Question is given below.

Explanation

To solve this problem, we need to determine the number of half-lives that have passed for each element within the given time frame. For element X, with a half-life of 25 minutes, after 150 minutes, we can calculate the number of half-lives as follows: Number of half-lives = 150 min / 25 min = 6 half-lives Similarly, for element Y, with a half-life of 75 minutes, after 150 minutes, we can calculate the number of half-lives as follows: Number of half-lives = 150 min / 75 min = 2 half-lives Since each half-life represents a halving of the number of nuclei, we can determine the relative ratios of the remaining nuclei for each element: For element X: (1/2) ^ 6 = 1/64 For element Y: (1/2) ^ 2 = 1/4 Therefore, the fraction of the number of nuclei of X remains unchanged to the number of nuclei of Y remains unchanged is: (1/64) / (1/4) = 1/64 * 4/1 = 1/16 This can be simplified to: 1:16 So, the correct answer is option (a) 1:16.