A word is represented by only one set of numbers as given in any one of the alternatives. The sets of numbers given in the alternatives are resented by two classes of alphabets as shown in the given two matrices. The columns and rows of Matrix-I are numbered from 0 to 4 and that a Matrix-II are numbered from 5 to 9. A letter from these matrices can be represented first by its row and next by its column, for example, ‘D’ can be represented by 24, 41 etc., and ‘T’ can be represented by 96, 87 etc. Similarly, you have to identify the set for the word ‘ GASH’. Matrix-I 0 1 2 3 4 0 C G D K M 1 I B L H B 2 K B L B D 3 I A C D E 4 L D G A E Matrix-II 5 6 7 8 9 5 P Q U W R 6 P Z V P W 7 U X Q X V 8 V O T N R 9 P T U S Y
42, 43, 98, 13
Understanding Matrix-Based Word Coding
This question requires us to decode a word using information provided in two matrices. Each letter is represented by a pair of numbers. The first number indicates the row number, and the second number indicates the column number in which the letter is located within the matrices.
We are given two matrices:
| 0 | 1 | 2 | 3 | 4 | |
|---|---|---|---|---|---|
| 0 | C | G | D | K | M |
| 1 | I | B | L | H | B |
| 2 | K | B | L | B | D |
| 3 | I | A | C | D | E |
| 4 | L | D | G | A | E |
| 5 | 6 | 7 | 8 | 9 | |
|---|---|---|---|---|---|
| 5 | P | Q | U | W | R |
| 6 | P | Z | V | P | W |
| 7 | U | X | Q | X | V |
| 8 | V | O | T | N | R |
| 9 | P | T | U | S | Y |
The word we need to find the code for is 'GASH'. We will find possible codes for each letter individually and then check the given options.
Finding Codes for GASH
Let's break down the word 'GASH' letter by letter and find their codes from the matrices:
- G:
- In Matrix-I: Row 0, Col 1 → 01; Row 4, Col 2 → 42.
- Possible codes for 'G' are 01, 42.
- A:
- In Matrix-I: Row 3, Col 1 → 31; Row 4, Col 3 → 43.
- Possible codes for 'A' are 31, 43.
- S:
- In Matrix-I: 'S' is not present.
- In Matrix-II: Row 9, Col 8 → 98.
- Possible code for 'S' is 98.
- H:
- In Matrix-I: Row 1, Col 3 → 13; Row 2, Col 3 → 23.
- In Matrix-II: 'H' is not present.
- Possible codes for 'H' are 13, 23.
Evaluating the Options
Now, let's examine each option and decode the numbers provided to see which one represents 'GASH'.
- Option 1: 23, 75, 44, 88
- 23 → Row 2, Col 3 in Matrix-I → H
- 75 → Row 7, Col 5 in Matrix-II → U
- 44 → Row 4, Col 4 in Matrix-I → E
- 88 → Row 8, Col 8 in Matrix-II → N
- This decodes to H U E N. This is not GASH.
- Option 2: 42, 43, 98, 13
- 42 → Row 4, Col 2 in Matrix-I → G
- 43 → Row 4, Col 3 in Matrix-I → A
- 98 → Row 9, Col 8 in Matrix-II → S
- 13 → Row 1, Col 3 in Matrix-I → H
- This decodes to G A S H. This matches the word.
- Option 3: 14, 95, 13, 58
- 14 → Row 1, Col 4 in Matrix-I → B
- 95 → Row 9, Col 5 in Matrix-II → P
- 13 → Row 1, Col 3 in Matrix-I → H
- 58 → Row 5, Col 8 in Matrix-II → W
- This decodes to B P H W. This is not GASH.
- Option 4: 11, 78, 20, 87
- 11 → Row 1, Col 1 in Matrix-I → B
- 78 → Row 7, Col 8 in Matrix-II → X
- 20 → Row 2, Col 0 in Matrix-I → K
- 87 → Row 8, Col 7 in Matrix-II → T
- This decodes to B X K T. This is not GASH.
Based on the evaluation, only Option 2 provides the correct code sequence for the word GASH.
Revision Table: Key Concepts
| Concept | Description | Application in this problem |
|---|---|---|
| Matrix Coding | Assigning numerical codes to letters based on their position (row, column) in a grid or matrix. | Used to represent letters of GASH using matrix coordinates. |
| Decoding | Converting the numerical codes back into letters. | Used to check if the options represent the word GASH. |
| Row-Column Format | The standard way to represent coordinates in matrix coding, usually (Row, Column). | The problem explicitly states "first by its row and next by its column". |
Additional Information: Matrix Coding Variations
Matrix coding questions are common in logical reasoning sections of competitive exams. Here are a few variations you might encounter:
- Single Matrix: Sometimes, only one matrix is used, with rows/columns potentially numbered differently (e.g., 1-5).
- Different Coding Rules: The problem might specify (Column, Row) instead of (Row, Column). Always check the rule carefully.
- Multiple Codes for a Letter: As seen in this problem, a letter can appear multiple times in the matrices, giving it several possible valid codes.
- Missing Letters: Some letters of the alphabet might not appear in the matrices at all.
- Numbers and Symbols: Matrices might include numbers or symbols in addition to letters, requiring you to code/decode them as well.
To solve these questions effectively, always:
- Understand the matrix structure and numbering scheme (rows/columns, starting number).
- Note the coding rule (Row-Column or Column-Row).
- Systematically find all possible codes for each letter in the target word.
- Decode each option provided in the question and compare it with the target word.
Important Questions from Matrix
Find the missing number from the below options.
\(\begin{array}{*{20}{c}} 6&{24}&{96}\\ 7&{28}&{112}\\ {13}&{52}&? \end{array}\)
A word is represented by only set of numbers as given in any one of the alternatives. The sets of numbers given in the alternatives are represented by two classes of alphabets as shown in the given two matrices. The columns and rows of Matrix-I are are numbered from 0 to 4 and that of Matrix-II are numbered from 5 to 9. A letter from these matrices can be represented first by its row and next by its column, for example ‘F’ can be represented by 12, 43 etc and ‘Z’ can be represented by 87, 98 etc. Similarly, you have to identify the set for the word ‘SOCK’.
Matrix-I
0
1
2
3
4
0
A
E
E
G
H
1
I
A
F
M
D
2
E
M
A
E
H
3
I
A
C
H
B
4
D
K
H
F
E
Matrix-II
5
6
7
8
9
5
Z
P
P
Q
S
6
V
U
S
R
N
7
U
U
N
V
X
8
N
O
Z
V
T
9
R
W
W
Z
N
A word is represented by only one set of numbers as given in any one of the alternatives. The sets of numbers given in the alternatives are represented by two classes of alphabets as shown in the given two matrices. The columns and rows of Matri×-I are numbered from 0 to 4 and that of Matri×-II are numbered from 5 to 9. A letter from these matrices can be represented first by its row and ne×t by its column, for e×ample ‘C’ can be represented by 21, 34 etc and ‘T’ can be represented by 97, 89 etc. Similarly, you have to identify the set for the word ‘MAZE’.
Matrix- I
0
1
2
3
4
0
E
F
H
E
I
1
E
G
E
M
M
2
K
C
H
G
L
3
L
J
G
G
C
4
J
A
M
J
J
Matrix- II
5
6
7
8
9
5
N
W
P
V
S
6
R
W
Q
Y
N
7
P
Z
P
U
U
8
N
Q
U
R
T
9
R
V
T
Q
O
A word is represented by only one set of numbers as given in any one of the alternatives. The sets of numbers given in the alternatives are resented by two classes of alphabets as shown in the given two matrices. The columns and rows of Matrix-I are numbered from 0 to 4 and that a Matrix-II are numbered from 5 to 9. A letter from these matrices can be represented first by its row and next by its column, for example, ‘K’ can be represented by 23, 41, etc., and ‘P’ can be represented by 59, 67, etc. Similarly, you have to identify the set for the word “NAME”.
Matrix-I
0
1
2
3
4
0
H
H
C
E
A
1
M
E
A
B
I
2
M
L
G
K
E
3
D
H
M
L
E
4
C
K
A
B
E
Matrix-II
5
6
7
8
9
5
O
S
Z
O
P
6
N
W
P
X
W
7
N
S
R
Q
Q
8
O
P
N
X
V
9
V
Z
S
S
T
A word is represented by only set of numbers as given in any one of the alternatives. The sets of numbers given in the alternatives are represented by two classes of alphabets as shown in the given two matrices. The columns and rows of Matrix-I are are numbered from 0 to 4 and that of Matrix-II are numbered from 5 to 9. A letter from these matrices can be represented first by its row and next by its column, for example ‘A’ can be represented by 23, 41 etc and ‘U’ can be represented by 86, 97 etc. Similarly, you have to identify the set for the word ‘GONE’.
Matrix-I
0
1
2
3
4
0
G
G
K
A
G
1
D
K
E
E
L
2
K
B
E
A
J
3
L
M
G
J
K
4
K
A
G
L
B
Matrix-II
5
6
7
8
9
5
N
Q
W
S
O
6
O
Q
V
R
R
7
W
O
N
T
Y
8
T
U
Y
R
V
9
N
X
U
S
Q
