Question

The set of values of $a$ for which $a^2-a-6<0$ and $\underset{x\to \infty }{lim}{a}^x$ does not exist is/are

• A. $(-2,3)$
• B. $(-2,-1)$
• C. $(1,3)$
• D. $(0,1)$

Answer 1

Answer: (B), (C)

$(1,3)$

Given : $a^2-a-6<0$ and $\underset{x\to \infty }{lim}{a}^x\left(\text{does not exist}\right)$
$\Rightarrow (a+2)(a-3)<0$ and $|a|>1$
$\Rightarrow -2<a<3$ and $a<-1\text{or}a>1$
$\therefore a\in (-2,-1)\cup (1,3)$