CUET Mathematics 2026 26th May Shift 2 PYQs

About linear programming problem (LPP), which of the following statements are correct?

(A) In a LPP, the linear inequalities or restrictions on the variables are called linear constraints.

(B) If the feasible region for an LPP is unbounded, then the maximum or minimum value of the objective function $Z = ax + by$ never exists.

(C) The feasible region for an LPP is always convex.

(D) The common region determined by all the linear constraints of an LPP is called the feasible region.

Choose the correct answer from the options given below:

Consider the linear programming problem (LPP):

Maximize Z = 6x + 3y subject to the conditions,

4x + y ≥ 80, x + 5y ≥ 115, 3x + 2y ≤ 150, x, y ≥ 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:

For a LPP, maximize $z=2x+3y$, subjected to constraints:

$x\ge2, x\le7, y\le x, x+y\le10, x\ge0, y\ge0$

Which of the following statements are TRUE ?

(A) Vertices of feasible region are (2, 0), (7, 0), (7, 3), (5, 5) and (2, 2).

(B) Maximum $z=25$ at point (5, 5).

(C) Maximum $z=25$ at infinite numbers of points.

(D) The feasible region is unbounded.

Choose the correct answer from the options given below: