JEE PYQ: Area Under Curves Question 22
Question 22 - 2019 (08 Apr Shift 2)
Let $S(\alpha) = {(x, y) : y^2 \leq x,\ 0 \leq x \leq \alpha}$ and $A(\alpha)$ is area of the region $S(\alpha)$. If for a $\lambda$, $0 < \lambda < 4$, $A(\lambda) : A(4) = 2 : 5$, then $\lambda$ equals:
(1) $2\left(\frac{4}{25}\right)^{1/3}$
(2) $2\left(\frac{2}{5}\right)^{1/3}$
(3) $4\left(\frac{2}{5}\right)^{1/3}$
(4) $4\left(\frac{4}{25}\right)^{1/3}$
Show Answer
Answer: (4) $4\left(\frac{4}{25}\right)^{1/3}$
Solution
$A(\lambda) = \frac{4}{3}\lambda^{3/2}$. $\frac{\lambda^{3/2}}{8} = \frac{2}{5} \Rightarrow \lambda = \left(\frac{16}{5}\right)^{2/3} = 4\left(\frac{4}{25}\right)^{1/3}$.
BETA
