Match List-I with List-II
| List-I | List-II | ||
|---|---|---|---|
| (A) | The number of possible matrices of order 3×3 with each entry 1 or 0 | (I) | \(2^4\) |
| (B) | The number of possible matrices of order 2×3 with each entry 1 or 0 | (II) | \(2^9\) |
| (C) | The number of possible matrices of order 2×3 with each entry 0, 1, 2 | (III) | \(2^6\) |
| (D) | The number of possible matrices of order 2×2 with each entry 1 or 0 | (IV) | \(3^6\) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A)-(II), (B)-(III), (C)-(IV), (D)-(I)
Each entry is filled independently, so by the multiplication principle the number of matrices is (choices per entry) raised to the power (number of entries).
(A) The number of possible matrices of order 3×3 with each entry 1 or 0
This matches (II) \(2^9\)
9 entries, 2 choices each: \(2^9\)
(B) The number of possible matrices of order 2×3 with each entry 1 or 0
This matches (III) \(2^6\)
6 entries, 2 choices each: \(2^6\)
(C) The number of possible matrices of order 2×3 with each entry 0, 1, 2
This matches (IV) \(3^6\)
6 entries, 3 choices each: \(3^6\)
(D) The number of possible matrices of order 2×2 with each entry 1 or 0
This matches (I) \(2^4\)
4 entries, 2 choices each: \(2^4\)
So the matching is (A)-(II), (B)-(III), (C)-(IV), (D)-(I).