CUET · MATHS · PYQ PAPER 2025

If z = 5x + 8y is the objective function of a LPP and (0,0), (3, 1), (2, 4), (0, 3), (5,0) are corner points of the bounded feasible region, then the maximum value of the objective function is

A 24
B 42
C 100
D 23

Verified Solution

Answer & Solution

Correct Answer

(B) 42

Step-by-step Solution

Detailed explanation

\( z(0,0) = 5(0) + 8(0) = 0 \) \( z(3,1) = 5(3) + 8(1) = 15 + 8 = 23 \) \( z(2,4) = 5(2) + 8(4) = 10 + 32 = 42 \) \( z(0,3) = 5(0) + 8(3) = 0 + 24 = 24 \) \( z(5,0) = 5(5) + 8(0) = 25 + 0 = 25 \) Maximum value \( = 42 \)

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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In the expression of Gauss's Law.
\( \oint \vec{E} \cdot d\vec{s} = \frac{q}{\epsilon_0} \)
(A) The electric field on LHS is only due to the charges inside the Gaussian surface.
(B) The electric field on LHS is due to charges inside and outside the Gaussian surface.
(C) The electric charge on RHS represents all the charges inside and outside the Gaussian surface.
(D) The electric charges on RHS represent only the charges outside the Gaussian surface.

CUET 2023 Hard

Match List-I with List-II
Let \(\theta\) be the angle between the vector \(\vec{a}\) and \(\vec{b}\).

List-I	List-II
(A) \(\vec{a} \cdot \vec{b}\)	(I) \(\frac{1}{10} \log \left\|\frac{5+x}{5-x}\right\|+C\)
(B) \(\vec{a} \times \vec{b}\)	(II) \(\frac{\vec{a} \cdot \vec{b}}{\|\vec{b}\|^2} \vec{b}\)
(C) Projection vector of \(\vec{a}\) on \(\vec{b}(\neq 0)\)	(III) \(\|\vec{a}\|\|\vec{b}\| \sin \theta \hat{n}\) where \(\hat{n}\) is a unit vector perpendicular to both \(\vec{a}\) and \(\vec{b}\)
(D) \(\vec{a}\) and \(\vec{b}\) are orthogonal vectors	(IV) \(\|\vec{a}\|\|\vec{b}\| \cos \theta\)

Choose the correct answer from the options given below:

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X	0	1	2	3	4	5	6	7	8
P(X)	a	3a	5a	7a	9a	11a	13a	15a	17a