JEE 2023 Mathematics PYQ — Let the point lie inside the region . If the set of all values of… | Mathem Solvex | Mathem Solvex
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JEE 2023 — Mathematics PYQ
JEE | Mathematics | 2023
Let the point (p,p+1) lie inside the region E={(x,y):3−x≤y≤9−x2,0≤x≤3}. If the set of all values of p is the interval (a,b), then b2+b−a2 is equal to _______
Choose the correct answer:
A.
1
B.
2
C.
3
(Correct Answer)
D.
None
Correct Answer:
3
Explanation
3 - x < y \leq \sqrt{9 - x^2}; 0 \leq x \leq 3 L(A) > 0 \Rightarrow p + p + 1 - 3 > 0 \Rightarrow p > 1 S(A) < 0 \Rightarrow p + 1 - \sqrt{9 - p^2} < 0 \Rightarrow p^2 + 2p + 1 < 9 - p^2 \Rightarrow 2p^2 + 2p - 8 < 0 \Rightarrow p^2 + p - 4 < 0 ⇒p∈(2−1−17,2−1+17) =p∈(1,2−1+17) b2+b−a2=4−1=3
Explanation
3 - x < y \leq \sqrt{9 - x^2}; 0 \leq x \leq 3 L(A) > 0 \Rightarrow p + p + 1 - 3 > 0 \Rightarrow p > 1 S(A) < 0 \Rightarrow p + 1 - \sqrt{9 - p^2} < 0 \Rightarrow p^2 + 2p + 1 < 9 - p^2 \Rightarrow 2p^2 + 2p - 8 < 0 \Rightarrow p^2 + p - 4 < 0 ⇒p∈(2−1−17,2−1+17) =p∈(1,2−1+17) b2+b−a2=4−1=3
