Match the LIST-I with LIST-II
| LIST-I | LIST-II | ||
| Number of the elements in a matrix | Number of matrices of possible order | ||
| A. | 17 | I. | 8 |
| B. | 8 | II. | 2 |
| C. | 12 | III. | 6 |
| D. | 24 | IV. | 4 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → A-II, B-IV, C-III, D-I
A matrix of order m × n has mn elements, so the number of possible orders is the number of ordered pairs (m, n) with mn equal to the given number, that is, the number of divisors of that number.
A. 17
This matches II. 2.
\( \displaystyle 1\times 17,\ 17\times 1 \)
B. 8
This matches IV. 4.
\( \displaystyle 1\times 8,\ 2\times 4,\ 4\times 2,\ 8\times 1 \)
C. 12
This matches III. 6.
\( \displaystyle 1\times 12,\ 2\times 6,\ 3\times 4,\ 4\times 3,\ 6\times 2,\ 12\times 1 \)
D. 24
This matches I. 8.
\( \displaystyle 1\times 24,\ 2\times 12,\ 3\times 8,\ 4\times 6,\ 6\times 4,\ 8\times 3,\ 12\times 2,\ 24\times 1 \)
So the matching is A-II, B-IV, C-III, D-I.
Tip: Count m × n and n × m separately: 2 × 4 and 4 × 2 are different orders.