CUET · MATHS · PYQ PAPER 2023

The linear constraints, for which the shaded area in the figure is the feasible region of an LPP, are:

A \(x + y \geq 50,2 x + y \leq 80, x , y \geq 0\)
B \(x+y \leq 50,2 x+y \geq 80, x, y \geq 0\)
C \(x+y \leq 50,2 x+y \leq 80, x, y \geq 0\)
D \(x+y \geq 50,2 x+y \geq 80, x, y \geq 0\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(x+y \leq 50,2 x+y \leq 80, x, y \geq 0\)

Step-by-step Solution

Detailed explanation

\(x+y \leq 50\) \(2x+y \leq 80\) \(x \geq 0, y \geq 0\)

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

Let X be a random variable. Let E(X) and Var(X) denote the mean and the variance of X respectively.
Match List - I with List - II

List - I	List - II
(A) If \(\operatorname{Var}( X )=\alpha\), then \(\operatorname{Var}(2 X +3)\) is	(I) \(11 \alpha\)
(B) If \(E ( X )=\alpha\), then \(E (2 X )\) is	(II) \(6 \alpha\)
(C) If \(\operatorname{Var}( X )=\alpha\), then \(\operatorname{Var}(3 X -\alpha)+\operatorname{Var}(\sqrt{2} X +\beta)\) is	(III) \(4 \alpha\)
(D) If \(E(X) = 3\) \(\frac{5\alpha}{12}, \text{ then E(12X + } \alpha)\) is	(IV) \(2 \alpha\)

Choose the correct answer from the options given below:

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