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Mathematics

Assertion (A) : 0 and 1112\dfrac{11}{12} are two rational numbers and 11120\dfrac{11}{12} \ne 0 then 0 ÷ 1112=0\dfrac{11}{12} = 0, a rational number.

Reason (R) : If a rational number is divided by some non - zero rational number, the result is always a rational number.

  1. Both A and R are correct, and R is the correct explanation for A.

  2. Both A and R are correct, and R is not the correct explanation for A.

  3. A is true, but R is false.

  4. A is false, but R is true.

Rational Numbers

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Answer

When 0 is divided by any non-zero number, the result is 0.

⇒ 0 ÷ 1112=0\dfrac{11}{12} = 0

Since, 0 = 01\dfrac{0}{1} is in the form of pq\dfrac{p}{q}.

So, assertion (A) is true.

The division of a rational number ab\dfrac{a}{b} by another non-zero rational number cd\dfrac{c}{d} is:

ab÷cdab×dcadbc\Rightarrow \dfrac{a}{b} ÷ \dfrac{c}{d}\\[1em] \Rightarrow \dfrac{a}{b} \times \dfrac{d}{c}\\[1em] \Rightarrow \dfrac{ad}{bc}

Since, adbc\dfrac{ad}{bc} is in the form of pq\dfrac{p}{q}.

So, reason is true. But it does not explains about assertion.

Hence, option 2 is the correct option.

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