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Mathematics

Assertion (A): Mean proportion between 23 and 152\dfrac{2}{3} \text{ and } \dfrac{15}{2} is 5.

Reason (R): Mean proportion between two numbers is the positive square root of their product.

  1. Assertion (A) is true, but Reason (R) is false.

  2. Assertion (A) is false, but Reason (R) is true.

  3. Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

  4. Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).

Ratio Proportion

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Answer

The mean proportion between two numbers a and b is defined as ab\sqrt{ab}

So, reason (R) is true.

When two numbers are 23 and 152\dfrac{2}{3} \text{ and } \dfrac{15}{2}

Mean proportion=23×152=306=5\text{Mean proportion} = \sqrt{\dfrac{2}{3} \times \dfrac{15}{2}}\\[1em] = \sqrt{\dfrac{30}{6}}\\[1em] = \sqrt{5}

So, assertion (A) is false.

Thus, Assertion (A) is false, but Reason (R) is true.

Hence, option 2 is the correct option.

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