Question 1

If the price of commodity' X' is 4 in the year 2003 and 5 in the year 2004. Then, the price index for the year 2004, used 2003 as base year is:
A)100
B)125
C)130
D)135

Accepted Answer

The price index is calculated as (Price in current year / Price in base year) * 100. So, for 2004 using 2003 as the base year, it is (5 / 4) * 100 = 125.

Question 2

Changes that have taken place as a result of such forces that could not be predicted like floods, earthquakes, famines, etc is known as:
A)Secular trend
B)Seasonal movements
C)Irregular variations
D)Cyclical variations

Accepted Answer

Irregular variations are changes in data or trends that occur due to unpredictable events, such as natural disasters (floods, earthquakes) or other unforeseen occurrences. These variations are not regular or repeating, making them distinct from seasonal, cyclical, or secular trends.

Question 3

In semi averages method, the given data is divided into:
A)Two equal parts
B)Three equal parts
C)Four equal parts
D)Difficult to tell

Accepted Answer

In the semi-averages method, the given data is divided into two equal parts to calculate the trend by finding the average of each part.

Question 4

The additive model of the time series is:
A)Y = T + S + C + I
B)Y = TSCI
C)Y = a + bX
D)Y = a + bX + cX

Accepted Answer

The additive model of the time series is represented as Y = T + S + C + I, where Y is the time series data, T is the trend component, S is the seasonal component, C is the cyclical component, and I is the irregular component. This model assumes that these components are added together to model the data.

Question 5

Two matrices A and B are multiplied to get AB if
A)Both are rectangular
B)Both have same order
C)No of columns of A is equal to columns of B
D)No of rows of A is equal to rows of B

Accepted Answer

For two matrices A and B to be multiplied, the number of columns in A must equal the number of rows in B.

Question 6

The determinant of identity matrix is :
A)1
B)0
C)Depends on the matrix
D)None of the above

Accepted Answer

The determinant of an identity matrix, regardless of its size, is always 1.

Question 7

The matrix [6] is
A)Square matrix
B)Row matrix
C)Column matrix
D)All of the above

Accepted Answer

The matrix [6] is a 1x1 matrix, which qualifies as a square matrix because it has the same number of rows and columns, a row matrix because it has a single row, and a column matrix because it has a single column.

Question 8

If matrix A is of order m×n then the matrix of order n×m is called
A)Transpose of A
B)Inverse of A
C)Main diagonal of A
D)Echelon form of A

Accepted Answer

The transpose of a matrix is obtained by swapping its rows with its columns, resulting in a new matrix where the original matrix's order of m×n becomes n×m.

Question 9

Which of the following is true?
A)A.B = A'.B
B)(c) A.B = A.B'
C)(AB)' = B'.A'
D)(d) (A=B)' = A'. B'

Accepted Answer

The answer of Which of the following is true?
A)A.B =...

Question 10

Two matrices A and B are multiplied to get AB if,
A)both are rectangular
B)both have the same order
C)number of columns of A is equal to number of rows of B
D)number of rows of A is equal to number of columns of B

Accepted Answer

For matrix multiplication to be defined, the number of columns in the first matrix (A) must be equal to the number of rows in the second matrix (B). This allows for the dot product to be calculated for each element of the resulting matrix.

Question 11

A matrix having 'm' rows and 'n' columns with m?n is said to be a
A)Scalar Matrix
B)Identity Matrix
C)Square Matrix
D)Null Matrix

Accepted Answer

The answer of A matrix having 'm' rows and 'n'...

Question 12

Increase in the number of patients in the hospital due to stroke is
A)Secular trend
B)Irregular variation
C)Seasonal variation
D)Cyclical variation

Accepted Answer

The answer of Increase in the number of patients in...

Question 13

Damages due to floods, droughts and strikes fires are associated with the components of which of the time series
A)Secular trend
B)Cyclical variation
C)Seasonal variation
D)Irregular variation

Accepted Answer

Damages due to floods, droughts, and strikes fires are associated with the irregular variation component of a time series. This is because these events are unpredictable and do not follow a regular pattern or cycle.

Question 14

Two matrices A and B are multiplied to get AB if
A)Both are rectangular
B)Both have same order
C)Number of columns of A is equal to columns of B
D)Number of rows of A is equal to columns of B

Accepted Answer

The answer of Two matrices A and B are multiplied...

Question 15

Cramer's rule fails for
A)Determinants > 0
B)Determinants < 0
C)Determinants = 0
D)None of the above

Accepted Answer

Cramer's rule fails for systems of linear equations when the determinant of the coefficient matrix is equal to 0, as it implies the matrix is singular and does not have a unique solution.

Question 16

Cramer's Rule is not suitable for which type of problems?
A)Small systems with 4 unknowns
B)Systems with 2 unknowns
C)Large systems
D)None of the above

Accepted Answer

Cramer's Rule, while applicable to systems of any size theoretically, becomes impractical for large systems due to the computational complexity involved in calculating determinants of large matrices.

Question 17

The element residing in the 3rd column and 4th row is represented by:
A)(a)a12
B)(b) a43
C)(c) a34
D)NOTA

Accepted Answer

In matrix notation, the element is denoted by a subscript where the first number represents the row and the second number represents the column. Therefore, the element in the 3rd column and 4th row is represented by $a_{43}$.

Question 18

A matrix that has elements in the horizontal line only is known as:
A)Square Matrix
B)Determinant
C)Row Matrix
D)Column Matrix

Accepted Answer

A matrix that has elements in the horizontal line only is known as a Row Matrix. It consists of a single row and multiple columns.

Question 19

For the equations 2x-y=5;3x+2y=-3; The values of x and y are
A)-1 and 3
B)1 and -3
C)2 and 3
D)NOTA

Accepted Answer

The answer of For the equations 2x-y=5;3x+2y=-3; The values of...

Quiz 10: Matrix Operations and Time Series Analysis

If the price of commodity' X' is 4 in the year 2003 and 5 in the year 2004. Then, the price index for the year 2004, used 2003 as base year is:

Changes that have taken place as a result of such forces that could not be predicted like floods, earthquakes, famines, etc is known as:

In semi averages method, the given data is divided into:

The additive model of the time series is:

Two matrices A and B are multiplied to get AB if

The determinant of identity matrix is :

The matrix [6] is

If matrix A is of order m×n then the matrix of order n×m is called

Which of the following is true?

Two matrices A and B are multiplied to get AB if,

A matrix having 'm' rows and 'n' columns with m?n is said to be a

Increase in the number of patients in the hospital due to stroke is

Damages due to floods, droughts and strikes fires are associated with the components of which of the time series

Two matrices A and B are multiplied to get AB if

Cramer's rule fails for

Cramer's Rule is not suitable for which type of problems?

The element residing in the 3rd column and 4th row is represented by:

A matrix that has elements in the horizontal line only is known as:

For the equations 2x-y=5;3x+2y=-3; The values of x and y are