IIT JEE & NEET Question Bank with Solution: 09/10/21

NCERT BOOK Linear Programming.
This MCQs are based on the Mathematics Part I Textbook of Maharashtra (click here for reference).

Linear Programming

Q.1. The objective function Z = 6x + 2y is subject to $5 x plus 9 y less or equal than 90 comma space x plus y greater or equal than 4 comma space y less or equal than 8 comma space x comma space y greater or equal than 0.$ the minimum value of Z occurs at

(A) (0, 2)

(B) (0, 4)

(C) (4, 0)

(D) (18, 0)

Q.2. The maximum value Z = 3x + 5y, subject to $x plus 4 y less or equal than 24 comma space y less or equal than 4 comma space x greater or equal than 0 comma space y greater or equal than 0$ is

(A) 44

(B) 72

(D) 20

Q.3. The maximum value of z = 10 10x + 6y subjected to the constraints $3 x space plus space y space less or equal than space 12 comma space 2 x plus space 5 y space less or equal than space 34 comma space x space greater or equal than space 0 comma space y space greater or equal than space 0.$ _______.

(A) 56

(B) 65

(D) 66

Q.4. The point at which the maximum value of x + y subject to the constraints $x space plus space 2 y space less or equal than space 70 comma space 2 x space plus space y space less or equal than space 95 comma space x space greater or equal than space 0 comma space y space greater or equal than space 0$ is obtained at_______.

(A) (30, 25)

(B) (20, 35)

(D) (40, 15)

Q.5. The maximum value of z = 5x + 3y subjected to the constraints $3 x space plus space 5 y space less or equal than space 15 comma space 5 x space plus space 2 y space less or equal than 10 comma space x comma space y comma space greater or equal than space 0$ is_______.

(A) 235

(B) $235 over 9$

(C) $235 over 19$

(D) $235 over 3$

Q.6. If the corner points of the feasible solution are (0, 10), (2, 2) and (4, 0) then the point of minimum z = 3x + 2y is_______.

(A) (2, 2)

(B) (0, 10)

(D) (3, 4)

Q.7. The value of objective function is maximum under linear constraints_______.

(A) at the centre of feasible region

(B) at (0, 0)

(C) at a vertex of feasible region

(D) the vertex which is of maximum distance from (0, 0)

Q.8. The corner points of the feasible solution given by the inequations $x plus y less or equal than 4 comma space 2 x plus y less or equal than 7 comma space x greater or equal than 0 comma space y greater or equal than 0$ are ________.

(A) (0, 0), (4, 0), (7, 1), (0, 4)

(B) $open parentheses 0 comma space 0 close parentheses comma space open parentheses 7 over 2 comma space 0 close parentheses comma space open parentheses 3 comma space 1 close parentheses comma space open parentheses 0 comma space 4 close parentheses$

(C) $open parentheses 0 comma space 0 close parentheses comma space open parentheses 7 over 2 comma space 0 close parentheses comma space open parentheses 3 comma space 1 close parentheses comma space open parentheses 0 comma space 7 close parentheses$

(D) $open parentheses 0 comma space 0 close parentheses comma space open parentheses 4 comma space 0 close parentheses comma space open parentheses 3 comma space 1 close parentheses comma space open parentheses 0 comma space 7 close parentheses$

Q.9. The corner points of the feasible solution are $open parentheses 0 comma space 0 close parentheses comma space open parentheses 2 comma space 0 close parentheses comma space open parentheses 12 over 7 comma 3 over 7 close parentheses comma space open parentheses 0 comma space 1 close parentheses.$ Then Z = 7x + y is maximum at _______.

(A) (0, 0)

(B) (2, 0)

(D) (0, 1)

Q.10. The half plane represented by $4 x plus 3 y greater than 14$ contains the point _______.

(A) (0, 0)

(B) (2, 2)

(C) (3, 4)

(D) (1, 1)

Q.11. Which of the following is correct_______.

(A) every L.P.P. has an optimal solution

(B) a L.P.P. has unique optimal solution

(C) if L.P.P. has two optimal solutions then it has infinite number of optimal solutions

(D) the set of all feasible solution of L.P.P. may not be convex set

Q.12. Objective function of L.P.P. is_______.

(A) a constraint

(B) a function to be maximized or minimized

(D) equation of a straight line

Q.13. If the corner points of the feasible solution are $open parentheses 0 comma space 0 close parentheses comma space open parentheses 3 comma space 0 close parentheses comma space open parentheses 2 comma space 1 close parentheses space a n d space open parentheses 0 comma 7 over 3 close parentheses comma$ the maximum value of z = 4x + 5y is_______.

(A) 12

(B) 13

(D) 0

Q.14. The half plane represented by $3 x plus 2 y less than 8$ constraints the point_______.

(A) $open parentheses 1 comma 5 over 2 close parentheses$

(B) (2, 1)

(C) (0, 0)

(D) (5, 1)

Q.15. The maximum value of 2x + y subject to $3 x space plus space 5 y space less or equal than space 26 space a n d space 5 x space plus 3 y space less or equal than space 30 comma space x space greater or equal than space 0 comma space y space greater or equal than space 0$ is

(A) 12

(B) 11.5

(D) 17.33

Q.16. If Z = 2x + y subject to $x less or equal than 4 comma space y less or equal than 6 comma space x plus y greater or equal than 6 comma space x greater or equal than 0 comma space y greater or equal than 0 comma$ then the maximum value of Z is

(A) 18

(B) 10

(D) 14

Q.17. Of all the points of the feasible region, the optimal value of z obtained at the point lies_______.

(A) inside the feasible region

(B) at the boundary of the feasible region

(C) at vertex of feasible region

(D) outside the feasible region

Q.18. Feasible region is the set of points which satisfy_______.

(A) the objective function

(B) all of the given constraints

(D) only one constraint

Q.19. Solution of L.P.P. to minimize z = 2x + 3y s.t. $x greater or equal than 0 comma space y greater or equal than 0 comma space 1 less or equal than x plus 2 y less or equal than 10$ is_______.

(A) $x equals 0 comma space y equals 1 half$

(B) $x equals 1 half comma space y equals 0$

(D) $x equals 1 half comma y equals 1 half$

Q.20. The objective function of LPP defined over the convex set attains its optimum value at

(A) At least two of the corner points

(B) All the corner points

(C) At least one of the corner points

(D) None of the corner points

IIT JEE & NEET Question Bank with Solution

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Friday, September 10, 2021

HSC Linear Programming Solved MCQ: Maharashtra Board