen value and
X(1) to the eigen vector.
Step 4: Compute AX(1) and again put in the form AX(1) = (2) X(2) by
normalization which gives the second approximation. Similarly we
evaluate AX(2) and put it in the form AX(2) = (3) X(3).
Step 5: Repeat this process till the difference between two successive
iterations is negligible. The values so obtained are respectively the
largest eigen value and the corresponding eigen vector of the given
square matrix A