CUET · MATHS · PYQ PAPER 2023

For the LPP, Min \(z=6 x+10 y\) subject to \(x \geq 6, y \geq 3,2 x+y \geq 10, x \geq 0, y \geq 0\), redundant constraint is:

A \(x 0, y \geq 0\)
B \(2 x+y \geq 10\)
C \(x \geq 6\)
D \(y \geq 3\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(2 x+y \geq 10\)

Step-by-step Solution

Detailed explanation

\(x \geq 6 \implies 2x \geq 12\) \(y \geq 3\) \(2x+y \geq 12+3 \implies 2x+y \geq 15\) Since \(15 \geq 10\), the constraint \(2x+y \geq 10\) is redundant.

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) If A and B are mutually exclusive events, then \(P ( A \cup B )=\)	(I) \(\frac{ P ( A \cap B )}{ P ( B )}, P ( B ) \neq 0\)
(B) If A and B are independent events, then \(P ( A \cap B )=\)	(II) \(\frac{ P ( A \cap B )}{ P ( A )}, P ( A ) \neq 0\)
(C) If A and B are two events of a sample space of an experiment, then \(P ( A / B )=\)	(III) \(P ( A ) \cdot P ( B )\)
(D) If A and B are two events of a sample space of an experiment, then \(P ( B / A )=\)	(IV) \(P ( A )+ P ( B )\)

Choose the correct answer from the options given below :

CUET 2023 Easy

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