Algebra

Linear Programming

Easy

core

If a, b, c > 0 and $ax+by>c$ , then its graph represents:

the half plane that contains the origin.

the half plane that neither contains the origin nor the points on the line $ax+by=c$ .

the entire x-y plane.

the entire x-y plane excluding the line $ax+by=c$ .

✅ Correct Option: 2

Testing the origin gives $0 > c$ , which is false since $c>0$ , so the origin is not in the region.

The inequality is strict, so points on the boundary line $ax+by=c$ are also excluded.

Hence the graph is the open half plane containing neither the origin nor the line.

2025: 3 June Shift 2

The point which provides the optimal solution of the linear programming problem

maximize $z = 21x + 35y$

$3x + 2y \leq 30$

$4x + 5y \leq 60$

$x \geq 0, y \geq 0$

has the coordinates

2026: 19 May Shift 2

Refer to the LPP given by $Z = 2.5x + y$ , subject to constraints

$3x + y \le 12; 3y + x \le 12; x, y \ge 0$ :

In the given figure, If $Z_A$ = value of Z at A, $Z_C$ = value of Z at C and Max.(Z) = maximum value of Z, then which of the following relations between $Z_A$ , $Z_C$ and Max.(Z) are correct?

A. $2Z_A = 5$ Max.(Z)

B. $5Z_A = 2Z_C$

C. $Z_A = 6 + Z_C$

D. $6+Z_A = Z_C$

Choose the correct answer from the options given below:

2025: 27 May Shift 1

Match List-I with List-II

List-I	List-II
(A) Corner point of a feasible region	(I) The line segment joining any two arbitrary points of the region always lies entirely within the region
(B) Bounded feasible region	(II) can not be enclosed within a circle
(C) Unbounded feasible region	(III) can be enclosed within a circle
(D) Convex region	(IV) Is a point of intersection of two boundary lines in the feasible region

Choose the correct answer from the options given below:

2025: 22 May Shift 2

For LPP: Maximize $z = 2x + 3y$ subject to the constraints

$x + y \geq 2$ , $x + 2y \geq 3$ , $x \geq 0$ , $y \geq 0$ ,

which of the following graph represents the feasible region of the above LPP as shaded portion?

2026: 30 May Shift 2

The corner points of the bounded feasible region of a linear programming problem are A(15,0), B(40,0), C(4, 18), D(6, 12) and objective function is $z = 20x+10y$ , then which of the following are TRUE?

(A) Value of z at point A(15, 0) = 300.

(B) Value of z at point B(40, 0) = 800.

(D) Maximum value of z = 800.

Choose the correct answer from the options given below:

2026: 22 May Shift 1

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).

(D) The feasible region is unbounded.

Choose the correct answer from the options given below:

If a, b, c > 0 and ax+by>cax+by>cax+by>c, then its graph represents:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If a, b, c > 0 and $ax+by>c$ , then its graph represents: