JEE Main 2022 · 30 Jun · Shift 1 · Mathematics Q8

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MathematicsSingle correct+4 / -1Question 8 of 90

If $xy^4$ attains maximum value at the point $(x,y)$ on the line passing through the points $(50+\alpha,0)$ and $(0,50+\alpha)$ , $\alpha>0$ , then $(x,y)$ also lies on the line :

y=4x

x=4y

y=4x+\alpha

x=4y-\alpha

Answer and worked solution

Official answer: A

Line $x+y=50+\alpha$ . $xy^4$ is largest when $x=\frac{50+\alpha}5$ , $y=\frac{4(50+\alpha)}5$ , so $y=4x$ .

(A)

Topics:Maxima and minima Equations of a line

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JEE Main 2022 · 30 Jun · Shift 1, Mathematics question 8