Match List-I with List-II

[a, b as given in the Euclidean algorithm, quotient (q), Remainder (r)]

Remainder (r)

$a = bq + r$

List-I	List-II
(A) a = 112, b = 7	(I) r = 1
(B) a = 118, b = 9	(II) r = 3
(C) a = 119, b = 6	(III) r = 5
(D) a = 115, b = 8	(IV) r = 0

Choose the correct answer from the options given below:

The problem requires finding the remainder $r$ when dividing $a$ by $b$ using the formula $a = bq + r$, where $q$ is the quotient and $r < b$.

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For $a = 112, b = 7$:

$112 \div 7 = 16$ with no remainder

$112 = 7 \times 16 + 0$

Therefore $r = 0$, which matches with (IV)

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For $a = 118, b = 9$:

$9 \times 13 = 117$

$118 - 117 = 1$

$118 = 9 \times 13 + 1$

Therefore $r = 1$, which matches with (I)

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For $a = 119, b = 6$:

$6 \times 19 = 114$

$119 - 114 = 5$

$119 = 6 \times 19 + 5$

Therefore $r = 5$, which matches with (III)

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For $a = 115, b = 8$:

$8 \times 14 = 112$

$115 - 112 = 3$

$115 = 8 \times 14 + 3$

Therefore $r = 3$, which matches with (II)

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Final matching:

List-I	Remainder	List-II
(A) $a = 112, b = 7$	$r = 0$	(IV)
(B) $a = 118, b = 9$	$r = 1$	(I)
(C) $a = 119, b = 6$	$r = 5$	(III)
(D) $a = 115, b = 8$	$r = 3$	(II)

The correct answer is: (A) - (IV), (B) - (I), (C) - (III), (D) - (II)