A. 1
B. 2
C. 3
D. 4
E. 5

Answer: C

Explanation:
Rule:
1. For a perfect square, the Power of the primes must be divisible by 2.
2. Similarly, for a perfect cube, the Power of the primes must be divisible by 3.
3. So, for a number to be both perfect square and perfect cube, it must be divisible by 6.
4. O and 1 are both perfect cubes and perfect squares.
So here,
Numbers between 0 and 1000(not inclusive),
So, here let’s start with 2 because we already know that 1 is both a perfect square and perfect cube.
Let’s raise the initial few natural numbers to the power of 6(Divisible by both 2 and 3), then we shall check whether the given range is under 1000.
2^6 = 64 is both a perfect square and a perfect cube.
3^6 = 729 is both a perfect square and a perfect cube.
4^6 = 2^12 = 4096 is both a perfect square and perfect cube but above 1000.
So, there are only three values, 1,2, and 3.

So, the answer is C.

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