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Pair of Lines

The condition...

Question

The condition to be imposed on $β$ so that $(0, β)$ lies on or inside the triangle having sides y + 3x + 2 = 0, 3y – 2x – 5 = 0 and 4y + x – 14 = 0 is

A

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B

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C

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D

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Solution

The correct option is C
Clearly point $0, β$ lies on y-axis.
Drawing the graph of the three straight lines, we see that
$q \equiv (0, \frac{7}{2}) a n d P \equiv (0, \frac{5}{3})$

Therefore, the point $0, β$ lies on or inside $δ$ ABC, when
$\frac{5}{3} \leq β \leq \frac{7}{2}$

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