Let points left(frac{11}{2}, αright) lie on or inside triangle with sides x + y =11, x +2 y =16 and

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9.Straight Line

hard

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 :

A$22$

B$44$

C$33$

D$55$

(JEE MAIN-2025)

Solution

Point of intersection of $x=\frac{11}{2}$ with $L_1 \& L_3$ gives, $\alpha_{\min }=\frac{11}{2}$
and $\alpha_{\max }=6$
$\therefore \alpha_{\min } \cdot \alpha_{\max }=\frac{11}{2} \times 6=33$

Standard 11

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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 :

Solution

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