CUET · MATHS · PYQ PAPER 2025

Linear inequalities corresponding to the shaded feasible region \(O A B C O\) in the given figure are

A \(4 x+3 y \leq 12,3 x+4 y \leq 12, x \geq 0, y \geq 0\)
B \(4 x+3 y \geq 12,3 x+4 y \geq 12, x \geq 0, y \geq 0\)
C \(4 x+3 y \leq 12,3 x+4 y \geq 12, x, \geq 0, y \geq 0\)
D \(4 x+3 y \geq 12,3 x+4 y \leq 12, x \geq 0, y \geq 0\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(4 x+3 y \leq 12,3 x+4 y \leq 12, x \geq 0, y \geq 0\)

Step-by-step Solution

Detailed explanation

Equation of line passing through \((3,0)\) and \((0,4)\): \(\frac{x}{3} + \frac{y}{4} = 1 \implies 4x + 3y = 12\). Testing origin \((0,0)\): \(4(0) + 3(0) = 0 \leq 12\), so the inequality is \(4x + 3y \leq 12\). Equation of line passing through \((4,0)\) and \((0,3)\):…

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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