CUET · MATHS · PYQ PAPER 2025

In a linear programming problem (LPP), the maximum value of the objective function \(Z=2 x+5 y\) subjected to the constraints :
\(\begin{array}{l}2 x+3 y \leq 6 \\2 x+y \leq 4 \\x, y \geq 0\end{array}\)
is

A 12
B 10
C 8
D 4

Verified Solution

Answer & Solution

Correct Answer

(B) 10

Step-by-step Solution

Detailed explanation

Vertices: \((0,0)\) \(2x+y=4 \Rightarrow (2,0)\) \(2x+3y=6 \Rightarrow (0,2)\) \(2x+3y=6, 2x+y=4 \Rightarrow y=1, x=3/2 \Rightarrow (3/2,1)\) Evaluate \(Z=2x+5y\): \(Z(0,0)=2(0)+5(0)=0\) \(Z(2,0)=2(2)+5(0)=4\) \(Z(0,2)=2(0)+5(2)=10\) \(Z(3/2,1)=2(3/2)+5(1)=3+5=8\) Maximum value…

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	List-II
(A) No red ball is	(I) \(\frac{12}{35}\)
(B) Only 1 red ball is	(II) \(\frac{1}{35}\)
(C) Exactly 2 red balls is	(III) \(\frac{4}{35}\)
(D) No white ball is	(IV) \(\frac{18}{35}\)

In a linear programming problem (LPP), the maximum value of the objective function \(Z=2 x+5 y\) subjected to the constraints :\(\begin{array}{l}2 x+3 y \leq 6 \\2 x+y \leq 4 \\x, y \geq 0\end{array}\)is

Step-by-step Solution

In a linear programming problem (LPP), the maximum value of the objective function \(Z=2 x+5 y\) subjected to the constraints :
\(\begin{array}{l}2 x+3 y \leq 6 \\2 x+y \leq 4 \\x, y \geq 0\end{array}\)
is