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  4. The number obtained after dividing the number formed by the last three digits of 17256 by 100 is

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Q. The number obtained after dividing the number formed by the last three digits of $17^{256}$ by $100$ is

NTA AbhyasNTA Abhyas 2020Binomial Theorem

Solution:

Last three digits of $17^{256}$
$=\left(289\right)^{128}=\left(- 1 + 290\right)^{128}$
$=^{128}C_{0}\left(- 1\right)^{128}-^{128}C_{1}\cdot 290+^{128}C_{2}\cdot \left(290\right)^{2}+.......$
$=1-128\times 290+64\times 127\times 29^{2}\times 100+.......$
$=1-......120+.....800+.......$
$=681$
Hence, $\frac{681}{100}=6.81$