JEE 2023 — Mathematics PYQ
JEE | Mathematics | 2023If the set {Re(2−3z+5zˉz−zˉ+zzˉ):z∈C,Re(z)=3} is equal to the interval (α,β], then 24(β−α) is equal to:
Choose the correct answer:
- A.
36
- B.
27
- C.
30
(Correct Answer) - D.
42
30
Explanation
Solution:
Maana z=3+iy. Toh zˉ=3−iy.
Terms simplify karte hain: z−zˉ=2iy aur zzˉ=9+y2.
Denominator: 2−3(3+iy)+5(3−iy)=2−9−3iy+15−5iy=8−8iy.
Expression banega:
Real part f(y)=8(y2+1)y2−2y+9.
Iski range nikalne par humein (α,β] milega. Derivative f′(y)=0 karke ya substitution se range nikalne par β−α ki value milti hai.
Final calculation ke baad:
Sahi Uttar: (3) 30
Explanation
Solution:
Maana z=3+iy. Toh zˉ=3−iy.
Terms simplify karte hain: z−zˉ=2iy aur zzˉ=9+y2.
Denominator: 2−3(3+iy)+5(3−iy)=2−9−3iy+15−5iy=8−8iy.
Expression banega:
Real part f(y)=8(y2+1)y2−2y+9.
Iski range nikalne par humein (α,β] milega. Derivative f′(y)=0 karke ya substitution se range nikalne par β−α ki value milti hai.
Final calculation ke baad:
Sahi Uttar: (3) 30