Question:
If $\{p\}$ denotes the fractional part of the number
$\mathrm{p}$, then $\left\{\frac{3^{200}}{8}\right\}$, is equal to
Correct Option: 1
Solution:
$\left\{\frac{3^{200}}{8}\right\}=\left\{\frac{\left(3^{2}\right)^{100}}{8}\right\}$
$=\left\{\frac{(1+8)^{100}}{8}\right\}$
$=\left\{\frac{1+{ }^{100} C_{1} \cdot 8+{ }^{100} C_{2} \cdot 8^{2}+\ldots+{ }^{100} C_{100} 8^{100}}{8}\right\}$
$=\left\{\frac{1+8 m}{8}\right\}$
$=\frac{1}{8}$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.