JEE 2023 Mathematics PYQ — A wire of length m is to be cut into two pieces. A piece of lengt… | Mathem Solvex | Mathem Solvex
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JEE 2023 — Mathematics PYQ
JEE | Mathematics | 2023
A wire of length 20 m is to be cut into two pieces. A piece of length l1 is bent to make a square of area A1 and the other piece of length l2 is made into a circle of area A2. If 2A1+3A2 is minimum then (πl1):l2 is equal to:
Choose the correct answer:
A.
1:6
(Correct Answer)
B.
6:1
C.
3:1
D.
4:1
Correct Answer:
1:6
Explanation
Solution:
Square ka side =4l1⟹A1=16l12.
Circle ki radius =2πl2⟹A2=4πl22.
Humein E=2(16l12)+3(4πl22) ko minimize karna hai, jahan l1+l2=20.
E=8l12+4π3(20−l1)2.
Differentiate karke zero ke equal rakhne par:
4l1−4π6(20−l1)=0⟹πl1=6l2
l2πl1=16
Sahi Option: (2)
Explanation
Solution:
Square ka side =4l1⟹A1=16l12.
Circle ki radius =2πl2⟹A2=4πl22.
Humein E=2(16l12)+3(4πl22) ko minimize karna hai, jahan l1+l2=20.
