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
42,65,77,13
Understanding Matrix Coding for Word Representation
This problem involves a coding scheme where letters are represented by pairs of numbers based on their position in two matrices. The first number in the pair indicates the row number, and the second number indicates the column number.
We are given two matrices:
| 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 |
| 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 |
We need to find the set of numbers representing the word 'GONE'. This means we need to find a code for 'G', then a code for 'O', then a code for 'N', and finally a code for 'E', in that specific order, from one of the given alternatives.
Finding Possible Codes for GONE Letters
Let's list some possible codes for each letter in the word 'GONE' from the matrices:
- G: Found in Matrix-I at (0,0), (0,1), (0,4), (3,2), (3,3), (4,2). Possible codes: 00, 01, 04, 32, 33, 42.
- O: Found in Matrix-II at (5,9), (6,5), (6,6), (7,6), (8,8). Possible codes: 59, 65, 66, 76, 88.
- N: Found in Matrix-II at (5,5), (7,7), (9,5), (9,6). Possible codes: 55, 77, 95, 96.
- E: Found in Matrix-I at (1,2), (1,3), (1,4), (2,2), (2,3), (2,4), (3,4). Possible codes: 12, 13, 14, 22, 23, 24, 34. (Note: 23 is also 'A' in Matrix-I, but 23 is a valid code for 'E' based on its position).
Checking the Alternatives for the Word GONE
Now, let's examine each given alternative and check if the sequence of codes represents 'GONE'.
Alternative 1: 40, 79, 42, 57
- 40: Matrix-I, Row 4, Column 0 is 'K'. This is not 'G'.
Alternative 1 is incorrect.
Alternative 2: 34, 69, 44, 75
- 34: Matrix-I, Row 3, Column 4 is 'E'. This is not 'G'.
Alternative 2 is incorrect.
Alternative 3: 33, 78, 24, 95
- 33: Matrix-I, Row 3, Column 3 is 'G'. (Matches G)
- 78: Matrix-II, Row 7, Column 8 is 'N'. This is not 'O'.
Alternative 3 is incorrect.
Alternative 4: 42, 65, 77, 13
- 42: Matrix-I, Row 4, Column 2 is 'G'. (Matches G)
- 65: Matrix-II, Row 6, Column 5 is 'O'. (Matches O)
- 77: Matrix-II, Row 7, Column 7 is 'N'. (Matches N)
- 13: Matrix-I, Row 1, Column 3 is 'E'. (Matches E)
All the codes in Alternative 4 match the letters in 'GONE' in the correct sequence.
Conclusion
Based on the analysis of the matrices and the given alternatives, the set of numbers 42, 65, 77, 13 correctly represents the word 'GONE'.
| Letter | Code | Matrix | Row | Column | Resulting Letter | Match? |
|---|---|---|---|---|---|---|
| G | 42 | Matrix-I | 4 | 2 | G | Yes |
| O | 65 | Matrix-II | 6 | 5 | O | Yes |
| N | 77 | Matrix-II | 7 | 7 | N | Yes |
| E | 13 | Matrix-I | 1 | 3 | E | Yes |
Revision Table: Matrix Coding Concepts
| Concept | Description |
|---|---|
| Matrix Coding | Representing letters or words using numbers based on their positions in a grid or matrix. |
| Code Format | Typically represented as (Row Number, Column Number). |
| Multiple Codes | A single letter might appear in multiple cells, allowing for multiple possible codes for that letter. |
| Word Coding | A word is coded by concatenating the codes of its individual letters in order. |
Additional Information on Coding and Decoding
Coding and decoding questions are common in logical reasoning sections of competitive exams. They test your ability to identify patterns and apply rules. Matrix-based coding is just one type among many, including letter-to-letter coding, letter-to-number coding, symbol coding, and more.
- Key Skill: Careful observation of the matrix/rule and systematic application to the target word or code.
- Process:
- Understand the coding rule (e.g., row-column format).
- Identify the matrices and their numbering scheme.
- For a given word, find possible codes for each letter from the matrices.
- For given options, verify if the sequence of codes matches a valid sequence for the target word.
- Practice: Solving various types of coding-decode problems helps improve speed and accuracy.
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 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
