Indian Institute of Foreign Trade 2012 Solved Paper

The unit digit in the product of ${\left(8267\right)}^{153}\times {\left(341\right)}^{72}$ is the same as the unit digit in the product of ${\left(7\right)}^{153}\times {\left(1\right)}^{72}$
1 raised to anything is 1.
7 has a cyclicity of 4. Thus, $7^{153}=7^1=7$
Hence, option C is the correct answer.