JEE Main 2026 — 28 January, Morning Shift — Question 20

Let first three terms of G.P. are $\frac{\mathrm{A}}{\mathrm{r}}, \mathrm{A}, \mathrm{Ar}$

$\frac{\mathrm{A}}{\mathrm{r}} \cdot \mathrm{A} \cdot \mathrm{Ar}=27$

$\mathrm{A}=3$ $3\left(\frac{1}{\mathrm{r}}+1+\mathrm{r}\right)=3+3\left(\mathrm{r}+\frac{1}{\mathrm{r}}\right)$

We know, $\mathrm{r}+\frac{1}{\mathrm{r}} \geq 2$ or

$\mathrm{r}+\frac{1}{\mathrm{r}} \leq-2$

$\mathrm{S} \in \mathrm{R}-(-3,9)$

$\mathrm{a}^{2}+\mathrm{b}^{2}=9+81=90$