Which of the following is true for an integer x?
  1. For any value of  x , x22 is always positive.
  2. If x is odd, (x+1)2 is even
  3. If x is even, (x1)2 is odd
  4. If x is even, (x+1)2 is even


The correct options are
B If x is odd, (x+1)2 is even
C If x is even, (x1)2 is odd
1. For x = -1, 0 and 1, the value of  x22 is negative, hence the given statement is false.
2.  If x is odd, then x+1 is even  which implies that (x+1)2 is even.
3. If x is even, then x1 is odd which implies that (x1)2 is odd.
4. If x is even, then x+1 is not even. Square of X+1 is not even. So, the given statement is false.

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