AfterBoards Logo
Skip to main contentSkip to solution

CUET Mathematics 2025 PYQs15 May Shift 2. Free, no login required.

Algebra

past year questions, CUET Mathematics 2025 15 May Shift 2

Linear Programming

past year questions, Algebra, CUET Mathematics 2025 15 May Shift 2

Medium

applied

If the corner points of the bounded feasible region for a linear programming problem (LPP) are (0, 2), (3, 0), (6, 0), (6, 8) and (0,5), then which of the following are correct for the objective function Z=4x+6yZ = 4x + 6y?

(A) The minimum value of the objective function occurs at (0, 2) and (3, 0) only.

(B) The minimum value of the objective function occurs at the mid-point of the line segment joining the points (0, 2) and (3, 0) only.

(C) The minimum value of the objective function occurs at every point of the line segment joining the points (0, 2) and (3, 0).

(D) The difference between the maximum value and minimum value of the objective function is 60.

Choose the correct answer from the options given below:

Solution

✅ Correct Option: 4

The objective function is Z=4x+6yZ = 4x + 6y.

Evaluating ZZ at each corner point:

Z(0,2)=4(0)+6(2)=12Z(0, 2) = 4(0) + 6(2) = 12

Z(3,0)=4(3)+6(0)=12Z(3, 0) = 4(3) + 6(0) = 12

Z(6,0)=4(6)+6(0)=24Z(6, 0) = 4(6) + 6(0) = 24

Z(6,8)=4(6)+6(8)=72Z(6, 8) = 4(6) + 6(8) = 72

Z(0,5)=4(0)+6(5)=30Z(0, 5) = 4(0) + 6(5) = 30

Minimum Z=12Z = 12 (at both (0,2)(0, 2) and (3,0)(3, 0))

Maximum Z=72Z = 72 (at (6,8)(6, 8))

Statement (A): Since both corner points give the same minimum value, the minimum occurs at every point on the line segment joining them — not just the endpoints. This is incorrect.

Statement (B): The midpoint does give Z=12Z = 12, but so does every other point on that segment — not the midpoint alone. This is incorrect.

Statement (C): Any point on the segment joining (0,2)(0, 2) and (3,0)(3, 0) can be written as (3t,  2−2t)(3t,\; 2 - 2t) where t∈[0,1]t \in [0, 1].

Z=4(3t)+6(2−2t)Z = 4(3t) + 6(2 - 2t)

=12t+12−12t= 12t + 12 - 12t

=12= 12 for every tt

Since Z=12Z = 12 (the minimum) for every point on this segment, Statement (C) is correct.

Statement (D):

Zmax⁡−Zmin⁡=72−12=60Z_{\max} - Z_{\min} = 72 - 12 = 60

Statement (D) is correct.

Therefore, the correct answer is (C) and (D) only.

Related questions:

2025: 13 May Shift 1

If a person rides his motorbike xx km at 30 km per hour, he has to spend ₹ 3 per kilometer on petrol. If he rides yy km at a faster speed of 40 km per hour, the petrol cost increases to ₹ 4 per kilometer. If he has ₹ 100 to spend on petrol and wishes to find the maximum distance he can travel within one hour, then linear programming problem (LPP) formulation is:

2026: 14 May Shift 2

The feasible region for a linear programming problem is shown in the figure.

Let Z=3x−4yZ = 3x - 4y be the objective function, then minimum of Z occurs at the point

2025: 16 May Shift 1

Consider the following L.P.P

Max. z = 5x + 2y; subject to -2x - 3y ≤ -6, x - 2y ≤ 2, 3x + 2y ≤ 12, -3x + 2y ≤ 3 and x, y ≥ 0 then

2026: 12 May Shift 2

The feasible region for an L.P.P is always a/an

2023: 23 May Shift 3

In a LPP, let R be the feasible region.

A. If R is unbounded then a max./min. value of objective function may not exist.

B. If R is bounded then a max. and min. value of objective function will always exist.

C. If a solution exists, it must occur at a corner point.

D. If R is bounded then max. will exist but min. may or may not exist for an objective function.

Choose the correct answer from the options given below:

2026: 22 May Shift 2

Consider the LPP: Minimize z=−50x+20yz=-50x+20y subject to 2x−y≥−5,3x+y≥3,2x−3y≤12,x≥0,y≥02x-y\ge -5, 3x+y\ge 3, 2x-3y\le 12, x\ge 0, y\ge 0. Then which of the following statements are TRUE?

(A) Corner points of the feasible region of the LPP are (0,5), (0,3), (1,0), (6,0).

(B) The optimum value of the objective function is -300

(C) Optimum value does not exist

(D) The optimum value of the objective function is 100

Choose the correct answer from the options given below:

Keyboard Shortcuts

  • Left arrow: Previous question
  • Right arrow: Next question
  • S key: Jump to solution
  • Q key: Jump to question

CUET Mathematics Past Year Questions (Topic-Wise)