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Question #41785

Difficulty: 8/10 | 🟢 Free

The Question

Let $S$ be the feasible region in the $xy$ -plane defined by the system of inequalities: $2x + y \le 10$ $Lx - y \ge 2$ $x \ge 0, y \ge 0$ where $L = \lim_{t \to 1} \frac{t^2 - 1}{\sqrt{t^2 - 2t + 1}}$ . If the limit $L$ exists and the feasible region $S$ is non-empty, let $M$ be the maximum value of $x+y$ on $S$ . If $S$ is empty, let $M = 0$ . If the system is ill-defined because the limit $L$ does not exist, let $M = -1$ . Find the value of $M$ .

Options

A.
-1
B.
7
C.
0
D.
5

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Specialist

Targeted practice for niche, high-difficulty concepts that frequently appear in JEE Advanced exams.

Concepts Behind This Question

Inconsistency Detection|Feasible Region Constancy|Limit Existence at Discontinuity

Why This Question Is Tricky

Common Mistakes

This question tests the student's vigilance in checking the existence of limits at points of discontinuity before applying them as coefficients in algebraic systems.

A common trap is to reflexively cancel $(t-1)$ from the numerator and denominator, incorrectly assuming $\sqrt{(t-1)^2} = t-1$ , which leads to $L=2$ and a false maximum value of $M=7$ .

By linking the existence of the feasible region to the LHL = RHL condition, it bridges Calculus and Linear Programming, penalizing mechanical algebraic simplification.

Quick Facts About This Question

Question Information

Subject	Mathematics
Chapter	Linear Programming - Class 12
Concept	Inconsistency Detection
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free