Linear Programming: Class 12 Previous Year Questions

Linear Programming questions asked in CBSE board exams

Repeated questions first. Open the free app to see each question as it appeared in the paper, with its marking scheme.

1. Solve the following linear programming problem graphically : 3 Minimize Z = 13x – 15y Subject to constraints x + y  7, 2x – 3y + 6  0, x  0, y 
   Board 20263 marksshort answerRepeated: 2023,2025,2026
2. Solve the following linear programming problem graphically : 3 Maximize Z = 10500x + 9000y Subject to constraints x + y  50 2x + y  80 x, y 
   Board 20263 marksshort answerRepeated: 2023,2025,2026
3. The degree of an objective function of a linear programming problem is 1 (A) 0 (B) 1 (C) 2 (D) Any natural number Assertion – Reason Based Questions Direction : Questions number 19 and 20 are Assertion and Reason based questions carrying 1 mark each. Two state…
   Board 20261 markAssertion-ReasonRepeated: 2023,2025,2026
4. Solve the following linear programming problem graphically : Maximise Z = x + 2y Subject to the constraints : x-y·0 x - 2y ·-2 x·0,y·0 x sin x
   Board 20253 marksshort answerRepeated: 2023,2025,2026
5. Solve the following linear programming problem graphically : Minimise Z = x - 5y subject to the constraints : x-y·0 - x + 2y · 2 x·3, y· 4, y·
   Board 20253 marksshort answerRepeated: 2023,2025,2026
6. Solve graphically the following linear programming problem : Maximise z = 6x + 3y, subject to the constraints 4x + y 80, 3x + 2y 150, x + 5y 115, x 0, y 0.
   Board 20233 marksshort answerRepeated: 2023,2025,2026
7. The corner points of the feasible region in the graphical representation of a linear programming problem are (2, 72), (15, 20) and (40, 15). If z = 18x + 9y be the objective function, then : (a) z is maximum at (2, 72), minimum at (15, 20) (b) z is maximum at …
   Board 20231 markMCQRepeated: 2023,2025,2026
8. The feasible region of a linear programming problem with objective function Z = 5x + 7y is shown below : 1 The maximum value of Z – minimum value of Z is (A) 8 (B) 29 (C) 35 (D) 43
   Board 20261 markMCQRepeated: 2023,2026
9. The corner points of the feasible region in graphical representation of a L.P.P. are (2, 72), (15, 20) and (40, 15). If Z = 18x + 9y be the objective function, then (A) Z is maximum at (2, 72), minimum at (15, 20) (B) Z is maximum at (15, 20) minimum at (40, 1…
   Board 20251 markMCQRepeated: 2023,2025
10. JJJJ Page 9 18. The number of corner points of the feasible region determined by the constraints x y 0, 2y x + 2, x 0, y 0 is : (a) 2 (b) 3 (c) 4 (d) 5 Questions number 19 and 20 are Assertion and Reason based questions carrying 1 mark each. Two statements are…
    Board 20231 markAssertion-ReasonRepeated: 2023,2026
11. The feasible region of a linear programming problem is bounded. The corresponding objective function is Z = 6x - 7y. 1 The objective function attains __________ in the feasible region. (a) only minimum (b) only maximum (c) both maximum and minimum (d) either m…
    CBSE practice 2023-241 markMCQRepeated: 2025,2026
12. { } 16. In a linear programming problem, the linear function which has to be maximized or minimized is called 1 (A) a feasible function (B) an objective function (C) an optimal function (D) a constraint 10 { } 17.         …
    Board 20261 markMCQ
13. { } 16. The length of perpendicular drawn from point (2, 5, 7) on line x 1 = y 0 = z 0 is 1 (A) 2 (B) 5 (C) 74 (D) 78 10 { } 17.  LPP    Z = 5x + 7y ,        : 1 Z    – Z     : (A) 8 (B) 29 (C)…
    Board 20261 markMCQ
14. For the feasible region shown below, the non-trivial constraints of the linear programming problem are 1 (A) x + y  5, x + 3y  9 (B) x + y  5, x + 3y  9 (C) x + y  5, x + 3y  9 (D) x + y  5, 3x + y 
    Board 20261 markMCQ
15. 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. Page 13 of 24 (5 × …
    Board 20251 markAssertion-Reason
16. 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 ? (A) The object…
    Board 20251 markMCQ
17. Page 14 of 23 31. E Am¡a F Xmo ñdV§Ì KQ>ZmE± Eogr h¢ {OZHo$ {bE P( –E) = 0·6 VWm P(E 4 F) = 0·6 h¡ & P(F) Am¡a P( –E 4 –F ) kmV H$s{OE & 666 Page 15 of 23 27. (a) If 2 x – 1 + 2 y – 1 = a (x – y), prove that dx dy = 2 2 x – 1 y – 1 . OR (b) If y = (tan x)x, th…
    Board 20243 marksshort answer
18. Page 8 of 23 18. `{X Xmo g_mZ H$mo{Q> dmbo eyÝ`oVa dJ© Amì`yhm| A Am¡a B Ho$ {bE (A + B)2 = A2 + B2 h¡, Vmo : (A) AB = O (B) AB = – BA (C) BA = O (D) AB = BA àíZ g§»`m 19 Am¡a 20 A{^H$WZ Ed§ VH©$ AmYm[aV àíZ h¢ & Xmo H$WZ {XE JE h¢ {OZ_| EH$ H$mo A{^H$WZ (A) V…
    Board 20241 markMCQ
19. The objective function Z = ax + by of an LPP has maximum value 42 at (4, 6) and minimum value 19 at (3, 2). Which of the following is true ? (A) a=9, b=l (B) a=5, b=2 (C) (D) a= 3, b= 5 a= 5, b=
    Board 20231 markMCQ
20. The corner points of the feasible region of a linear programming problem 20 are (0, 4), (8, 0) and If Z = 30x + 24y is the objective function, then (maximum value of Z - minimum value of Z) is equal to (A) 40 (B) 96 (C) 120 (D) 136 ASSERTION-REASON BASED QUEST…
    Board 20231 markAssertion-Reason

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