If  x + y  = 11 then, $$(-1)^x + (-1)^y$$​ is equal to (where x, y are whole numbers).

Correct option is C

Given:

x + y = 11, and x, y are whole numbers.

Concept Used:

The expression (-1)$$^x$$​+ (-1)$$^y$$​ depends on the parity (whether the number is even or odd) of x and y.

Solution:

Consider the possible cases for x and y:

If x is even, then (-1)$$^x$$​ = 1.

If x is odd, then (-1)$$^x$$​ = -1.

Similarly for y.

Since x + y = 11 (an odd number), one of the numbers must be odd and the other must be even.

Therefore, the expression (-1)$$^x$$​ + (-1)$$^y$$​ becomes:

(-1)$$^x$$​ + (-1)$$^y$$​= 1 + (-1) = 0

The value of (-1)$$^x$$​ + (-1)$$^y$$​ is 0.