JEE 2023 — Mathematics PYQ

1. AM-GM Inequality ka setup:

Hume $a^5{b}^3{c}^2{d}^1$ ko maximize karna hai. Iske liye hum $a,b,c,d$ ko unki powers ke mutabiq divide karenge:

• $a$ ko 5 barabar bhagon mein: $\frac{a}{5}$

• $b$ ko 3 barabar bhagon mein: $\frac{b}{3}$

• $c$ ko 2 barabar bhagon mein: $\frac{c}{2}$

• $d$ ko 1 bhag mein: $\frac{d}{1}$

Kul milakar hamare paas $5+3+2+1=11$ terms hain.

2. AM-GM Apply karna:

3. Value substitute karna:

Chunki $a+b+c+d=11$ hai:

4. Maximum value calculate karna:

5. $\beta$ ki value nikalna:

Sawal ke mutabiq, Max Value $=3750\beta$.

Correct Option: (3) 90