JEE MAIN - Mathematics (2025 - 24th January Evening Shift - No. 15)
Let the points $\left(\frac{11}{2}, \alpha\right)$ lie on or inside the triangle with sides $x+y=11, x+2 y=16$ and $2 x+3 y=29$. Then the product of the smallest and the largest values of $\alpha$ is equal to :
22
33
55
44
Explanation
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Point of intersection of $x=\frac{11}{2}$ with $L_1 \& L_3$ gives,
$\alpha_{\min }=\frac{11}{2}$
and $\alpha_{\max }=6$
$$\therefore \alpha_{\min } \cdot \alpha_{\max }=\frac{11}{2} \times 6=33$$
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