MCQ
If $a, b, c$ are in A.P. and $x, y, z$ are in G.P., then the value of $x^{b-c} y^{c-a} z^{a-b}$ is:
- A0
- ✓1
- C$x y z$
- D$x^a y^b z^c$
✓
Answer
Correct option: B.
1
- 1
a, b and c are in A.P.
$\therefore2\text{b}=\text{a}+\text{c}\ \cdots(\text{i})$
And, x, y and z are in G.P.
$\therefore\text{y}^2=\text{zy}$
Now, $\text{x}^{\text{b}-\text{a}}\text{ y}^{\text{c}-\text{a}}\text{ z}^{\text{a}-\text{b}}$
$=\text{x}^{\text{b}+\text{a}-2\text{b}}\text{ y}^{2\text{b}-\text{a}-\text{a}}\text{ z}^{\text{a}-\text{b}}$ [From (i)]
$=\text{x}^{\text{a}-\text{b}}\text{ y}^{2(\text{b}-\text{a})}\text{ z}^{\text{a}-\text{b}}$
$=(\text{xz})^{\text{a}-\text{b}}(\text{xz})^{\text{b}-\text{a}}$ $[\text{From}(\text{ii}),\text{y}^2=\text{xz}]$
$=(\text{xz})^0$
$=1$
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