Let the points (11 2 , ) lie on or inside the triangle with sides… - Vidyadip

MCQ

Let the points $\left(\frac{11}{2}, \alpha\right)$ lie on or inside the triangle with sides $\mathrm{x}+\mathrm{y}=11, \mathrm{x}+2 \mathrm{y}=16$ and $2 \mathrm{x}+3 \mathrm{y}=29$. Then the product of the smallest and the largest values of $\alpha$ is equal to :

A
22
B
44
✓
33
D
55

✓

Answer

Correct option: C.

33

(C)
Sol.

Point of intersection of $x=\frac{11}{2}$ with $L_{1} \& L_{3}$ gives, $\alpha_{\min }=\frac{11}{2}$
and $\alpha_{\text {max }}=6$
$\therefore \alpha_{\min } \cdot \alpha_{\max }=\frac{11}{2} \times 6=33$

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