Question

Assertion (A): The mean proportion between $$a^2b$$ and $$\frac{1}{b}$$ is $$\frac{a}{b}$$.

Reason (R): The mean proportion between x and y is given by $$\sqrt{xy}$$.

Options

• Both A and R are true, and R is the correct explanation of A.

• Both A and R are true, but R is not the correct explanation of A.

• A is true, but R is false.

• A is false, but R is true.

Answer 1

A is false, but R is true.

Explanation:

Step 1 – Assertion: A is false. Using the stated rule for mean proportion, the mean proportion is $$\sqrt{a^2b\times\frac{1}{b}}=\sqrt{a^2},$$ which is not generally $$\frac{a}{b}$$.

Step 2 – Reason: R is true. The mean proportion between two quantities $$x$$ and $$y$$ is given by $$\sqrt{xy}$$.