Let p, q, r and s be distinct positive integers. Let p, q be odd and r, s be even. Consider the following statements:
1. (p - r)^2 (qs) is even.
2. (q - s) $q^2$ s is even.
3. (q + r)^2 (p + s) is odd.

Which of the statements given above are correct?

Correct Option: (d) 1, 2 and 3

We are given that p and q are odd integers, and r and s are even integers. Let us evaluate each statement: Statement 1: (p - r)^2 (qs). Since p is odd and r is even, (p - r) is odd, so (p - r)^2 is odd. Since q is odd and s is even, the product (qs) is even. An odd number multiplied by an even number always results in an even number. Thus, (p - r)^2 (qs) is even. Statement 1 is correct. Statement 2: (q - s) q^2 s. Since q is odd and s is even, (q - s) is odd. q^2 is also odd. Since s is even, the product containing the even factor s is even. Thus, (q - s) q^2 s is even. Statement 2 is correct. Statement 3: (q + r)^2 (p + s). Since q is odd and r is even, (q + r) is odd, so (q + r)^2 is odd. Since p is odd and s is even, (p + s) is odd. The product of two odd numbers is always odd. Thus, (q + r)^2 (p + s) is odd. Statement 3 is correct. Since all statements are correct, option (d) is the correct answer.