Q.

The range of value of α such that (0,α) lies on or inside  the triangle formed by the lines y+3x+2=0,3y−2x−5=0,4y+x−14=0 is

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a

5<α≤7

b

12≤α≤1

c

53≤α≤72

d

None of these

answer is C.

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Detailed Solution

Point (0, α) lies on they-axis. In such questions, it is easier to see the location of point if lines are drawn on the axis. From the diagram, it is clear that 53≤α≤72
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The range of value of α such that (0,α) lies on or inside  the triangle formed by the lines y+3x+2=0,3y−2x−5=0,4y+x−14=0 is