CUET · MATHS · PYQ PAPER 2023

For a maximizing LPP, the constraints are:

A \(x \geq 0 ; y \geq 0\)
B \(x \leq 20\)
C \(y \leq 10\)
D \(2 x+y \leq 30\)
Then which of the above constraints is redundant?

Verified Solution

Answer & Solution

Correct Answer

(B) \(x \leq 20\)

Step-by-step Solution

Detailed explanation

Vertices of the feasible region formed by \(x \geq 0, y \geq 0, y \leq 10, 2x+y \leq 30\): \(V_1 = (0,0)\) \(V_2: y=0, 2x+y=30 \Rightarrow (15,0)\) \(V_3: y=10, 2x+y=30 \Rightarrow (10,10)\) \(V_4: x=0, y=10 \Rightarrow (0,10)\) Check constraint \(x \leq 20\) against these…

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) \(f(x)=\|x\|+1\)	(I) Not differentiable at \(x=3\) only
(B) \(f(x)=\|x-3\|\)	(II) Not differentiable at \(x=-3\) only
(C) \(f(x)=\|x+3\|\)	(III) Not differentiable at \(x=3\), \(-3\) only
(D) \(f(x)=\left\|x^2-9\right\|\)	(IV) Not differentiable at \(x=0\) only

Choose the correct answer from the options given below:

CUET 2025 Hard

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LIST-I (Equation of curves)	LIST-II (Slope of tangent at \(x=2\))
(A) \(y=x^3-x\)	(I) 8
(B) \(y=(x-2)^2\)	(II) \(frac{2}{3}\)
(C) \(y=2 x^2+3\)	(III) \(11\)
(D) \(y=\sqrt{4 x+1}-7\)	(IV) \(0\)

List - I	List - II
(A) Diamagnetic solid	(I) \(CrO _2\)
(B) Ferromagnetic solid	(II) \(Fe _3 O _4\)
(C) Antiferromagnetic	(III) NaCl
(D) Ferrimagnetic solid	(IV) MnO