Hint: In this particular question to find the quick answer assume any to different or same odd number which represents a and b then check options one by one, so use these concepts to reach the solution of the question.
Complete step-by-step answer:
a and b are the odd numbers.
Odd numbers are those which cannot be divisible by 2.
For example: 1, 3, 5 …
Even numbers are those which are divisible by 2.
For example: 2, 4, 6 …
Now consider two different or same odd numbers which represent the given odd number a and b.
Let, a = 3 and b = 5.
Now check options one by one.
a + b = 3 + 5 = 8.
As we know that 8 is divisible by 2 so 8 is an even number.
So a + b is even.
a + b + 1 = 3 + 5 + 1 = 9.
As we know that 9 is not divisible by 2, so 9 is an odd number.
So, a + b + 1 is odd.
ab = 3(5) = 15.
As we know that 15 is not divisible by 2, so 15 is an odd number.
So, ab is odd.
ab + 2 = 3(5) + 2 = 15 + 2 = 17
As we know that 17 is not divisible by 2, so 17 is an odd number.
So, a b + 2 is odd.
Hence only option (a) represents the even if a and b are odd numbers.
Note: Whenever we face such types of questions the key concept we have to remember is that odd numbers are not divisible by 2 whereas an even number is always divisible by 2, this is the basis of the above problem, so use this concept as above used and check all of the given options we will get the required answer.