CUET · MATHS · PYQ PAPER 2025

Which one of the following set of constraints represents the shaded region given below?

A \(x+y \leq 800,2 x+y \leq 1000, x \leq 400, y \leq 700, x \geq 0, y \geq 0\)
B \(x+y \geq 800,2 x+y \leq 1000, x \leq 400, y \geq 700, x \geq 0, y \geq 0\)
C \(x+y \leq 800,2 x+y \geq 1000, x \geq 400, y \leq 700, x, y \geq 0\)
D \(x+y \geq 800,2 x+y \geq 1000, x \leq 400, y \leq 700, x \geq 0, y \geq 0\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(x+y \geq 800,2 x+y \leq 1000, x \leq 400, y \geq 700, x \geq 0, y \geq 0\)

Step-by-step Solution

Detailed explanation

Vertical boundary: \(x \leq 400\). Horizontal boundary: \(y \leq 700\). Line through \((0,800)\) and \((800,0)\): \(x+y \leq 800\). Line through \((0,1000)\) and \((500,0)\): \(2x+y \leq 1000\). Non-negativity: \(x \geq 0, y \geq 0\). Combined constraints:…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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