CUET · MATHS · PYQ PAPER 2025

The corner points of the feasible region with the constraints \(x+y \leq 30, x+y \geq 15, y \leq 20, x \leq 15\), and \(x, y \geq 0\) are

A (0,0), (0,15), (0,20), (15,0), (10,20)
B (0,15), (20,0), (15,0), (10,20)
C (15,0), (15, 15), (10, 20), (0,20), (0,15)
D (0,0), (20,0), (0,15), (15,15)

Verified Solution

Answer & Solution

Correct Answer

(C) (15,0), (15, 15), (10, 20), (0,20), (0,15)

Step-by-step Solution

Detailed explanation

Identify boundary lines: \(L_1: x+y=15\) \(L_2: x+y=30\) \(L_3: y=20\) \(L_4: x=15\) \(L_5: x=0\) \(L_6: y=0\) Find intersection points satisfying all constraints: \(L_5 \cap L_1 \Rightarrow (0,15)\) \(L_6 \cap L_1 \Rightarrow (15,0)\)…

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.

Same subject

Match List I with List II

List - I	List - II
(A) \(\int x^2 e^{x^3} d x\)	(I) \(\frac{1}{2 a} \log \left\|\frac{a+x}{a-x}\right\|+C\)
(B) \(\int e^x\left(\tan ^{-1} x+\frac{1}{1+x^2}\right) d x\)	(II) \(\frac{1}{a} \tan ^{-1}\left(\frac{x}{a}\right)+C\)
(C) \(\int \frac{d x}{a^2-x^2}\)	(III) \(\frac{1}{3} e^{x^3}+C\)
(D) \(\int \frac{d x}{x^2+a^2}\)	(IV) \(e^x \tan ^{-1} x+C\)

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