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Assuming you don't want a 0 as the leading digit, there are 9000 combinations, or 9*10*10*10. If you don't mind 0 as a leading digit, then 10000 combinations, or 10*10*10*10.
There are 12 such numbers.
There is 90 four digit palindromes.
There are 24.
There are no four-digit perfect squares that are palindromes.
3*3*2*1 = 18