Linear programming class 12 cbse maths Previous year important questions

Linear Programming

(2025)
Q.1 The corner points of the feasible region of a Linear Programming Problem
are (0,2), (3,0), (6,0), (6,8) and (0,5). If Z=ax+by;(a, b>0) be the objective
function, and maximum value of Z is obtained at (0, 2) and (3,0), then the
relation between a and b is : (1 Mark) (CBSE 2025 - 65/4/1)
A. a = 3b
B. 3a = 2b
C. a = b
D. b = 6a
Q.2 Assertion (A) : In a Linear Programming Problem, if the feasible region is
empty, then the Linear Programming Problem has no solution.
Reason (R) : A feasible region is defined as the region that satisfies all the
constraints. (1 Mark) (CBSE 2025 - 65/4/1)
A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct
explanation of the Assertion (A).
B. Assertion (A) is true, but Reason (R) is false.
C. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the
correct explanation of the Assertion (A).
D. Assertion (A) is false, but Reason (R) is true.
Q.3 For a Linear Programming Problem (LPP), the given objective function
is Z=x+2y. The feasible region PQRS determined by the set of constraints is
shown as a shaded region in the graph. (1 Mark) (CBSE 2025 - 65/6/1)

,A. (Value of Z at P)> (Value of Z at Q)
B.



C.



D. (Value of Z at Q) < (Value of Z at R)
Q.4 In a Linear Programming Problem (LPP), the objective function Z=2x+5y is
to be maximised under the following constraints :
x+y≤4,3x+3y≥18, x, y≥0
Study the graph and select the correct option. (1 Mark) (CBSE 2025 - 65/6/1)

,The solution of the given LPP :
A. lies in the combined region of △AOB and unbounded shaded region.
B. lies in the shaded unbounded region.
C. does not exist.
D. lies in △AOB.
Q.5 A factory produces two products X and Y . The profit earned by selling X and
Y is represented by the objective function Z=5x+7y, where x and y are the
number of units of X and Y respectively sold. Which of the following statement
is correct? (1 Mark) (CBSE 2025 - 65/2/1)
A. The objective function measures the total production of products X and Y .
B. The objective function maximizes the difference of the profit earned from
products X and Y .
C. The objective function maximizes the combined profit earned from
selling X and Y.
D. The objective function ensures the company produces more of product X
than product Y
Q.6 Assertion (A) : Every point of the feasible region of a Linear Programming
Problem is an optimal solution.
Reason (R) : The optimal solution for a Linear Programming Problem exists
only at one or more corner point(s) of the feasible region.
(1 Mark) (CBSE 2025 - 65/2/1)
A. Both Assertion (A) and Reason (R) are true and the Reason (R) is the
correct explanation of the Assertion (A).
B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the
correct explanation of the Assertion (A).
C. Assertion (A) is true but Reason (R) is false.
D. Assertion (A) is false but Reason (R) is true.

, Q.7 For a Linear Programming Problem (LPP), the given objective function


is subject to constraints :




The correct feasible region is : (1 Mark) (CBSE 2025 - 65/2/1)
A. CED
B. Open unbounded region BCD
C. ABC
D. AOEC
Q.8 Assertion (A) : The shaded portion of the graph represents the feasible
region for the given Linear Programming Problem (LPP).
(1 Mark) (CBSE 2025 - 65/5/1)