Match List-I with List-II, where List-II gives the remainder when the number 473702 is divided by the number in List-I.
| List-I | List-II | ||
| (A) | 9 | (I) | 2 |
| (B) | 11 | (II) | 5 |
| (C) | 4 | (III) | 6 |
| (D) | 8 | (IV) | 9 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A)-(II), (B)-(IV), (C)-(I), (D)-(III)
Since \(10 \equiv 1 \pmod{9}\), \(10 \equiv -1 \pmod{11}\), \(100 \equiv 0 \pmod{4}\) and \(1000 \equiv 0 \pmod{8}\), each remainder can be found from the digits of the number.
(A) 9
This matches (II) 5. A number leaves the same remainder on division by 9 as the sum of its digits.
\(4 + 7 + 3 + 7 + 0 + 2 = 23\)
\(23 = 9 \times 2 + 5\)
(B) 11
This matches (IV) 9. The digits are added and subtracted in turn, starting from the units digit.
\(2 - 0 + 7 - 3 + 7 - 4 = 9\)
(C) 4
This matches (I) 2. Only the number formed by the last two digits matters.
\(02 = 4 \times 0 + 2\)
(D) 8
This matches (III) 6. Only the number formed by the last three digits matters.
\(702 = 8 \times 87 + 6\)