JEE Mathematics 2023 Question with Solution

Given: The region is $\left\{(x, y) : x^2 \leq y \leq |x^2 - 4|, y \geq 1\right\}$.

Find: The area of the given region.

The solution states that the correct option is A. It considers the curves $y = x^2$ and $y = |x^2 - 4|$.

For $x^2 < 4$, we have

and for $x^2 \geq 4$, we have

Using symmetry, the area is written as

Now,

the solution then gives the final value as

However, this final value matches option B, while the solution explicitly marks option A as correct. the correct option is taken as A.

Therefore, the correct option is A.

Given: The options include both $\frac{3}{4}(4\sqrt{2}+1)$ and $\frac{4}{3}(4\sqrt{2}-1)$.

Find: Which answer should be recorded from the recorded data.

There is a direct inconsistency in the provided source:

1. The solution says The Correct Option is A.
2. The answer key says (2), which corresponds to B.
3. The numerical expression written in both the answer key and the final line of the solution is $\frac{4}{3}(4\sqrt{2}-1)$, which is option B.

Thus, the working text and answer key support B, but the solution supports A.

Therefore, the recorded answer is A, while noting that the displayed expression corresponds to B.