Which measures of central tendency get affected if the extreme observations on both the ends of a data arranged in descending order are removed?

Correct option is C

Mean: The mean is calculated by summing all observations and dividing by the number of observations. Removing extreme values will directly affect the sum and therefore the mean.  
Median: The median is the middle value when the data is arranged in order. If you remove values from both ends, the median might change, but it won't necessarily always change. If the dataset is large enough, removing a few extreme values may not shift the middle position.  
Mode: The mode is the most frequent value. Extreme values are, by definition, at the extremes of the distribution. They are unlikely to be the most frequent values. However, if the extreme values are repeated multiple times, then they could have an influence on the mode. So, the mode may change when extreme values are removed.