CUET · MATHS · PYQ PAPER 2023

The solution of LPP :
Min. \(z=100 x+400 y\)
s.t. \(x+2 y \geq 8\)
\(2 x+5 y \leq 20\)
\(x \geq 0, y \geq 0\)
occurs at :

A \(x=0, y=4\)
B \(x=4, y=8\)
C \(x=8, y=0\)
D \(x=10, y=0\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(x=8, y=0\)

Step-by-step Solution

Detailed explanation

\(z(0,4) = 100(0) + 400(4) = 1600\) \(z(8,0) = 100(8) + 400(0) = 800\) \(z(10,0) = 100(10) + 400(0) = 1000\) The minimum value of \(z\) is 800 at \(x=8, y=0\).

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.

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List-I (Enzymes)	List-II (Products)
(A) RNA polymerase I	(I) hnRNA
(B) RNA polymerase III	(II) hydrolysis of lactose
(C) RNA polymerase II	(III) rRNA
(D) \( eta\)-galactosidase	(IV) tRNA, 5SrRNA, snRNA

The solution of LPP :Min. \(z=100 x+400 y\)s.t. \(x+2 y \geq 8\)\(2 x+5 y \leq 20\)\(x \geq 0, y \geq 0\)occurs at :

Step-by-step Solution

The solution of LPP :
Min. \(z=100 x+400 y\)
s.t. \(x+2 y \geq 8\)
\(2 x+5 y \leq 20\)
\(x \geq 0, y \geq 0\)
occurs at :