JEE Main 2022 · 24 Jun · Shift 2 · Mathematics Q4

MathematicsSingle correct+4 / -1Question 4 of 90

Let $x,y>0$ . If $x^3y^2=2^{15}$ , then the least value of $3x+2y$ is

Answer and worked solution

Official answer: D

AM-GM on five terms. $3x+2y=x+x+x+y+y\ge5\left(x^3y^2\right)^{1/5}=5\left(2^{15}\right)^{1/5}=5\cdot8=40$ .

Equality when $x=y$ , i.e. $x^5=2^{15}$ , $x=y=8$ , which is allowed.

(D)

Topics:AM-GM-HM inequalities

JEE Main 2022 · 24 Jun · Shift 2, Mathematics question 4