CUET · MATHS · PYQ PAPER 2025
Consider the LPP : Maximize \(z=5 x+3 y\) subject to \(3 x+5 y \leq 15,5 x+2 y \leq 10, x, y \geq 0\).
The optimal feasible solution occurs at
- A (2,0) only
- B neither \((2,0)\) nor \(\left(\frac{20}{19}, \frac{45}{19}\right)\)
- C (0,3) only
- D \(\left(\frac{20}{19}, \frac{45}{19}\right)\) only
Answer & Solution
Correct Answer
(D) \(\left(\frac{20}{19}, \frac{45}{19}\right)\) only
Step-by-step Solution
Detailed explanation
\(3x+5y=15 \text{ and } 5x+2y=10 \Rightarrow x=\frac{20}{19}, y=\frac{45}{19}\) Feasible corner points: \((0,0), (2,0), (0,3), \left(\frac{20}{19}, \frac{45}{19}\right)\) \(z(0,0) = 5(0)+3(0)=0\) \(z(2,0) = 5(2)+3(0)=10\) \(z(0,3) = 5(0)+3(3)=9\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from MATHS
- In the context of linear programming, Match List I with List II
List - I List - II (A) Z = 250x +75y I. non-trivial constraints (B) \(5 x+y \leq 100, x-y \leq 4\) II. feasible solution (C) \(x, y \geq 0\) III. objective function (D) points within and on the boundary of shaded region IV. Trivial constraints CUET 2023 Easy - If \(x=2 a t, y=a t^2\), where ' a ' is a constant, then \(\frac{d^2 y}{d x^2}\) at \(x=2\) is :CUET 2023 Hard
- If the integral \(I=\int\left\{\log _e\left(\log _e x\right)^2+\frac{\alpha}{\log _e x}\right\} d x=x \log _e\left(\log _e x\right)^2+C\), where \(C\) is constant of integration. Then the value of \(\alpha\) is :CUET 2025 Medium
- Consider the linear programming problem (LPP) :
Maximize \(Z=6 x+3 y\)
subject to the conditions
\(4 x+y \geq 80\)
\(x+5 y \geq 115\)
\(3 x+2 y \leq 150\)
\(x \geq 0, y \geq 0\)
In reference to the above LPP, which of the following are correct?
(A) The feasible region is bounded.
(B) The corner points of the feasible region are (15,20), (40,15) and (0,75).
(C) The maximum value of the objective function is 285.
(D) The LPP does not have optimal solution.
Choose the correct answer from the options given below :CUET 2025 Hard - Consider the following hypothesis \(H_0: \mu=315\) and \(H_a: \mu \neq 315\).
A sample of 60 provided a sample mean of 324.6 . The standard deviation ( \(\sigma\) ) is 14 and level of significance \(\alpha=0.05\). Then the confidence interval is :
[Given : \(Z_{\alpha / 2} \frac{14}{\sqrt{60}}=3.54\)]CUET 2025 Easy - Consider the following L.L.P.
Minimize \(z=30 x-30 y+1800\);
subject to \(x+y \leq 30, x \leq 15, y \leq 20, x+y \geq 15\) and \(x, y \geq 0\).
Then it attains its optimal value at the pointCUET 2025 Hard
More PYQs from CUET
- Match List I with List - II. -
List – l List – II (A) Aspergillus niger (l) Blood cholesterol lowering agent (B) Trichoderma polysporum (II) Citric Acid (C) Saccharomyces cerevisiae (III) Immunosuppressive agent (D) Monascus purpureus (IV) Ethanol
Choose the correct answer from the options given below:CUET 2023 Easy - A charged particle enters a magnetic field with velocity v at an angle \( \theta \) with the field and experiences a magnetic force. The kinetic energy of the particleCUET 2025 Medium
- The photoelectric current is directly proportional to the number of photo electrons emitted per second. This implies thatCUET 2025 Medium
- Consider the LPP: Maximize \(Z=x+y\) subject to the constraints \(x+2 y \leq 70,2 x+y \leq 95, x, y \geq 0\). The optimal feasible solution is:CUET 2025 Easy
- A right angled triangle has its longest side \(B C\) as the diameter of a circle of radius \(r\) and a vertex \(A\) lying on the circle. Maximum area that the triangle \(A B C\) can enclose is:CUET 2023 Hard
- The area bounded by the curve \(y=x^2|x|, x\)-axis and the ordinates \(x=-1\) and \(x=0\) is given by :CUET 2023 Hard