Question:
<p>The true set of real values of <span class="math-tex">\(\lambda\)</span> for which the point P with co-ordinate <span class="math-tex">\(\left(\lambda, \lambda^{2}\right)\)</span> does not lie inside the triangle formed by the lines, x - y = 0; x + y - 2 = 0 and x + 3 = 0 is :</p>
<p style="display:inline"><span class="math-tex">\((-\infty,-2] \cup[0, \infty]\)</span></p>
<p style="display:inline"><span class="math-tex">\((-\infty,-2]\)</span></p>
<p style="display:inline"><span class="math-tex">\([0, \infty]\)</span></p>
<p style="display:inline">[-2, 0]</p>
Step-by-Step Solution
Key Concept: A point lies inside a triangle if it lies on the same side of each bounding line as the opposite vertex, so the 'not inside' region is the complement of the intersection of these three linear inequalities.
<p><span class="math-tex">\((-\infty,-2] \cup[0, \infty]\)</span></p>
Correct Answer: A