Let a curve $y = y(x)$ pass through the point $(3,\ 3)$ and the area of the region under this curve, above the $x$-axis and between the abscissae 3 and $x(>3)$ be $\left(\frac{y}{x}\right)^3$. If this curve also passes through the point $\left(\alpha,\ 6\sqrt{10}\right)$ in the first quadrant, then $\alpha$ is equal to __________.

JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 26 July 2022, Shift 1, Maths Q27

Question 27 of 90 in this shift, Maths question 27 of 30, Section B.

Let a curve

y = y(x)

pass through the point

(3,\ 3)

and the area of the region under this curve, above the

x

-axis and between the abscissae 3 and

x(>3)

\left(\frac{y}{x}\right)^3

. If this curve also passes through the point

\left(\alpha,\ 6\sqrt{10}\right)

in the first quadrant, then

\alpha

is equal to __________.

Official answer

NTA final key.

Chapter: Differential Equations
Topic: Area Under Curves
Idea tested: Curves from Area Properties

Same idea in other shifts

Asked 3× in all

8 Apr 2024, Shift 1 · Q12Let $f(x)$ be a positive function such that the area bounded by $y=f(x)$ , $y=0$ from $x=0$ to $x=a>0$ is $e^{-a}+4a^2+a-1$ . Then the…HardSingle correct
27 Jul 2022, Shift 2 · Q10Consider a curve $y = y(x)$ in the first quadrant as shown in the figure. Let the area $A_1$ is twice the area $A_2$ . Then the normal to…HardDiagram basedHas a figure

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.