Introduction:
In this question, we are asked to find the smallest 4-digit perfect square among the given options. A perfect square is a number that can be expressed as the square of an integer.

Approach:
To determine the smallest 4-digit perfect square, we need to find the smallest perfect square that is greater than or equal to 1000 and less than 10000. We can start by finding the square root of 1000 and the square root of 10000 to get an idea of the range of perfect squares.

Finding the square root of 1000:
The square root of 1000 falls between 31 and 32 because 31^2 = 961 and 32^2 = 1024.

Finding the square root of 10000:
The square root of 10000 falls between 100 and 101 because 100^2 = 10000 and 101^2 = 10201.

Analysis of options:
Now let's analyze the given options to determine the smallest 4-digit perfect square.

a) 1024: The square root of 1024 is approximately 32. This number is a perfect square as 32^2 = 1024. Therefore, option 'A' is a possible answer.

b) 1025: The square root of 1025 is approximately 32.02. This number is not a perfect square.

c) 1000: The square root of 1000 is approximately 31.62. This number is not a perfect square.

d) 1016: The square root of 1016 is approximately 31.89. This number is not a perfect square.

Conclusion:
After analyzing the given options, we can conclude that option 'A' (1024) is the smallest 4-digit perfect square.