If S is an even integer, then which of the following are true?

A. S + 1 will be odd

B. 2S - 1 will be odd

C. S² + 1 will be odd

D. S² - 1 will be odd

E. S² + 2 will be odd

Choose the correct answer from the options given below:

Question

Question

This question was previously asked in

UGC NET Official Paper-I (Held On: 03 Mar, 2023 Shift 1)

Answer 1

Let's analyze each option:

A. S + 1 will be odd:

If S is an even integer, adding 1 to it will result in an odd number. This is

because an even number plus 1 will always give an odd number.

B. 2S - 1 will be odd:

Multiplying an even number by 2 will result in an even number. Subtracting 1

from an even number will give an odd number. Therefore, 2S - 1 will be odd.

C. S² + 1 will be odd:

Squaring an even number will always result in an even number. Adding 1 to an even number will give an odd number. Therefore, S^2 + 1 will be odd.

D. S² - 1 will be odd:

Similar to option C, squaring an even number will give an even number.

Subtracting 1 from an even number will result in an odd number. Therefore,

S² - 1 will be odd.

E. S² + 2 will be odd:

Again, squaring an even number will give an even number. Adding 2 to an

even number will also result in an even number. Therefore, S^2 + 2 will be

even.

Based on the analysis above, the correct answer is A, B, C, and D Only.