Question

If $\left[{\log }_{10}x\right]=1$, then $x$ lies in which of the following interval

(Here $[.]$ is the greatest integer less than or equal to the number.)

• A. $[10,100)$
• B. $(10,20)$
• C. $(100,\infty )$
• D. none of these

Answer 1

The correct option is A $[10,100)$

$\left[{\log }_{10}x\right]=1$

$\Rightarrow 1\le {\log }_{10}x<2$

$\Rightarrow 10\le x<100$

Therefore, $x\in [10,100)$
Ans: A