question_answer

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

A) \[5<\alpha \le 7\]

B) \[\frac{1}{2}\le \alpha \le 1\]

C) \[\frac{5}{3}\le \alpha \le \frac{7}{2}\]

D) None of these

Correct Answer: C

Solution :

[c] Point \[(0,\alpha )\] lies on the y-axis. In such equations, it is easier to see the location of point if lines are drawn on the axis. From the diagram, it is clear that \[\frac{5}{3}\le \alpha \le \frac{7}{2}\]