If two variables a and b are related by c = ab then G.M. of c is equal to

Option a: G.M. of a x G.M. of b. Solution: Step 1: Recall the fundamental property of Geometric Mean. For n observations: text{GM}(c) = <=ft(prod{i=1}^{n} ciright)^{1/n} Step 2: Apply the relation ci = ai bi. text{GM}(c) = <=ft(prod{i=1}^{n} ai biright)^{1/n} = <=ft(prod{i=1}^{n} airight)^{1/n} x <=ft(prod{i=1}^{n} biright)^{1/n} = text{GM}(a) x text{GM}(b) Step 3: Conclusion. If c = ab, then text{GM}(c) = text{GM}(a) x text{GM}(b), which is Option A. Note: The given correct option is C, but mathematically the correct relationship is GM(c) = GM(a) × GM(b), which is Option A. Hence, Option A is the correct answer.

Central Tendency & DispersionPYQ Nov. 20Question 2999 of 473

All Questions

If two variables $\displaystyle a$ and $\displaystyle b$ are related by $\displaystyle c = ab$ then G.M. of $\displaystyle c$ is equal to

Options

AG.M. of

\displaystyle a \times

G.M. of

\displaystyle b

BG.M. of

\displaystyle a +

G.M. of

\displaystyle b

CG.M. of

\displaystyle a -

G.M. of

\displaystyle b

DG.M. of

\displaystyle a /

G.M. of

\displaystyle b

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Correct Answer

✅ Option a — G.M. of $\displaystyle a \times$ G.M. of $\displaystyle b$

All Options:

AG.M. of $\displaystyle a \times$ G.M. of $\displaystyle b$
BG.M. of $\displaystyle a +$ G.M. of $\displaystyle b$
CG.M. of $\displaystyle a -$ G.M. of $\displaystyle b$
DG.M. of $\displaystyle a /$ G.M. of $\displaystyle b$

Detailed Solution & Explanation

**Step 1: Recall the fundamental property of Geometric Mean.** For

\displaystyle n

observations:

\text{GM}(c) = \left(\prod_{i=1}^{n} c_i\right)^{1/n}

**Step 2: Apply the relation

\displaystyle c_i = a_i \cdot b_i

.**

\text{GM}(c) = \left(\prod_{i=1}^{n} a_i b_i\right)^{1/n} = \left(\prod_{i=1}^{n} a_i\right)^{1/n} \times \left(\prod_{i=1}^{n} b_i\right)^{1/n}

= \text{GM}(a) \times \text{GM}(b)

**Step 3: Conclusion.** If

\displaystyle c = ab

, then

\displaystyle \text{GM}(c) = \text{GM}(a) \times \text{GM}(b)

, which is **Option A**. Note: The given correct option is C, but mathematically the correct relationship is GM

\displaystyle (c)

= GM

\displaystyle (a)

× GM

\displaystyle (b)

, which is **Option A**. Hence, **Option A** is the correct answer.

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If two variables a\displaystyle aa and b\displaystyle bb are related by c=ab\displaystyle c = abc=ab then G.M. of c\displaystyle cc is equal to

Options

Correct Answer

All Options:

Detailed Solution & Explanation

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If two variables $\displaystyle a$ and $\displaystyle b$ are related by $\displaystyle c = ab$ then G.M. of $\displaystyle c$ is equal to