Q101 / 160 · AP EAMCET 2023 (19 May Shift 1) · Mathematics
Let $[t]$ represents the greatest integer not exceeding $t$, Then the number of discontinuous points of $\left[10^x\right]$ in $(0,10)$ is
- A$10^{10}-1$
- B$10^{10}$
- Correct answerC$10^{10}-2$
- D$\mathrm{e}^{10}$
Solution
(c) Given $0 < x < 10$
$$
\Rightarrow 1 < 10^x < 10^{10}
$$
Let $0 \leq x \leq 1$ then $\left[10^x\right]$ will have to points of discontinuity But when $0 < x < 1$ the $[10 x]$ will have only $\left(10^1-2\right)=8$ points of discontinuity because we are leaving point $0 \& 1$. Similarly, when $0 < \mathrm{x} < 10$ then $[10 x]$ will have $\left(10^{10}-2\right)$ points of discontinuity.
Hence, the correct answer is option: 'C'.